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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /info/pstricks_calcnotes
Initial commit
Diffstat (limited to 'info/pstricks_calcnotes')
-rw-r--r--info/pstricks_calcnotes/AppThreePDF.pdfbin0 -> 333665 bytes
-rw-r--r--info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/Readme.txt17
-rw-r--r--info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/convert.tex172
-rw-r--r--info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/test.pdfbin0 -> 11866 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/AppThreePDF.tex510
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/BZ1.pdfbin0 -> 8620 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/BZ10.pdfbin0 -> 12575 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/BZ2.pdfbin0 -> 4200 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/BZ3.pdfbin0 -> 4198 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/BZ4.pdfbin0 -> 4151 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/BZ5.pdfbin0 -> 5556 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/BZ6.pdfbin0 -> 9991 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/BZ7.pdfbin0 -> 11308 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/BZ8.pdfbin0 -> 10011 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/BZ9.pdfbin0 -> 11477 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig13.pdfbin0 -> 5097 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig14.pdfbin0 -> 5435 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig1a.pdfbin0 -> 8151 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig1b.pdfbin0 -> 9319 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig1c.pdfbin0 -> 9382 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig2a.pdfbin0 -> 8163 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig2b.pdfbin0 -> 8884 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig3.pdfbin0 -> 8702 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig4.pdfbin0 -> 9533 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig5.pdfbin0 -> 5974 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig6.pdfbin0 -> 10906 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig7.pdfbin0 -> 6977 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig8.pdfbin0 -> 11202 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/Fig9.pdfbin0 -> 16065 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/ThreeAppsPDF.tex1036
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/b6of1.pdfbin0 -> 9000 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/b6of2.pdfbin0 -> 10095 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/b6of3.pdfbin0 -> 12823 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/b6of4.pdfbin0 -> 13025 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/vecb1.pdfbin0 -> 12497 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/vecb2.pdfbin0 -> 19468 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/vecb3.pdfbin0 -> 13080 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/vecb4.pdfbin0 -> 12926 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/vecb5.pdfbin0 -> 11692 bytes
-rw-r--r--info/pstricks_calcnotes/For_Pdf_Output/vecb6.pdfbin0 -> 11897 bytes
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/AppThreePS.tex551
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/BZ10.eps17247
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/BZ6.eps15604
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/BZ7.eps16443
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/BZ8.eps15604
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/BZ9.eps16441
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/ThreeAppsPS.tex1165
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/b6of1.eps11111
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/b6of2.eps11891
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/b6of3.eps28461
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/b6of4.eps33594
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/vecb1.eps14943
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/vecb2.eps22808
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/vecb3.eps14969
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/vecb4.eps14951
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/vecb5.eps13687
-rw-r--r--info/pstricks_calcnotes/For_Ps_Output/vecb6.eps13656
-rw-r--r--info/pstricks_calcnotes/README11
-rw-r--r--info/pstricks_calcnotes/ThreeAppsPDF.pdfbin0 -> 652952 bytes
59 files changed, 264872 insertions, 0 deletions
diff --git a/info/pstricks_calcnotes/AppThreePDF.pdf b/info/pstricks_calcnotes/AppThreePDF.pdf
new file mode 100644
index 0000000000..e1bc137289
--- /dev/null
+++ b/info/pstricks_calcnotes/AppThreePDF.pdf
Binary files differ
diff --git a/info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/Readme.txt b/info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/Readme.txt
new file mode 100644
index 0000000000..a871f3a825
--- /dev/null
+++ b/info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/Readme.txt
@@ -0,0 +1,17 @@
+Dear friends,
+
+To convert a PSTricks-code picture into a graphic file ".pdf", process
+the file "convert.tex" through the following steps:
+
+ 1) latex convert.tex (you automatically get the output file "convert-fig1.tex", then put the definitions in the preamble
+ of the convert.tex file in that of the convert-fig1.tex file).
+ 2) latex convert-fig1.tex
+ 3) dvips convert-fig1.dvi
+ 4) call the file "convert-fig1.ps" by the Ghostview progam to convert this file into its
+ eps version (you can rename the result, say "fig1.eps").
+ 5) use the eps2pdf program to convert the file "fig1.eps" into the file "fig1.pdf".
+
+The file "test.pdf" gives an illustration for a partition of a plane domain.
+Check your file "fig1.pdf" to see this partition.
+
+Enjoy!
diff --git a/info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/convert.tex b/info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/convert.tex
new file mode 100644
index 0000000000..a71fc05eac
--- /dev/null
+++ b/info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/convert.tex
@@ -0,0 +1,172 @@
+\documentclass[11pt,a4paper,oneside]{article}
+\usepackage{pdftricks}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcount\Fa\newcount\Fct\newcount\tempA
+\def\Factor{\ifnum\Fa=1\relax\else\advance\Fa by -1\multiply\Fct by \Fa\Factor\fi}
+\def\FACTORIAL#1{\Fa=#1 \ifnum\Fa=0 \Fct=1\relax\else\Fct=\Fa \Factor\fi\global\tempA=\Fct}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcount\BINOM
+\newcount\temp
+\newcount\tmp
+\def\BINOMIAL#1#2{%
+\temp=#1\advance\temp by -#2
+\FACTORIAL{#1}
+\tmp=\tempA
+\FACTORIAL{\temp}
+\temp=\tempA
+\divide\tmp by \temp
+\FACTORIAL{#2}
+\temp=\tempA
+\divide\tmp by \temp\global\BINOM=\tmp}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\xch{\catcode`\p=12 \catcode`\t=12}\def\ych{\catcode`\p=11 \catcode`\t=11}
+\xch \def\dec#1pt{#1}\ych \def\decimal#1{\expandafter\dec \the#1}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newdimen\Xa\newdimen\Yb\newcount\kc
+\newdimen\BSTemp
+\def\xmult#1{\ifnum\kc<#1\advance\kc by 1\Yb=\decimal\Xa\Yb\xmult{#1}\else\relax\fi}
+\def\BERNSTEIN#1#2#3{\Xa=#3pt\kc=0\Yb=1pt\xmult{#1}\kc=0\Xa=-\Xa\advance\Xa by 1pt\xmult{#2}
+\BINOMIAL{5}{#1}\global\BSTemp=\BINOM\Yb}
+
+\newdimen\Xrf
+\newdimen\Yrf
+\newdimen\XoneBST\newdimen\YoneBST
+\newdimen\XtwoBST\newdimen\YtwoBST
+\newdimen\XBST\newdimen\YBST
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XoneBC#1{%
+\BERNSTEIN{2}{3}{#1}
+\Xrf=1.5pt
+\XoneBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{3}{2}{#1}
+\Xrf=3pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{4}{1}{#1}
+\Xrf=5pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{5}{0}{#1}
+\Xrf=5pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\global\XBST=\XoneBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XtwoBC#1{%
+\BERNSTEIN{0}{5}{#1}
+\Xrf=5pt
+\XtwoBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{1}{4}{#1}
+\Xrf=5pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{2}{3}{#1}
+\Xrf=3.5pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{3}{2}{#1}
+\Xrf=2pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\global\XBST=\XtwoBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\YoneBC#1#2#3{%
+\BERNSTEIN{1}{4}{#1}
+\Yrf=1.5pt
+\YoneBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{2}{3}{#1}
+\Yrf=1pt
+\Yrf=#2\Yrf
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{2}{#1}
+\Yrf=2pt
+\Yrf=#3\Yrf
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{1}{#1}
+\Yrf=1.5pt
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\global\YBST=\YoneBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\YtwoBC#1#2#3{%
+\BERNSTEIN{1}{4}{#1}
+\Yrf=-1.5pt
+\YtwoBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{2}{3}{#1}
+\Yrf=-1pt
+\Yrf=#2\Yrf
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{2}{#1}
+\Yrf=-2pt
+\Yrf=#3\Yrf
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{1}{#1}
+\Yrf=-1.5pt
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\global\YBST=\YtwoBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XoneFive{15*t^2*(1-t)^3+30*t^3*(1-t)^2+25*t^4*(1-t)+5*t^5}
+\def\YoneFive#1#2{7.5*t*(1-t)^4+(#1)*10*t^2*(1-t)^3+(#2)*20*t^3*(1-t)^2+7.5*t^4*(1-t)}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XtwoFive{5*(1-t)^5+25*t*(1-t)^4+35*t^2*(1-t)^3+20*t^3*(1-t)^2}
+\def\YtwoFive#1#2{(-7.5)*t*(1-t)^4+(#1)*(-10)*t^2*(1-t)^3+(#2)*(-20)*t^3*(1-t)^2+(-7.5)*t^4*(1-t)}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\NetDrawOne#1#2#3{%
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\Xsize=7pt \divide\Xsize by #1
+\Ysize=6pt \divide\Ysize by #1
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!85,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XoneFive|\YoneFive{#2}{#3}}
+\multido{\nz=0.00+0.005}{200}{\XoneBC{\nz}\YoneBC{\nz}{#2}{#3}
+\multido{\nx=-1.00+\decimal\Xsize}{#1}
+{\tempx=\nx pt\multido{\ny=-3.00+\decimal\Ysize}{#1}
+{\tempy=\ny pt\ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else\pspolygon[fillstyle=solid,fillcolor=blue!70,linecolor=black,linewidth=0.2pt]
+ (\nx,\ny)(\decimal\tempx,\ny)(\decimal\tempx,\decimal\tempy)(\nx,\decimal\tempy)(\nx,\ny)\fi\fi\fi\fi}
+}}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\NetDrawTwo#1#2#3{%
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\Xsize=7pt \divide\Xsize by #1
+\Ysize=6pt \divide\Ysize by #1
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!85,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XtwoFive|\YtwoFive{#2}{#3}}
+\multido{\nz=0.00+0.005}{200}{\XtwoBC{\nz}\YtwoBC{\nz}{#2}{#3}
+\multido{\nx=-1.00+\decimal\Xsize}{#1}
+{\tempx=\nx pt\multido{\ny=-3.00+\decimal\Ysize}{#1}
+{\tempy=\ny pt\ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else\pspolygon[fillstyle=solid,fillcolor=blue!70,linecolor=black,linewidth=0.2pt]
+ (\nx,\ny)(\decimal\tempx,\ny)(\decimal\tempx,\decimal\tempy)(\nx,\decimal\tempy)(\nx,\ny)\fi\fi\fi\fi}
+}}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\title{Making files \texttt{.ps} from \texttt{PSTricks}}
+\begin{document}
+\maketitle
+\begin{psinputs}
+\usepackage{pstricks}
+\usepackage[dvips]{geometry}
+\usepackage{pst-plot,pst-coil,multido,pst-xkey,pst-node}
+\usepackage{calculator}
+\usepackage{calculus}
+\usepackage{pst-func}
+\usepackage{pstricks-add}
+\end{psinputs}
+\section{Here is the PSTricks code to be converted}
+\begin{pdfpic}
+\begin{pspicture}(-1,-3)(6,3) \psset{unit=24pt}
+\NetDrawOne{54}{1.7}{0.2}
+\NetDrawTwo{54}{0.1}{1.8}
+\multido{\nx=-1.00+\decimal\Xsize}{55}
+{\psline[linewidth=0.2pt](\nx,-3)(\nx,3)}
+\multido{\ny=-3.00+\decimal\Ysize}{55}
+{\psline[linewidth=0.2pt](-1,\ny)(6,\ny)}
+\parametricplot[algebraic,plotpoints=200,linecolor=white,linewidth=0.5pt]{0}{1}{\XoneFive|\YoneFive{1.7}{0.2}}
+\parametricplot[algebraic,plotpoints=200,linecolor=white,linewidth=0.5pt]{0}{1}{\XtwoFive|\YtwoFive{0.1}{1.8}}
+\end{pspicture}
+\end{pdfpic}
+\end{document}
diff --git a/info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/test.pdf b/info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/test.pdf
new file mode 100644
index 0000000000..61297a2443
--- /dev/null
+++ b/info/pstricks_calcnotes/Convert_PstricksCode_To_Pdf/test.pdf
Binary files differ
diff --git a/info/pstricks_calcnotes/For_Pdf_Output/AppThreePDF.tex b/info/pstricks_calcnotes/For_Pdf_Output/AppThreePDF.tex
new file mode 100644
index 0000000000..97a5769ece
--- /dev/null
+++ b/info/pstricks_calcnotes/For_Pdf_Output/AppThreePDF.tex
@@ -0,0 +1,510 @@
+\documentclass[11pt,a4paper,oneside]{article}
+\usepackage{multirow}
+\usepackage{longtable}
+\usepackage{amsthm}
+\usepackage{amsmath}
+\usepackage{url}
+\usepackage{cmtt}
+\usepackage[dvips]{geometry}
+\usepackage{pstricks}
+\usepackage{graphicx}
+\usepackage{graphics}
+\usepackage{pst-plot}
+\usepackage{pst-node}
+\usepackage{multido}
+\usepackage{pst-xkey}
+\usepackage{pst-func}
+\usepackage{pstricks-add}
+\usepackage[pdftex,colorlinks,linktocpage]{hyperref}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\hantt{\^e}\def\accentcircflx{\hskip-.3em\raisebox{0.32ex}{\'{}}}
+\DeclareRobustCommand{\cs}[1]{\textmtt{\char`\\#1}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcount\Fa\newcount\Fct\newcount\tempA
+\def\Factor{\ifnum\Fa=1\relax\else\advance\Fa by -1\multiply\Fct by \Fa\Factor\fi}
+\def\FACTORIAL#1{\Fa=#1 \ifnum\Fa=0 \Fct=1\relax\else\Fct=\Fa \Factor\fi\global\tempA=\Fct}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcount\BINOM
+\newcount\temp
+\newcount\tmp
+\def\BINOMIAL#1#2{%
+\temp=#1\advance\temp by -#2
+\FACTORIAL{#1}
+\tmp=\tempA
+\FACTORIAL{\temp}
+\temp=\tempA
+\divide\tmp by \temp
+\FACTORIAL{#2}
+\temp=\tempA
+\divide\tmp by \temp\global\BINOM=\tmp}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\xch{\catcode`\p=12 \catcode`\t=12}\def\ych{\catcode`\p=11 \catcode`\t=11}
+\xch \def\dec#1pt{#1}\ych \def\decimal#1{\expandafter\dec \the#1}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newdimen\Xa\newdimen\Yb\newcount\kc
+\newdimen\BSTemp
+\def\xmult#1{\ifnum\kc<#1\advance\kc by 1\Yb=\decimal\Xa\Yb\xmult{#1}\else\relax\fi}
+\def\BERNSTEIN#1#2#3{\Xa=#3pt\kc=0\Yb=1pt\xmult{#1}\kc=0\Xa=-\Xa\advance\Xa by 1pt\xmult{#2}
+\BINOMIAL{5}{#1}\global\BSTemp=\BINOM\Yb}
+
+\newdimen\Xrf
+\newdimen\Yrf
+\newdimen\XoneBST\newdimen\YoneBST
+\newdimen\XtwoBST\newdimen\YtwoBST
+\newdimen\XBST\newdimen\YBST
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XoneBC#1{%
+\BERNSTEIN{2}{3}{#1}
+\Xrf=1.5pt
+\XoneBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{3}{2}{#1}
+\Xrf=3pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{4}{1}{#1}
+\Xrf=5pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{5}{0}{#1}
+\Xrf=5pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\global\XBST=\XoneBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XtwoBC#1{%
+\BERNSTEIN{0}{5}{#1}
+\Xrf=5pt
+\XtwoBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{1}{4}{#1}
+\Xrf=5pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{2}{3}{#1}
+\Xrf=3.5pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{3}{2}{#1}
+\Xrf=2pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\global\XBST=\XtwoBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\YoneBC#1#2#3{%
+\BERNSTEIN{1}{4}{#1}
+\Yrf=1.5pt
+\YoneBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{2}{3}{#1}
+\Yrf=1pt
+\Yrf=#2\Yrf
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{2}{#1}
+\Yrf=2pt
+\Yrf=#3\Yrf
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{1}{#1}
+\Yrf=1.5pt
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\global\YBST=\YoneBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\YtwoBC#1#2#3{%
+\BERNSTEIN{1}{4}{#1}
+\Yrf=-1.5pt
+\YtwoBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{2}{3}{#1}
+\Yrf=-1pt
+\Yrf=#2\Yrf
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{2}{#1}
+\Yrf=-2pt
+\Yrf=#3\Yrf
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{1}{#1}
+\Yrf=-1.5pt
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\global\YBST=\YtwoBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XoneFive{15*t^2*(1-t)^3+30*t^3*(1-t)^2+25*t^4*(1-t)+5*t^5}
+\def\YoneFive#1#2{7.5*t*(1-t)^4+(#1)*10*t^2*(1-t)^3+(#2)*20*t^3*(1-t)^2+7.5*t^4*(1-t)}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XtwoFive{5*(1-t)^5+25*t*(1-t)^4+35*t^2*(1-t)^3+20*t^3*(1-t)^2}
+\def\YtwoFive#1#2{(-7.5)*t*(1-t)^4+(#1)*(-10)*t^2*(1-t)^3+(#2)*(-20)*t^3*(1-t)^2+(-7.5)*t^4*(1-t)}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\NetDrawOne#1#2#3{%
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\Xsize=7pt \divide\Xsize by #1
+\Ysize=6pt \divide\Ysize by #1
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!85,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XoneFive|\YoneFive{#2}{#3}}
+\multido{\nz=0.00+0.005}{200}{\XoneBC{\nz}\YoneBC{\nz}{#2}{#3}
+\multido{\nx=-1.00+\decimal\Xsize}{#1}
+{\tempx=\nx pt\multido{\ny=-3.00+\decimal\Ysize}{#1}
+{\tempy=\ny pt\ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else\pspolygon[fillstyle=solid,fillcolor=blue!70,linecolor=black,linewidth=0.2pt]
+ (\nx,\ny)(\decimal\tempx,\ny)(\decimal\tempx,\decimal\tempy)(\nx,\decimal\tempy)(\nx,\ny)\fi\fi\fi\fi}
+}}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\NetDrawTwo#1#2#3{%
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\Xsize=7pt \divide\Xsize by #1
+\Ysize=6pt \divide\Ysize by #1
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!85,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XtwoFive|\YtwoFive{#2}{#3}}
+\multido{\nz=0.00+0.005}{200}{\XtwoBC{\nz}\YtwoBC{\nz}{#2}{#3}
+\multido{\nx=-1.00+\decimal\Xsize}{#1}
+{\tempx=\nx pt\multido{\ny=-3.00+\decimal\Ysize}{#1}
+{\tempy=\ny pt\ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else\pspolygon[fillstyle=solid,fillcolor=blue!70,linecolor=black,linewidth=0.2pt]
+ (\nx,\ny)(\decimal\tempx,\ny)(\decimal\tempx,\decimal\tempy)(\nx,\decimal\tempy)(\nx,\ny)\fi\fi\fi\fi}
+}}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagestyle{headings}
+\topmargin=-0.6cm
+\textwidth=16.7cm
+\textheight=23cm
+\headheight=2.5ex
+\headsep=0.6cm
+\oddsidemargin=.cm
+\evensidemargin=-.4cm
+\parskip=0.7ex plus0.5ex minus 0.5ex
+\baselineskip=17pt plus2pt minus2pt
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\catcode`\@=11
+\gdef\@seccntformat#1{\csname the#1\endcsname.\hskip.6em}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\gdef\acknw{\section*{%
+{\acknwname}\markright{\protect\textsl{\acknwname}}}%
+\addcontentsline{toc}{section}{\acknwname}}
+\gdef\acknwname{Acknowledgment}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\renewcommand\sectionmark[1]{\markright{\thesection. #1}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\title{Drawing partitions of a simply connected plane domain}
+\author{Le Phuong Quan\\
+\small{(Cantho University)}\\
+\small{\texttt{lpquan@ctu.edu.vn}}}
+\begin{document}
+\maketitle
+
+This drawing procedure takes shape from the macros \verb+\psline+, \verb+\pspolygon+, \verb+\multido+
+and \verb+\parametricplot+ in PSTricks\footnote{\footnotesize PSTricks is the original work of Timothy Van Zandt (email address: \texttt{tvz@econ.insead.fr}).
+It is currently edited by Herbert Vo\ss\ (\texttt{hvoss@tug.org}).}. The \TeX\ arithmetic gives the pointwise parametrization of curves.
+\section{How to make a boundary using B\'{e}zier curves}
+We can make the closed boundary of a plane domain by joining B\'{e}zier curves. This can produce various boundaries. We consider here
+two B\'{e}zier curves of degree $5$ whose vector functions are
+$$\mathbf{r}_a(t)=\sum_{i=0}^5\binom{5}{i}t^i(1-t)^{5-i}\mathbf{a}_i,\quad \mathbf{r}_b(t)=\sum_{i=0}^5\binom{5}{i}t^i(1-t)^{5-i}\mathbf{b}_i,$$
+where $\mathbf{a}_i$ and $\mathbf{b}_i$ are the position vectors of control points $M_i$, $N_i$ of the two curves, respectively, $i=0,\ldots,5$.
+Here we choose:
+$M_0=(0,0)$, $M_1=(0,1.5)$, $M_2=(1.5,1)$, $M_3=(3,2)$, $M_4=(5,1.5)$, $M_5=(5,0)$, and
+$N_0=(5,0)$, $N_1=(5,-1.5)$, $N_2=(3.5,-1)$, $N_3=(2,-2)$, $N_4=(0,-1.5)$, $N_5=(0,0)$. The two curves and
+their control points are shown in Figure \ref{BZ-1} and the picture in it gives us an obvious explanation of how to combine two B\'{e}zier curves to make a closed and smooth boundary.
+\begin{figure}[htbp]
+\centering\includegraphics[width=7cm]{BZ1}
+\caption{A B\'{e}zier-spline boundary.}\label{BZ-1}
+\end{figure}
+To change the shape of the boundary, we take one couple of multipliers for the second coordinates of $M_2$, $M_3$ and another one for those of $N_2$, $N_3$. To
+draw the curves $\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$ we need their parametrization $(X_a(t),Y_a(t))$ and $(X_b(t),Y_b(t))$, $t\in[0,1]$. From
+their control points and the given couple of multipliers $\alpha_M,\beta_M$, we derive
+\begin{align*}
+X_a(t)&=15t^2(1-t)^3+30t^3(1-t)^2+25t^4(1-t)+5t^5,\\
+Y_a(t)&=7.5t(1-t)^4+10\alpha_M t^2(1-t)^3+20\beta_M t^3(1-t)^2+7.5t^4(1-t).
+\end{align*}
+Similarly, we have
+\begin{align*}
+X_b(t)&=5(1-t)^5+25t(1-t)^4+35t^2(1-t)^3+20t^3(1-t)^2,\\
+Y_b(t)&=-7.5t(1-t)^4-10\alpha_N t^2(1-t)^3-20\beta_N t^3(1-t)^2-7.5t^4(1-t),
+\end{align*}
+where $\alpha_N$, $\beta_N$ are multipliers. Then, these curves will be depicted by the macro \verb+\parametricplot+
+with the corresponding declarations in the \texttt{algebraic} form:
+\begin{verbatim}
+\def\XoneFive{15*t^2*(1-t)^3+30*t^3*(1-t)^2+25*t^4*(1-t)+5*t^5}
+\def\YoneFive#1#2%
+{7.5*t*(1-t)^4+(#1)*10*t^2*(1-t)^3+(#2)*20*t^3*(1-t)^2+7.5*t^4*(1-t)}
+\def\XtwoFive{5*(1-t)^5+25*t*(1-t)^4+35*t^2*(1-t)^3+20*t^3*(1-t)^2}
+\def\YtwoFive#1#2%
+{(-7.5)*t*(1-t)^4+(#1)*(-10)*t^2*(1-t)^3+(#2)*(-20)*t^3*(1-t)^2+(-7.5)*t^4*(1-t)}
+\end{verbatim}
+where \verb+#1+, \verb+#2+ stand for $\alpha_M$ and $\beta_M$ in the definition of \verb+\YoneFive+ and
+for $\alpha_N$ and $\beta_N$ in that of \verb+\YtwoFive+, respectively.
+In Figure \ref{BZ-2}, the boundaries are drawn by using together the commands
+\begin{verbatim}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XoneFive|\YoneFive{alphaM}{betaM}}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XtwoFive|\YtwoFive{alphaN}{betaN}}
+\end{verbatim}
+where, \verb+alphaM+, \verb+betaM+, \verb+alphaN+ and \verb+betaN+ are chosen values of $\alpha_M$, $\beta_M$,
+$\alpha_N$ and $\beta_N$, respectively.
+\begin{figure}[htbp]
+\centering\includegraphics[width=4.5cm]{BZ2}
+\hskip0.5cm\includegraphics[width=4.5cm]{BZ3}
+\hskip0.5cm\includegraphics[width=4.5cm]{BZ4}
+\caption{From left to right, corresponding to the couple of values: $\alpha_M=-0.5$, $\beta_M=2.1$, $\alpha_N=2.4$, $\beta_N=-0.4$;
+$\alpha_M=1.1$, $\beta_M=1.4$, $\alpha_N=1.2$, $\beta_N=1.5$; $\alpha_M=1.7$, $\beta_M=0.2$, $\alpha_N=0.1$, $\beta_N=1.8$}\label{BZ-2}
+\end{figure}
+\section{How to draw a partition of a plane domain}
+To draw a partition of a plane domain whose boundary is made by the way that has just been described, we need the two
+procedures \verb+\NetDrawOne+ and \verb+\NetDrawTwo+, corresponding to $\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$. Their calling sequences take three arguments in order: one for $c$ (the number of cells) and
+the others for $\alpha_M$ and $\beta_M$ or $\alpha_N$ and $\beta_N$.
+Both of \verb+\NetDrawOne+ and \verb+\NetDrawTwo+ are used here to find cells in a given grid that have points in common with
+$\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$, and to color those cells. To obtain the definition of these procedures, we first state the
+problem that we are considering here.
+
+A grid of rectangular cells will be put on a rectangle $R$ containing a domain $D$ whose boundary consist of $\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$, including
+the given values of $c$, $\alpha_M$, $\beta_M$, $\alpha_N$ and $\beta_N$. Then, the steps for drawing a partition of $D$ can be listed as follows:
+\begin{itemize}
+\item Coloring cells that have points in common with the boundary of $D$.
+This is the result of calling \textmtt{\mtt\\NetDrawOne\{$c$\}\{$\alpha_M$\}\{$\beta_M$\}} and \textmtt{\mtt\\NetDrawTwo\{$c$\}\{$\alpha_N$\}\{$\beta_N$\}} together.
+\item Drawing the grid on $R$, which has been chosen as $R=\{(x,y)\colon -1\le x\le 6,\,-3\le y\le 3\}$.
+\item Drawing the two curves $\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$.
+\end{itemize}
+
+In practice, a partition of $D$ can be given by a calling sequence that has the following structure inside the \verb+\begin{pspicture}+ \ldots \verb+\end{pspicture}+
+environment:
+\begin{center}\begin{tabular}{l|l}\hline
+\textbf{Commands}&\textbf{Result}\\ \hline
+\textmtt{\mtt\\NetDrawOne\{$c$\}\{$\alpha_M$\}\{$\beta_M$\}}\textmtt{\mtt\\NetDrawTwo\{$c$\}\{$\alpha_N$\}\{$\beta_N$\}}&Coloring cells\\ \hline
+\textmtt{\mtt\\multido\{\mtt\\nx=-1.00+\mtt\\decimal\mtt\\Xsize\}\{$c+1$\}}\\
+\textmtt{\mtt\\psline[linewidth=0.2pt](\mtt\\nx,-3)(\mtt\\nx,3)}\\
+\textmtt{\mtt\\multido\{\mtt\\ny=-3.00+\mtt\\decimal\mtt\\Ysize\}\{$c+1$\}}\\
+\textmtt{\mtt\\psline[linewidth=0.2pt](-1,\mtt\\ny)(6,\mtt\\ny)}&Drawing the grid on $R$ \\ \hline
+\textmtt{\mtt\\parametricplot[algebraic,plotpoints=200,linecolor=white,}\\
+\textmtt{linewidth=0.5pt]\{0\}\{1\}\{\mtt\\XoneBFive|\mtt\\YoneBFive\{$\alpha_M$\}\{$\beta_M$\}\}}\\
+\textmtt{\mtt\\parametricplot[algebraic,plotpoints=200,linecolor=white,}\\
+\textmtt{linewidth=0.5pt]\{0\}\{1\}\{\mtt\\XtwoFive|\mtt\\YtwoFive\{$\alpha_N$\}\{$\beta_N$\}\}}&Drawing $\mathbf{r}_a(t)$, $\mathbf{r}_b(t)$\\ \hline
+\end{tabular}
+\end{center}
+
+In the following, beside the definitions of \verb+\XoneFive+, \verb+\YoneFive+, \verb+\XtwoFive+ and \verb+\YtwoFive+,
+we list all the remaining macros by their control sequences only and the results derived from running them. They form the whole drawing package, and of course they are also put in the preamble or in
+a single \TeX\ file to be loaded when running the package.
+\begin{itemize}
+\item \verb+\def\xch+: Setting \verb+\catcode'\p=12+, \verb+\catcode'\t=12+.
+\item \verb+\def\ych+: Setting \verb+\catcode'\p=11+, \verb+\catcode'\t=11+.
+\item \verb+\def\decimal#1+: Getting the numeric value of \verb+#1+ without unit.
+\item \verb+\def\FACTORIAL#1+: The factorial function. Ex: $\textmtt{\mtt\\FACTORIAL\{3\}}=6$.
+\item \verb+\def\BINOMIAL#1#2+: Binomial coefficients. Ex: $\textmtt{\mtt\\BINOMIAL\{5\}\{2\}}=10$.
+\item \verb+\def\BERNSTEIN#1#2#3+: Bernstein's functions. Ex: $\textmtt{\mtt\\BERNSTEIN\{3\}\{2\}\{t\}}=\displaystyle\binom{5}{3}t^3(1-t)^2$.
+\item \verb+\def\XoneBC#1+, \verb+\def\XtwoBC#1+: The values of $X_a(t)$, $X_b(t)$. Ex: $\textmtt{\mtt\\XoneBC\{0.5\}}=X_a(0.5)$.
+\item \verb+\def\YoneBC#1#2#3+, \verb+\def\YtwoBC#1#2#3+:
+The value of $Y_a(t)$ with given values of $\alpha_M$, $\beta_M$, and the value of $Y_b(t)$ with given values of $\alpha_N$, $\beta_N$.
+Ex: $\textmtt{\mtt\\YoneBC\{0.5\}\{1.8\}\{1.2\}}=Y_a(0.5)$, with $\alpha_M=1.8$, $\beta_M=1.2$.
+\end{itemize}
+
+We recall here the main idea for this drawing procedure. We have already the expressions of $\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$ to draw
+these B\'{ezier} curves by the macro \verb+\parametricplot+. But, we need to have in hand their points' coordinates to determine
+cells of a grid containing points in common with these curves. Fortunately, we may use the \TeX\ arithmetic
+to design expressions of $X_a(t)$, $Y_a(t)$, $X_b(t)$ and $Y_b(t)$, hence we can evaluate their values at each given $t\in[0,1]$.
+For instance, the macro \verb+\def\XoneBC#1+ is destined for evaluating the value of $X_a(t)$, and since it is a linear combination of Bernstein's functions,
+we need binomial coefficients. We do not take directly numeric values of those coefficients, and we have had the macro \verb+\def\BINOMIAL#1#2+ do that instead.
+It might be possible to use this macro in other problems later.
+In Appendix \ref{appendixA}, we list the replacement texts of the above macros and all the local and global variables they need.
+
+From the listed macros, \verb+\NetDrawOne+ may now have its definition as
+\begin{verbatim}
+==================================================================================
+\def\NetDrawOne#1#2#3{%
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\Xsize=7pt \divide\Xsize by #1
+\Ysize=6pt \divide\Ysize by #1
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!80,plotpoints=200,
+linewidth=0.5pt]{0}{1}{\XoneFive|\YoneFive{#2}{#3}}
+\multido{\nz=0.00+0.005}{200}{\XoneBC{\nz}\YoneBC{\nz}{#2}{#3}
+\multido{\nx=-1.00+\decimal\Xsize}{#1}
+{\tempx=\nx pt\multido{\ny=-3.00+\decimal\Ysize}{#1}
+{\tempy=\ny pt
+ \ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else\pspolygon[fillstyle=solid,fillcolor=blue!70,
+linecolor=black,linewidth=0.2pt](\nx,\ny)(\decimal\tempx,\ny)
+(\decimal\tempx,\decimal\tempy)(\nx,\decimal\tempy)(\nx,\ny)\relax\fi\fi\fi\fi}}}}
+==================================================================================
+\end{verbatim}
+To obtain the definition of \verb+\NetDrawTwo+, we just replace by \verb+\XtwoFive+,
+\verb+\Ytwofive+, \verb+\XtwoBC+ and \verb+\YtwoBC+ for \verb+\XoneFive+,
+\verb+\YoneFive+, \verb+\XoneBC+ and \verb+\YoneBC+ in that of \verb+\NetDrawaOne+, respectively.
+
+Because of its inevitable shortcoming, \TeX\ often gives approximate results of calculations on dimensions.
+In the following table, let us see a slight difference between results obtained from the same expression (by declaration of
+operations) in Maple and in the \TeX\ arithmetic:
+\begin{table}[htbp]
+\centering\begin{tabular}{c||c|c|c|c|c}
+$t$&$0.12$&$0.33$&$0.54$&$0.74$&$0.97$\\ \hline
+\textmtt{\mtt\\XoneBC\{$t$\}}&$\XoneBC{0.12}\decimal\XBST$&$\XoneBC{0.33}\decimal\XBST$&$\XoneBC{0.54}\decimal\XBST$&$\XoneBC{0.74}\decimal\XBST$&$\XoneBC{0.97}\decimal\XBST$\\ \hline
+Maple&$0.19203$&$1.1935$&$2.6328$&$4.02479$&$4.98266$
+\end{tabular}
+\end{table}
+
+Actually, calculations in determining if a point of the two curves belongs a cell almost give the desired result.
+\begin{figure}[htbp]
+\centering\includegraphics[width=5cm]{BZ5}
+\caption{A typical cell.}\label{BZ-3}
+\end{figure}
+
+Before taking some examples, we give an explanation about what the main algorithm in the procedure \verb+\NetDrawOne+ (or \verb+\NetDrawTwo+) is. Let us take an approximate sequence of points
+for the curve $\mathbf{r}_a(t)$, say $P_i(\textmtt{\mtt\\XoneBC\{$t_i$\}},\textmtt{\mtt\\YoneBC\{$t_i$\}\{$\alpha_M$\}\{$\beta_M$\}})$, $i=1,\ldots,200$. Then, each $P_i$ is examined whether to be in a cell that has the reference point $C=(x,y)$ by the instruction that: do nothing if
+$P_i$ is
+
+\begin{figure}[htbp]
+\centering\includegraphics[width=6cm]{BZ6}\hskip1cm\includegraphics[width=6cm]{BZ7}
+\caption{From left to right: $c=25$ and $c=45$.}\label{BZ-4}
+\end{figure}
+
+\begin{itemize}
+\item below $d_3$, or
+\item above $d_4$, or
+\item on the left side of $d_1$, or
+\item on the right side of $d_2$;
+\end{itemize}
+otherwise, color the cell. This algorithm can be expressed in the form of
+\begin{center}
+\begin{tabular}{llll}
+\multicolumn{4}{l}{\textmtt{\mtt\\ifdim\mtt\\YBST<$y$ \mtt\\relax\mtt\\else\mtt\\advance $y$ by ysize}}\\
+&\multicolumn{3}{l}{\textmtt{\mtt\\ifdim\mtt\\YBST>$y$ \mtt\\relax\mtt\\else}}\\
+&&\multicolumn{2}{l}{\textmtt{\mtt\\ifdim\mtt\\XBST<$x$ \mtt\\relax\mtt\\else\mtt\\advance $x$ by xsize}}\\
+&&&\textmtt{\mtt\\ifdim\mtt\\XBST>$x$ \mtt\\relax\mtt\\else\mtt\\pspolygon[fillstyle=solid,$\ldots$]}
+\end{tabular}
+\end{center}
+where \verb+\XBST+ and \verb+\YBST+ hold the values of \textmtt{\mtt\\XoneBC\{$t_i$\}} and \textmtt{\mtt\\YoneBC\{$t_i$\}\{$\alpha_M$\}\{$\beta_M$\}}, respectively.
+This structure is almost the same as that in the procedure \verb+\NetDrawOne+ (or \verb+\NetDrawTwo+), but the variables here are declared according to the gloss in
+Figure \ref{BZ-3}.
+
+Finally, let us take two examples where we just give values of $c$ for the caption of figures. In Figure \ref{BZ-4}, we take the
+same couples $\alpha_M=1.7$, $\beta_M=0.2$, $\alpha_N=0.1$ and $\beta_N=1.8$ for its two pictures. In Figure \ref{BZ-5}, we take the
+same couples $\alpha_M=-0.5$, $\beta_M=2.1$, $\alpha_N=2.4$ and $\beta_N=-0.4$ for its three pictures.
+\begin{figure}[htbp]
+\centering\includegraphics[width=5cm]{BZ8}\hskip0.5cm\includegraphics[width=5cm]{BZ9}\hskip0.5cm\includegraphics[width=5cm]{BZ10}
+\caption{From left to right: $c=25$, $c=45$ and $c=63$.}\label{BZ-5}
+\end{figure}
+\appendix
+\section{Appendix: detailed definitions}\label{appendixA}
+The following is the list of all the detailed definitions needed for the procedure, except those of \verb+\XoneFive+, \verb+\YoneFive+, \verb+\XtwoFive+, \verb+\YtwoFive+,
+\verb+\NetDrawOne+ and \verb+\NetDrawTwo+.
+
+\begin{verbatim}
+----------------------------------------------------------------------------------
+\def\xch{\catcode`\p=12 \catcode`\t=12}
+\def\ych{\catcode`\p=11 \catcode`\t=11}\xch
+\def\dec#1pt{#1}\ych
+\def\decimal#1{\expandafter\dec \the#1}
+\newcount\Fa\newcount\Fct\newcount\tempA
+
+\def\Factor{\ifnum\Fa=1\relax\else\advance\Fa by -1\multiply\Fct by \Fa\Factor\fi}
+\def\FACTORIAL#1{\Fa=#1 \ifnum\Fa=0 \Fct=1\relax\else\Fct=\Fa
+\Factor\fi\global\tempA=\Fct}
+----------------------------------------------------------------------------------
+\newcount\BINOM
+\newcount\temp
+\newcount\tmp
+
+\def\BINOMIAL#1#2{%
+\temp=#1\advance\temp by -#2
+\FACTORIAL{#1}
+\tmp=\tempA
+\FACTORIAL{\temp}
+\temp=\tempA
+\divide\tmp by \temp
+\FACTORIAL{#2}
+\temp=\tempA
+\divide\tmp by \temp\global\BINOM=\tmp}
+----------------------------------------------------------------------------------
+\newdimen\Xa\newdimen\Yb\newcount\kc
+\newdimen\BSTemp
+
+\def\xmult#1{\ifnum\kc<#1\advance\kc by 1\Yb=\decimal\Xa\Yb\xmult{#1}
+\else\relax\fi}
+\def\BERNSTEIN#1#2#3{\Xa=#3pt\kc=0\Yb=1pt\xmult{#1}\kc=0\Xa=-\Xa\advance\Xa
+by 1pt\xmult{#2}\BINOMIAL{5}{#1}\global\BSTemp=\BINOM\Yb}
+----------------------------------------------------------------------------------
+\newdimen\Xrf
+\newdimen\Yrf
+\newdimen\XoneBST\newdimen\YoneBST
+\newdimen\XtwoBST\newdimen\YtwoBST
+\newdimen\XBST\newdimen\YBST
+
+\def\XoneBC#1{%
+\BERNSTEIN{2}{3}{#1}
+\Xrf=1.5pt
+\XoneBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{3}{2}{#1}
+\Xrf=3pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{4}{1}{#1}
+\Xrf=5pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{5}{0}{#1}
+\Xrf=5pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\global\XBST=\XoneBST}
+----------------------------------------------------------------------------------
+\def\XtwoBC#1{%
+\BERNSTEIN{0}{5}{#1}
+\Xrf=5pt
+\XtwoBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{1}{4}{#1}
+\Xrf=5pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{2}{3}{#1}
+\Xrf=3.5pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{3}{2}{#1}
+\Xrf=2pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\global\XBST=\XtwoBST}
+----------------------------------------------------------------------------------
+\def\YoneBC#1#2#3{%
+\BERNSTEIN{1}{4}{#1}
+\Yrf=1.5pt
+\YoneBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{2}{3}{#1}
+\Yrf=1pt
+\Yrf=#2\Yrf
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{2}{#1}
+\Yrf=2pt
+\Yrf=#3\Yrf
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{1}{#1}
+\Yrf=1.5pt
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\global\YBST=\YoneBST}
+----------------------------------------------------------------------------------
+\def\YtwoBC#1#2#3{%
+\BERNSTEIN{1}{4}{#1}
+\Yrf=-1.5pt
+\YtwoBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{2}{3}{#1}
+\Yrf=-1pt
+\Yrf=#2\Yrf
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{2}{#1}
+\Yrf=-2pt
+\Yrf=#3\Yrf
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{1}{#1}
+\Yrf=-1.5pt
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\global\YBST=\YtwoBST}
+----------------------------------------------------------------------------------
+\end{verbatim}
+
+\begin{thebibliography}{10}
+\bibitem{one} Dominique Rodriguez, Michael Sharpe \&\ Herbert Vo\ss. \textsl{\texttt{pstricks-add}: Additional Macros for PSTricks\/}.
+Version 3.60,
+\url{http://ctan.org/tex-archive/graphics/pstricks/contrib}, 2013
+\bibitem{two}Eitan M. Gurari. \textsl{Writing With \TeX \/}, McGraw-Hill, Inc., 1994, ISBN 0-07-025207-6
+\bibitem{three} Helmut Kopka \&\ Patrick W. Daly. \textsl{Guide to \LaTeX \/}.
+Addison-Wesley, Fourth Edition, 2004, ISBN 0321173856
+\bibitem{four} Timothy Van Zandt. \textsl{User's Guide\/}. Version 1.5,\\
+\url{http://ctan.org/tex-archive/graphics/pstricks/base}, 2007
+\end{thebibliography}
+\end{document}
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@@ -0,0 +1,1036 @@
+\documentclass[11pt,a4paper,oneside]{article}
+\usepackage{calculator}
+\usepackage{calculus}
+\usepackage{amsthm}
+\usepackage{amsmath}
+\usepackage{cmtt}
+\usepackage[dvips]{geometry}
+\usepackage{pstricks}
+\usepackage{graphicx}
+\usepackage{graphics}
+\usepackage{pst-plot}
+\usepackage{pst-node}
+\usepackage{multido}
+\usepackage{pst-xkey}
+\usepackage{pst-func}
+\usepackage{pstricks-add}
+\usepackage[pdftex,colorlinks,linktocpage]{hyperref}
+\def\hantt{\^e}\def\accentcircflx{\hskip-.3em\raisebox{0.32ex}{\'{}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\RiemannSum#1#2#3#4#5#6#7#8#9{%
+\psplot[linecolor=blue]{#1}{#2}{#3}
+\pscustom[linecolor=red]{%
+\psline{-}(#1,0)(#1,0)
+\multido{\ni=#5,\ne=#6}{#4}
+{\psline(*{\ni} {#8})(*{\ne} {#9})}}
+\multido{\ne=#6,\nc=#7}{#4}
+{\psdot(*{\nc} {#3})
+\psline[linestyle=dotted,dotsep=1.5pt](\nc,0)(*{\nc} {#3})
+\psline[linecolor=red](\ne,0)(*{\ne} {#9})}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcount\Fa\newcount\Fct\newcount\tempA
+\def\Factor{\ifnum\Fa=1\relax\else\advance\Fa by -1\multiply\Fct by \Fa\Factor\fi}
+\def\FACTORIAL#1{\Fa=#1 \ifnum\Fa=0 \Fct=1\relax\else\Fct=\Fa \Factor\fi\global\tempA=\Fct}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcount\BINOM
+\newcount\temp
+\newcount\tmp
+\def\BINOMIAL#1#2{%
+\temp=#1\advance\temp by -#2
+\FACTORIAL{#1}
+\tmp=\tempA
+\FACTORIAL{\temp}
+\temp=\tempA
+\divide\tmp by \temp
+\FACTORIAL{#2}
+\temp=\tempA
+\divide\tmp by \temp\global\BINOM=\tmp}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newdimen\Xa\newdimen\Yb\newcount\kc
+\newdimen\BSTemp
+\def\xmult#1{\ifnum\kc<#1\advance\kc by 1\Yb=\decimal\Xa\Yb\xmult{#1}\else\relax\fi}
+\def\BERNSTEIN#1#2#3{\Xa=#3pt\kc=0\Yb=1pt\xmult{#1}\kc=0\Xa=-\Xa\advance\Xa by 1pt\xmult{#2}
+\BINOMIAL{6}{#1}\global\BSTemp=\BINOM\Yb}
+\newdimen\Xrf\newdimen\Yrf
+\newdimen\XBST\newdimen\YBST
+\def\XBC#1#2#3{%
+\BERNSTEIN{0}{6}{#2}
+\Xrf=#1pt
+\XBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{1}{5}{#2}
+\Xrf=#1pt\advance\Xrf by -1.5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{2}{4}{#2}
+\Xrf=#1pt\advance\Xrf by 2pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{3}{3}{#2}
+\Xrf=#1pt\advance\Xrf by 6pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{4}{2}{#2}
+\Xrf=#1pt\advance\Xrf by 5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{5}{1}{#2}
+\Xrf=#1pt\advance\Xrf by 1.5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{6}{0}{#2}
+\Xrf=#1pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\global\XBST=#3\XBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\YBC#1#2#3{%
+\BERNSTEIN{0}{6}{#2}
+\Yrf=#1pt
+\YBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{1}{5}{#2}
+\Yrf=#1pt\advance\Yrf by 2pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{2}{4}{#2}
+\Yrf=#1pt\advance\Yrf by 5pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{3}{#2}
+\Yrf=#1pt\advance\Yrf by 3pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{2}{#2}
+\Yrf=#1pt\advance\Yrf by -1pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{5}{1}{#2}
+\Yrf=#1pt\advance\Yrf by -2pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{6}{0}{#2}
+\Yrf=#1pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\global\YBST=#3\YBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XBsix#1#2{%
+(1-t)^6*(#1)*(#2)+6*t*(1-t)^5*(#1-1.5)*(#2)+15*t^2*(1-t)^4*(#1+2)*(#2)+
+20*t^3*(1-t)^3*(#1+6)*(#2)+15*t^4*(1-t)^2*(#1+5)*(#2)+6*t^5*(1-t)*(#1+1.5)*(#2)+t^6*(#1)*(#2)}
+\def\YBsix#1#2{%
+(1-t)^6*(#1)*(#2)+6*t*(1-t)^5*(#1+2)*(#2)+15*t^2*(1-t)^4*(#1+5)*(#2)+
+20*t^3*(1-t)^3*(#1+3)*(#2)+15*t^4*(1-t)^2*(#1-1)*(#2)+6*t^5*(1-t)*(#1-2)*(#2)+t^6*(#1)*(#2)}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\NetDraw#1#2#3#4#5{%
+\newcount\CellNum
+\newdimen\XRef
+\newdimen\YRef
+\newdimen\Xfact
+\newdimen\Yfact
+\newdimen\XMin
+\newdimen\XMax
+\newdimen\YMin
+\newdimen\YMax
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\CellNum=#1
+\XRef=#2pt
+\YRef=#3pt
+\Xfact=#4pt
+\Yfact=#5pt
+\XMin=\decimal\Xfact\XRef \advance\XMin by -1.50\Xfact
+\XMax=\decimal\Xfact\XRef \advance\XMax by 5.00\Xfact
+\YMin=\decimal\Yfact\YRef \advance\YMin by -6.00\Yfact
+\YMax=\decimal\Yfact\YRef \advance\YMax by \Yfact
+\Xsize=\XMax \advance\Xsize by -\XMin \divide\Xsize by \CellNum
+\Ysize=\YMax \advance\Ysize by -\YMin \divide\Ysize by \CellNum
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!30,plotpoints=200,linewidth=0.5pt]{0}{0.5}
+{\XBeight{\decimal\XRef}{\decimal\Xfact}|\YBeight{\decimal\YRef}{\decimal\Yfact}}
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!30,plotpoints=200,linewidth=0.5pt]{0.5}{1}
+{\XBeight{\decimal\XRef}{\decimal\Xfact}|\YBeight{\decimal\YRef}{\decimal\Yfact}}
+\multido{\nz=0.00+0.05}{200}{\XBC{\decimal\XRef}{\nz}{\decimal\Xfact}\YBC{\decimal\YRef}{\nz}{\decimal\Yfact}
+\multido{\nx=\decimal\XMin+\decimal\Xsize}{\the\CellNum}
+{\tempx=\nx pt\multido{\ny=\decimal\YMin+\decimal\Ysize}{\the\CellNum}
+{\tempy=\ny pt\ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize%
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else
+ \pspolygon[fillstyle=solid,fillcolor=red!90,linecolor=black,linewidth=0.2pt]
+ (\nx,\ny)(\decimal\tempx,\ny)(\decimal\tempx,\decimal\tempy)(\nx,\decimal\tempy)(\nx,\ny)\relax\fi\fi\fi\fi}
+}}
+\advance\CellNum by 1
+\multido{\nx=\decimal\XMin+\decimal\Xsize}{\the\CellNum}
+{\psline[linewidth=0.2pt](\nx,\decimal\YMax)(\nx,\decimal\YMin)}
+\multido{\ny=\decimal\YMin+\decimal\Ysize}{\the\CellNum}
+{\psline[linewidth=0.2pt](\decimal\XMin,\ny)(\decimal\XMax,\ny)}
+\parametricplot[algebraic,linecolor=white,plotpoints=200,linewidth=0.5pt]{0}{0.5}
+{\XBeight{\decimal\XRef}{\decimal\Xfact}|\YBeight{\decimal\YRef}{\decimal\Yfact}}
+\parametricplot[algebraic,linecolor=white,plotpoints=200,linewidth=0.5pt]{0.5}{1}
+{\XBeight{\decimal\XRef}{\decimal\Xfact}|\YBeight{\decimal\YRef}{\decimal\Yfact}}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\avecfld#1#2#3#4#5#6{%
+\multido{#2}{#4}
+{\multido{#1}{#3}
+{\parametricplot[algebraic,arrows=->,linecolor=red]{0}{1}
+{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\anothervecfld#1#2#3#4#5#6{%
+\multido{#2}{#4}
+{\multido{#1}{#3}
+{\curvepnodes[algebraic,plotpoints=2]{0}{1}
+{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}{P}
+\psline[linewidth=0.7pt,linecolor=red]{->}(P0)(P1)}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\xch{\catcode`\p=12 \catcode`\t=12}\def\ych{\catcode`\p=11 \catcode`\t=11}
+\xch \def\dec#1pt{#1}\ych \def\decimal#1{\expandafter\dec \the#1}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\vecfldnew#1#2#3#4#5#6#7#8{%
+\newcount\intg \newdimen\fx \newdimen\fy \newdimen\slope \newdimen\interm
+\def\fintg{\interm=#8 \interm=\intg\interm \ifdim\ifdim\slope<0pt-\fi\slope<\interm\advance\intg by -1\relax\else\advance\intg by 1\fintg\fi}
+\multido{#2}{#4}
+{\multido{#1}{#3}
+{\curvepnodes[algebraic,plotpoints=2]{0}{1}{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}{P}
+#7 \slope=10\slope\fintg
+\ifnum\intg>10\psline[linecolor=red]{->}(P0)(P1)\else\ifnum\intg=0\psline[linecolor=red!5]{->}(P0)(P1)\else\multiply\intg by 10
+\psline[linecolor=red!\the\intg]{->}(P0)(P1)\fi\fi
+\intg=0\slope=0pt
+}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagestyle{headings}
+\topmargin=-0.6cm
+\textwidth=16.7cm
+\textheight=23cm
+\headheight=2.5ex
+\headsep=0.6cm
+\oddsidemargin=.cm
+\evensidemargin=-.4cm
+\parskip=0.7ex plus0.5ex minus 0.5ex
+\baselineskip=17pt plus2pt minus2pt
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\catcode`@=11
+\renewcommand\section{\@startsection {section}{1}{\z@}%
+ {-3.5ex \@plus -1ex \@minus -.2ex}%
+ {2.3ex \@plus.2ex}%
+ {\normalfont\large\bfseries}}
+\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
+ {-3.25ex\@plus -1ex \@minus -.2ex}%
+ {1.5ex \@plus .2ex}%
+ {\normalfont\normalsize\bfseries}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\gdef\acknw{\section*{%
+{\acknwname}\markright{\protect\textsl{\acknwname}}}%
+\addcontentsline{toc}{section}{\acknwname}}
+\gdef\acknwname{Acknowledgment}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\renewcommand\sectionmark[1]{\markright{\thesection. #1}}
+\newcounter{lk}
+\newenvironment{listof}{\begin{list}{\rm(\roman{lk})}{\usecounter{lk}%
+\setlength{\topsep}{0ex plus0.1ex}%
+\setlength{\labelwidth}{1cm}%
+\setlength{\itemsep}{0ex plus0.1ex}%
+\setlength{\itemindent}{0.5cm}%
+}}{\end{list}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\title{Three applications of macros in \texttt{PSTricks}\thanks{PSTricks is the original work of Timothy Van Zandt (email address: \texttt{tvz@econ.insead.fr}).
+It is currently edited by Herbert Vo\ss\ (\texttt{hvoss@tug.org}).}}
+\author{Le Phuong Quan\\
+\small{(Cantho University, Vietnam)}\\
+\small{\texttt{lpquan@ctu.edu.vn}}}
+\begin{document}
+\maketitle
+\tableofcontents
+\section{Drawing approximations to the area under a graph by rectangles}
+\subsection{Description}
+
+We recall here an operation in Calculus. Let $f(x)$ be a function, defined and bounded on
+an interval $[a,b]$. If $f$ is integrable (in Riemann sense) on $[a,b]$, then its definite integral over this interval
+is
+$$\int_a^bf(x)dx=\lim_{\|P\|\to 0}\sum_{i=1}^nf(\xi_i)\Delta x_i,$$
+where $P\colon a=x_0<x_1<\cdots<x_n=b$, $\Delta x_i=x_i-x_{i-1}$ is a partition of $[a,b]$, $\xi_i\in[x_{i-1},x_i]$, $i=1,2,\ldots,n$,
+and $\|P\|=\max\{\Delta x_i\colon i=1,2,\ldots,n\}$. Hence, when $\|P\|$ is small enough, we may have an
+approximation
+\begin{equation}\label{eqn1}
+I=\int_a^bf(x)dx\approx\sum_{i=1}^nf(\xi_i)\Delta x_i.
+\end{equation}
+Because $I$ is independent to the choice of $P$ and $\xi_i$, we may
+divide $[a,b]$ into $n$ subintervals with equal length and choose $\xi_i=(x_i+x_{i-1})/2$.
+Then, $I$ can be approximately seen as the sum of areas of the rectangles with sides
+$f(\xi_i)$ and $\Delta x_i$.
+
+We will make a drawing procedure to illustrate the approximation (\ref{eqn1}). Firstly, we establish
+commands to draw the ``sum'' of rectangles, like the area under piecewise-constant functions
+(called \textsl{step shape\/}, for brevity). The chosen procedure here
+obviously includes a combination of the macros \texttt{\symbol{92}pscustom} (to \textsl{join\/} horizontal segments, automatically)
+and \texttt{\symbol{92}multido}. In particular, horizontal segments are depicted within the loop
+\texttt{\symbol{92}multido} by
+$$\textmtt{\symbol{92}psplot[{\it settings}]\{$x_{i-1}$\}\{$x_i$\}\{$f(\xi_i)$\}}$$
+Then, \texttt{\symbol{92}pscustom} will join these segments altogether with the ending points
+$(a,0)$, $(b,0)$ to make the boundary of the step shape. Next, we draw the points $(\xi_i,f(\xi_i))$, $i=1,2,\ldots,n$,
+and the dotted segments between these points and the points $(\xi_i,0)$, $i=1,2,\ldots,n$, by
+\begin{align*}
+&\textmtt{\symbol{92}psdot[algebraic,\dots](*\{$\xi_i$\} \{$f(x)$\})}\\
+&\textmtt{\symbol{92}psline[algebraic,linestyle=dotted,\dots]($\xi_i$,$0$)(*\{$\xi_i$\} \{$f(x)$\})}
+\end{align*}
+where we use the structure \textmtt{(*\{{\it value}\} \{$f(x)$\})} to obtain $(\xi_i,f(\xi_i))$. Finally, we draw
+vertical segments to split the step shape into rectangular cells by
+$$\textmtt{\symbol{92}psline[algebraic,\dots]($x_i$,$0$)(*\{$x_i$\} \{$f(x-\Delta x_i/2)$\})}$$
+The process of approximation is depicted in Figure \ref{Fig1}.
+\begin{figure}[htbp]
+\centering\includegraphics[height=5.5cm]{Fig1a}
+\hskip3em\includegraphics[height=5.5cm]{Fig1b}\\[2ex]
+\centering\includegraphics[height=5cm]{Fig1c}
+\caption{Steps to make the drawing procedure.}\label{Fig1}
+\end{figure}
+
+We now combine the above steps to make a procedure whose calling sequence consists of main parameters
+$a$, $b$, $f$ and $n$, and dependent parameters $x_{i-1}$, $x_i$, $\xi_i$, $f(\xi_i)$ and
+$f(x\pm\Delta x_i/2)$. For instance, let us consider approximations to the integral of $f(x)=\sin x-\cos x$
+over $[-2,3]$ in cases of $n=5$ and $n=20$. They are given in Figure \ref{Fig2}.
+\begin{figure}[htbp]
+\centering\includegraphics[height=6.1cm]{Fig2a}
+\hskip4em\includegraphics[height=6.1cm]{Fig2b}
+\caption{Approximations to the integral of $f(x)=\sin x-\cos x$ over $[-2,3]$.}\label{Fig2}
+\end{figure}
+
+In summary, we can make a procedure to illustrate the approximation (\ref{eqn1}), say \texttt{RiemannSum}, whose calling sequence has the form of
+$$\textmtt{\symbol{92}RiemannSum\{$a$\}\{$b$\}\{$f(x)$\}\{$n$\}\{$x_{\rm ini}$\}\{$x_{\rm end}$\}\{$x_{\rm choice}$\}\{$f(x+\Delta x_i/2)$\}\{$f(x-\Delta x_i/2)$\}},$$
+where $x_0=a$ and for each $i=1,2\ldots,n$:
+\begin{align*}
+x_i&=a+\dfrac{b-a}{n}i,\quad\Delta x_i=x_i-x_{i-1}=\dfrac{b-a}{n},\\
+x_{\rm ini}&=x_0+\Delta x_i,\quad x_{\rm end}=x_1+\Delta x_i,\quad x_{\rm choice}=\dfrac{x_{\rm ini}+x_{\rm end}}{2}=\dfrac{x_0+x_1}{2}+\Delta x_i.
+\end{align*}
+Note that $x_{\rm ini}$, $x_{\rm end}$ and $x_{\rm choice}$ are given in such forms to be
+suitable to variable declaration in \texttt{\symbol{92}multido}. They are nothing but
+$x_{i-1}$, $x_i$ and $\xi_i$, respectively, at the step $i$-th in the loop.
+
+Tentatively, in \texttt{PSTricks} language, the definition of \texttt{RiemannSum} is suggested to be
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\def\RiemannSum#1#2#3#4#5#6#7#8#9{%!\\
+\verb!\psplot[linecolor=blue]{#1}{#2}{#3}!\\
+\verb!\pscustom[linecolor=red]{%!\\
+\verb!\psline{-}(#1,0)(#1,0)!\\
+\verb!\multido{\ni=#5,\ne=#6}{#4}!\\
+\verb!{\psline(*{\ni} {#8})(*{\ne} {#9})}}!\\
+\verb!\multido{\ne=#6,\nc=#7}{#4}!\\
+\verb!{\psdot(*{\nc} {#3})!\\
+\verb!\psline[linestyle=dotted,dotsep=1.5pt](\nc,0)(*{\nc} {#3})!\\
+\verb!\psline[linecolor=red](\ne,0)(*{\ne} {#9})}}!
+\end{tabular}\hrule
+\subsection{Examples}
+We give here two more examples just to see that using the drawing procedure is very easy. In the first example, we approximate
+the area under the graph of the function $f(x)=x-(x/2)\cos x+2$ on the interval $[0,8]$. To draw the approximation, we try
+the case $n=16$; thus $x_0=0$ and for each $i=1,\ldots,16$, we have
+$x_i=0.5\,i$, $\Delta x_i=0.5$, $x_{\rm ini}=0.00+0.50$, $x_{\rm end}=0.50+0.50$ and $x_{\rm choice}=0.25+0.50$.
+\begin{figure}[htbp]
+\centering\includegraphics[height=6.6cm]{Fig3}
+\vskip0.5ex
+\caption{An approximation to the area under the graph of $f(x)=x-(x/2)\cos x+2$ on $[0,8]$.}\label{Fig3}
+\end{figure}
+
+To get Figure \ref{Fig3}, we have used the following \LaTeX\ code:
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\begin{pspicture}(0,0)(4.125,5.5)!\\
+\verb!\psset{plotpoints=500,algebraic,dotsize=2.5pt,unit=0.5}!\\
+\verb!\RiemannSum{0}{8}{x-(x/2)*cos(x)+2}{16}{0.00+0.50}{0.50+0.50}{0.25+0.50}!\\
+\verb!{x+0.25-((x+0.25)/2)*cos(x+0.25)+2}{x-0.25-((x-0.25)/2)*cos(x-0.25)+2}!\\
+\verb!\psaxes[ticksize=2.2pt,labelsep=4pt]{->}(0,0)(8.5,11)!\\
+\verb!\end{pspicture}!
+\end{tabular}\hrule\bigskip
+
+In the second example below, we will draw an approximation to the integral of $f(x)=x\sin x$ over $[1,9]$.
+Choosing $n=10$ and computing parameters needed, we get Figure \ref{Fig4}, mainly by
+the command
+\begin{align*}
+&\textmtt{\symbol{92}RiemannSum\{$1$\}\{$9$\}\{$x\sin x$\}\{$10$\}\{$1.00+0.80$\}\{$1.80+0.80$\}\{$1.40+0.80$\}}\\
+&\textmtt{\{$(x+0.4)\sin(x+0.4)$\}\{$(x-0.4)\sin(x-0.4)$\}}
+\end{align*}
+in the drawing procedure.
+\begin{figure}[htbp]
+\centering\includegraphics[height=6.75cm]{Fig4}
+\caption{An approximation to the integral of $f(x)=x\sin x$ over $[1,9]$.}\label{Fig4}
+\end{figure}
+\section{Drawing the vector field of an ordinary differential equation of order one}
+\subsection{Description}\label{sect1}
+
+Let us consider the differential equation
+\begin{equation}\label{eqn2}
+\frac{dy}{dx}=f(x,y).
+\end{equation}
+At each point $(x_0,y_0)$ in the domain $D$ of $f$, we will put a vector $\mathbf{v}$ with slope
+$k=f(x_0,y_0)$. If $y(x_0)=y_0$, then $k$ is the slope of the tangent to the solution curve $y=y(x)$
+of (\ref{eqn2}) at $(x_0,y_0)$. The $\mathbf{v}$'s make a \textsl{vector field\/} and the picture
+of this field would give us information about the shape of solution curves of (\ref{eqn2}), even
+we have not found yet any solution of (\ref{eqn2}).
+
+The vector field of (\ref{eqn2}) will be depicted on a finite grid of points in $D$. This grid is made of
+lines, paralell to the axes $Ox$ and $Oy$. The intersectional points of those lines are called \textsl{grid points\/}
+and often indexed by $(x_i,y_j)$, $i=0,\ldots,N_x$, $j=0,\ldots,N_y$. For convenience, we will use
+polar coordinates to locate the terminal point $(x,y)$ of a field vector, with the initial point at
+grid point $(x_i,y_j)$. Then, we can write
+\begin{align*}
+x&=x_i+r\cos\varphi,\\
+y&=y_j+r\sin\varphi.
+\end{align*}
+Because $k=f(x_i,y_j)=\tan\varphi$ is finite, we may take $-\pi/2<\varphi<\pi/2$.
+From $\sin^2\varphi+\cos^2\varphi=1$ and $\sin\varphi=k\cos\varphi$, we derive
+$$\cos\varphi=\frac{1}{\sqrt{1+k^2}},\quad\sin\varphi=\frac{k}{\sqrt{1+k^2}}.$$
+\begin{figure}[htbp]
+\centering\includegraphics[height=5cm]{Fig5}
+\caption{Field vectors on a grid.}\label{Fig5}
+\end{figure}
+The field vectors should all have the same magnitude and we choose here that length to be
+$1/2$, that means $r=1/2$. Thus, vectors on the grid have their initial and terminal points as
+$$(x_i,y_j),\quad \Big(x_i+\frac{1}{2}\cos\varphi,y_j+\frac{1}{2}\sin\varphi\Big),$$
+respectively. Hence, we easily get the parametrization of a vector at grid point
+$(x_i,y_j)$:
+\begin{align*}
+x&=x_i+\frac{t}{2}\cos\varphi=x_i+\frac{t}{2\sqrt{1+k^2}},\\
+y&=y_j+\frac{t}{2}\sin\varphi=y_j+\frac{tk}{2\sqrt{1+k^2}},
+\end{align*}
+where $t$ goes from $0$ to $1$, as along the direction of the vector.
+
+Of macros in \texttt{PSTricks} to draw lines from their parametrization, we select \texttt{\symbol{92}parametricplot}\footnote{\footnotesize
+This macro is of ones, often added and updated in the package \texttt{pstricks-add}, the authors:
+Dominique Rodriguez (\texttt{dominique.rodriguez@waika9.com}), Herbert Vo\ss\ (\texttt{voss@pstricks.de}).}
+for its fitness. The macro has the syntax
+$$\textmtt{\symbol{92}parametricplot[{\it settings}]\{$t_{\rm min}$\}\{$t_{\rm max}$\}\{$x(t)$|$y(t)$\}},$$
+where we may use the option \texttt{algebraic} to make the declaration of $x(t)$ and $y(t)$ simpler
+in \texttt{ASCII} code.
+
+From the above description of one field vector, we now construct the vector field
+on a grid within a domain $R=\{(x,y)\colon a\le x\le b,\,c\le y\le d\}$. To determine the grid, we confine grid points to the range
+\begin{equation}\label{eqn3}
+a\le x_i\le b,\quad c\le y_j\le d.
+\end{equation}
+We start with initial values $x_0=a$ and $y_0=c$ to have points $(x_i,y_j)$ with increments $\Delta x=\Delta y=\delta$, corresponding to the length of vectors and the distance
+between grid points as indicated in Figure \ref{Fig5}. Thus, to draw vectors at grid points
+$(x_i,y_j)$, we need two loops for indices $i$ and $j$, with $0\le i\le\lfloor m/\delta\rfloor$, $0\le j\le\lfloor n/\delta\rfloor$, where
+$m=b-a$, $n=d-c$. Apparently, these two loops are nested \texttt{\symbol{92}multido}s, with variable declaration
+for each loop as follows
+\begin{align*}
+\texttt{\symbol{92}nx}&=\text{initial value}+\text{increment}=x_0+\Delta x,\\
+\texttt{\symbol{92}ny}&=\text{initial value}+\text{increment}=y_0+\Delta y.
+\end{align*}
+Finally, we will replace \texttt{\symbol{92}nx}, \texttt{\symbol{92}ny} by $x_i$, $y_j$ in the
+below calling sequence for simplicity.
+
+Thus, the main command to draw the vector field of the equation (\ref{eqn2}) on the grid (\ref{eqn3})
+is
+\begin{align*}
+&\textmtt{\symbol{92}multido\big\{$y_j=y_0+\Delta y$\big\}\big\{$\lfloor n/\delta\rfloor$\big\}}\textmtt{\bigg\{\symbol{92}multido\big\{$x_i=x_0+\Delta x$\big\}\big\{$\lfloor m/\delta\rfloor$\big\}}\\
+&\quad\textmtt{\Big\{\symbol{92}parametricplot[{\it settings}]\{$0$\}\{$1$\}\Big\{$x_i+\frac{t}{2\sqrt{1+\big[f(x_i,y_j)\big]^2}}$\Big|
+$y_j+\frac{tf(x_i,y_j)}{2\sqrt{1+\big[f(x_i,y_j)\big]^2}}$\Big\}\bigg\}}
+\end{align*}
+where we at least use \texttt{arrows=->} and \texttt{algebraic} for \textit{settings}.
+
+We can combine the steps mentioned above to define a drawing procedure, say \texttt{\symbol{92}avecfld},
+that consists of $6$ parameters in the order as
+\texttt{\symbol{92}nx=}$x_0+\Delta x$, \texttt{\symbol{92}ny=}$y_0+\Delta y$, $\lfloor m/\delta\rfloor$, $\lfloor n/\delta\rfloor$, $\delta$
+and $f(\texttt{\symbol{92}nx},\texttt{\symbol{92}ny})$. We may change these values to modify
+the vector field or to avoid the vector intersection. Such a procedure is suggested to be
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\def\avecfld#1#2#3#4#5#6{%!\\
+\verb!\multido{#2}{#4}{\multido{#1}{#3}!\\
+\verb!{\parametricplot[algebraic,arrows=->,linecolor=red]{0}{1}!\\
+\verb!{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}}}}!
+\end{tabular}\hrule\bigskip
+
+Actually, the procedure \texttt{\symbol{92}parametricplot} is used here only to draw a vector by its parametrization $(x(t),y(t))$, so we can use the structure \texttt{\symbol{92}curvepnodes} in the package \texttt{pst-node}\footnote{\footnotesize
+Package authors: Timothy Van Zandt (\texttt{tvz@econ.insead.fr}), Michael Sharpe (\texttt{msharpe@euclid.ucsd.edu}) and Herbert Vo\ss\ (\texttt{hvoss@tug.org}).} to
+extract the two ending points of the curve $(x(t),y(t))$ by the command
+$$\textmtt{\symbol{92}curvepnodes[algebraic,plotpoints=2]\{0\}\{1\}\{$x(t)$|$y(t)$\}\{P\}},$$
+where \texttt{P} is a name of the root of nodes and we just get the two nodes \texttt{P0}, \texttt{P1} when executing this command. Then, the corresponding
+vector is drawn by the command
+$$\textmtt{\symbol{92}psline[linecolor={\it settings}]\{->\}(P0)(P1)}$$
+
+Therefore, another procedure to draw a vector field may be defined as
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\def\anothervecfld#1#2#3#4#5#6{%!\\
+\verb!\multido{#2}{#4}{\multido{#1}{#3}!\\
+\verb!{\curvepnodes[algebraic,plotpoints=2]{0}{1}!\\
+\verb!{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}{P}!\\
+\verb!\psline[linecolor=red]{->}(P0)(P1)}}}!
+\end{tabular}\hrule
+\subsection{Examples}
+Firstly, we consider the equation that describes an object falling in a resistive medium:
+\begin{equation}\label{eqn4}
+\frac{dv}{dt}=9.8-\frac{v}{5},
+\end{equation}
+where $v=v(t)$ is the speed of the object in time $t$. In Figure \ref{Fig6}, the vector field of (\ref{eqn4}) is given
+on the grid $R=\{(t,y)\colon 0\le t\le 9,\,46\le v\le 52\}$, together with the graph of the equilibrium solution
+$v=49$.
+\begin{figure}[htbp]
+\centering\includegraphics[height=5.85cm]{Fig6}
+\caption{The vector field of (\ref{eqn4}).}\label{Fig6}
+\end{figure}
+
+Figure \ref{Fig6} is made of the following \LaTeX\ code:
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\begin{pspicture}(0,46)(9.5,52.5)!\\
+\verb!\anothervecfld{\nx=0.25+0.50}{\ny=46.25+0.50}{18}{12}{0.5}{9.8-0.2*\ny}!\\
+\verb!\psplot[algebraic,linewidth=1.2pt]{0}{9}{49}!\\
+\verb!\psaxes[Dy=1,Dx=1,Oy=46]{->}(0,46)(0,46)(9.5,52.5)!\\
+\verb!\rput(9.5,45.8){$t$}\rput(-0.2,52.5){$y$}!\\
+\verb!\end{pspicture}!
+\end{tabular}\hrule\bigskip
+
+Let us next consider the problem
+\begin{equation}\label{eqn5}
+\frac{dy}{dx}=x+y,\quad y(0)=0.
+\end{equation}
+It is easy to check that $y=e^x-x-1$ is the unique solution to (\ref{eqn5}). We now draw
+the vector field of (\ref{eqn5}) and the solution curve\footnote{\footnotesize
+We have used ${\rm ch}(1)+{\rm sh}(1)$ for the declaration of $e$, natural base of logarithmic function.} on the grid $R=\{(x,y)\colon 0\le x\le 3,\,0\le y\le 5\}$ in
+Figure \ref{Fig7}.
+\begin{figure}[htbp]
+\centering\includegraphics[height=5.5cm]{Fig7}
+\caption{The vector field of (\ref{eqn5}).}\label{Fig7}
+\end{figure}
+
+We then go to the logistic equation, which is chosen to be a model for the dependence
+of the population size $P$ on time $t$ in Biology:
+\begin{equation}\label{eqn6}
+\frac{dP}{dt}=kP\Big(1-\frac{P}{M}\Big),
+\end{equation}
+where $k$ and $M$ are constants, respectively various to selected species and environment.
+For specification, we take, for instance, $k=0.5$ and $M=100$. The right hand side of
+(\ref{eqn6}) then becomes $f(t,P)=0.5\,P(1-0.01\,P)$. In Figure \ref{Fig8}, we draw the vector field
+of (\ref{eqn6}) on the grid $R=\{(t,P)\colon 0\le t\le 10,\,95\le P\le 100\}$ and the equilibrium
+solution curve $P=100$. Furthermore, with the initial condition $P(0)=95$, the equation (\ref{eqn6})
+has the unique solution $P=1900(e^{-0.5t}+19)^{-1}$. This solution curve is also given in Figure \ref{Fig8}.
+\begin{figure}[htbp]
+\centering\includegraphics[height=4.4cm]{Fig8}
+\caption{The vector field of (\ref{eqn6}) with $k=0.5$ and $M=100$.}\label{Fig8}
+\end{figure}
+
+The previous differential equations are all of seperated variable or linear cases that
+can be solved for closed-form solutions by some simple integration formulas. We will consider one more
+equation of the non-linear case whose solution can only be approximated by numerical methods.
+The vector field of such an equation is so useful and we will use the Runge-Kutta curves (of order $4$)
+to add more information about the behaviour of solution curves. Here, those Runge-Kutta curves are depicted by the procedure
+\texttt{\symbol{92}psplotDiffEqn}, also updated from the package \texttt{pstricks-add}.
+
+The vector field of the non-linear differential equation
+\begin{equation}\label{eqn7}
+\frac{dy}{dx}=y^2-xy+1
+\end{equation}
+will be depicted on the grid $R=\{(x,y)\colon -3\le x\le 3,\,-3\le y\le 3\}$ and the solutions
+of Cauchy problems for (\ref{eqn7}), corresponding to initial conditions
+\begin{listof}
+\item $y(-3)=-1$,
+\item $y(-2)=-3$,
+\item $y(-3)=-0.4$,
+\end{listof}
+will be approximated by the method of Runge-Kutta, with the grid size $h=0.2$. It is very easy
+to recognize approximate curves, respective to (i), (ii) and (iii) in Figure \ref{Fig9} below.
+\begin{figure}[htbp]
+\centering\includegraphics[height=7.8cm]{Fig9}
+\caption{The vector field of (\ref{eqn7}) and the Runge-Kutta curves.}\label{Fig9}
+\end{figure}
+\subsection{Remarks on how to color arrows properly for a vector field}
+There remains a problem in drawing a vector field. That is coloring arrows.
+Obviously, their color shade should vary according to their slope and this would give us the picture of domains containing
+increase or decrease solutions of a differential equation. In some cases, we even know how large the rate of change of those
+solutions is in a specific domain.
+
+In Subsection \ref{sect1}, we know for the equation (\ref{eqn2}) that $f(x_i,y_j)$ is right the slope of
+field vectors at grid points $(x_i,y_j)$, and we will divide these slopes into some number of scales, corresponding to the
+degree of color shades. Here, we confine our interest to a continuous function $f(x,y)$ in two independent variables on a domain
+$R=\{(x,y)\colon a\le x\le b,\,c\le y\le d\}$ and choose the scale of $10$ degrees. This number of degrees can be changed to any positive integer.
+
+According to the input data from the differential equation (\ref{eqn2}), the set $R$ and the grid points on it and the value $M=\max\{|f(x_i,y_j)|\colon
+0\le i\le\lfloor m/\Delta x\rfloor,\,0\le j\le\lfloor n/\Delta y\rfloor\}$, where $m=b-a$ and $n=d-c$,
+we can now define the degree of color shade for each arrow in our vector field. It should be an integer $n_{ij}$ such that
+$n_{ij}=\lfloor 10|f(x_i,y_j)|/M\rfloor$, that is
+\begin{equation}\label{eqn8}n_{ij}M\le 10|f(x_i,y_j)|<(n_{ij}+1)M.\end{equation}
+For finding such an integer, in \TeX\ codes, we need one \texttt{\symbol{92}newcount} for it and two \texttt{\symbol{92}newdimen} for
+$f(x_i,y_j)$ and intermediate values to be compared with $|f(x_i,y_j)|$. For more explanation, let us begin with settings
+\texttt{\symbol{92}newcount\symbol{92}intg} (referring (ref.) to ``integer''), \texttt{\symbol{92}newdimen\symbol{92}slope} (ref. to ``slope'') and \texttt{\symbol{92}newdimen\symbol{92}interm}
+(ref. to ``intermediate values''). Then, the integer $n_{ij}$ at stage $(i,j)$ within the two \texttt{\symbol{92}multido} loops can be defined by the recursive macro \texttt{\symbol{92}fintg} (ref. to ``find the integer'') as follows
+\begin{verbatim}
+ \def\fintg{\interm=Mpt \interm=\intg\interm%
+ \ifdim\ifdim\slope<0pt -\fi\slope<\interm\advance\intg by -1\relax
+ \else\advance\intg by 1\fintg\fi}
+\end{verbatim}
+where \texttt{M} and \texttt{\symbol{92}slope} are holding the values $M$ and $f(x_i,y_j)$, respectively. Note that, before running our macro, \verb!\slope! should be multiplied
+by $10$ with the assignment \texttt{\symbol{92}slope=10\symbol{92}slope}, as defined in (\ref{eqn8}). Besides, by simulating the expression of $f(x,y)$, the calculation of $f(x_i,y_j)$
+should be declared with operations on \texttt{\symbol{92}newcount}s and \texttt{\symbol{92}newdimen}s. Then, the integer $n_{ij}$, which is found at stage $(i,j)$, should take its
+degree, say $k$, from $0$ to $10$ by its value, suitably associated to the command \textmtt{\symbol{92}psline[linecolor=red!case-k]\{->\}(P0)(P1)}.
+Here, we choose \texttt{red} for the main color (it can be changed, of course), and \texttt{case-k} will be replaced with an appropriate percentage of \texttt{red}. Finally,
+such a color scale is local and relative, so we can use one more parameter in the procedure to adjust color shades.
+The old procedures take $6$ parameters and the new one will take two more parameters: one for declaration of computing $f(x_i,y_j)$ and the other
+for adjusting color shades.
+
+Let us take some examples on how to compute $f(x_i,y_j)$ by \TeX\ codes or by commands from the package \texttt{calculator}\footnote{\footnotesize
+Package author: Robert Fuster (\texttt{rfuster@mat.upv.es}).}. For a simple polynomial $f(x,y)$,
+computing $f(x_i,y_j)$ by \TeX\ codes might be facile. Because \verb!\nx! and \verb!\ny! are respectively holding values of
+$x_i$ and $y_j$, we need the two corresponding variables \verb!\newdimen\fx! and \verb!\newdimen\fy! to take these values. By assigning \verb!\fx=\nx pt\fy=\ny pt!,
+we compute $f(\verb!\nx!,\verb!\ny!)$ and assign its value to \verb!\slope!. The declaration of calculations for some cases of $f(x,y)$ is given in the following table.
+
+\begin{table}[htbp]
+\centering\begin{tabular}{c|l}
+$f(x,y)$&\multicolumn{1}{c}{\TeX\ codes for computing $f(\texttt{\symbol{92}nx},\texttt{\symbol{92}ny})$} \\ \hline
+$x+y$&\verb!\advance\slope by \fx \advance\slope by \fy!\\ \hline
+$1-xy$&\verb!\advance\slope by -\decimal\fx\fy \advance\slope by 1pt!\\ \hline
+$y(3-y)$&\verb!\advance\slope by -\decimal\fy\fy \advance\slope by 3\fy!\\ \hline
+$y^2-xy$&\verb!\advance\slope by \decimal\fy\fy \advance\slope by -\decimal\fx\fy!\\ \hline
+\end{tabular}
+\end{table}
+In the table, the command \verb!\decimal!, which is quotative from \cite{five} for producing decimal numbers from dimensions, is put in the preamble using a definition as
+\begin{verbatim}
+ \def\xch{\catcode`\p=12 \catcode`\t=12}\def\ych{\catcode`\p=11 \catcode`\t=11}
+ \xch \def\dec#1pt{#1}\ych \def\decimal#1{\expandafter\dec \the#1}
+\end{verbatim}
+
+For a transcendental or rational function $f(x,y)$, we may use the package \texttt{calculator} for
+computing $f(x_i,y_j)$. The following table shows how to perform calculations.
+\begin{table}[htbp]
+\centering\begin{tabular}{c|l}
+$f(x,y)$&\multicolumn{1}{c}{The commands from the package \texttt{calculator} for computing $f(\texttt{\symbol{92}nx},\texttt{\symbol{92}ny})$} \\ \hline
+$\sin(y-x)$&\verb!\SUBTRACT{\ny}{\nx}{\sola}\SIN{\sola}{\solb}\slope=\solb pt!\\ \hline
+\raisebox{-2ex}[0pt][0pt]{$2xy/(1+y^2)$}&\verb!\SUMfunction{\ONEfunction}{\SQUAREfunction}{\Fncty}!\\
+&\verb!\Fncty{\ny}{\soly}{\Dsoly}\DIVIDE{\Dsoly}{\soly}{\tempa}!\\
+&\verb!\MULTIPLY{\nx}{\tempa}{\tempb}\slope=\tempb pt!\\ \hline
+\end{tabular}
+\end{table}
+
+From the old macros \verb!\avecfld! or \verb!\anothervecfld!, we will construct the new one \verb!\vecfldnew! by adding up to the former the two parameters as described above. According to
+the description of new parameters and of known ones, the calling sequence of \verb!\vecfldnew! may have the form of
+$$\textmtt{\symbol{92}vecfldnew\{\symbol{92}nx$=x_0+\Delta x$\}\{\symbol{92}ny$=y_0+\Delta y$\}\{$n_x$\}\{$n_y$\}\{$\ell$\}\{$f(\texttt{\symbol{92}nx},\texttt{\symbol{92}ny})$\}\{{\rm\TeX\ codes}\}\{$n_a$\}}$$
+where $n_a$ is an estimate value for $M$ and can be adjusted to be greater or less than $M$. This flexible mechanism might be to increase or decrease the degree of
+color shades. Finally, \verb!\intg! and \verb!\slope! should be reset to
+zero at the end of each stage. Now, all materials to make the new macro are ready, and its definition is suggested to be
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\def\vecfldnew#1#2#3#4#5#6#7#8{%!\\
+\verb!\newcount\intg \newdimen\slope \newdimen\interm \newdimen\fx \newdimen\fy!\\
+\verb!\def\fintg{\interm=#8 \interm=\intg\interm%!\\
+\verb! \ifdim\ifdim\slope<0pt -\fi\slope>\interm \advance\intg by 1\fintg\fi}!\\
+\verb!\multido{#2}{#4}!\\
+\verb!{\multido{#1}{#3}!\\
+\verb!{\curvepnodes[algebraic,plotpoints=2]{0}{1}!\\
+\verb!{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}{P}!\\
+\verb!#7\slope=10\slope \fintg \ifnum\intg>10\psline[linecolor=red]{->}(P0)(P1)!\\
+\verb+\else\ifnum\intg=0\psline[linecolor=red!5]{->}(P0)(P1)+\\
+\verb+\else\multiply\intg by 10\psline[linecolor=red!\the\intg]{->}(P0)(P1)\fi\fi+\\
+\verb+\intg=0\slope=0pt+\\
+\verb+}}}+
+\end{tabular}\hrule\bigskip
+
+If we predefine some scale of degrees, instead of the code $\verb!\ifnum\intg>10!\ldots\verb!\fi\fi!$, the structure \verb!\ifcase! can be used as
+$$\begin{array}{c}
+\verb!\ifcase\intg!\\
+\verb+\psline[linecolor=red!5]{->}(P0)(P1)\or+\\
+\verb+\psline[linecolor=red!10]{->}(P0)(P1)\or+\\
+\vdots\\
+\verb!\psline[linecolor=red]{->}(P0)(P1)\fi!
+\end{array}$$
+
+The first example is given with two values of $n_a$ to see how different the color shades are between the two cases. The left vector field in Figure \ref{Fig10}
+is made of the calling sequence
+\begin{verbatim}
+\vecfldnew{\nx=-2.00+0.3}{\ny=-2.00+0.3}{14}{14}{0.3}{(\nx)-2*(\ny)}
+{\fy=\ny pt \fx=\nx pt \advance\slope by -2\fy \advance\slope by \fx}{7pt}
+\end{verbatim}
+\begin{figure}[htbp]
+\centering\includegraphics[width=4.6cm]{vecb5}
+\hskip1cm\includegraphics[width=4.6cm]{vecb6}
+\caption{The vector fields of the equation $y'=x-2y$ with $n_a=\texttt{7pt}$ (the left) and $n_a=\texttt{4pt}$ (the right)}\label{Fig10}
+\end{figure}
+
+In Figure \ref{Fig11}, the vector fields of the equations $y'=y-x$ and $y'=x(2-y)$ are respectively drawn by the calling sequences
+\begin{verbatim}
+\vecfldnew{\nx=-3.00+0.4}{\ny=-3.00+0.4}{15}{15}{0.35}{(\ny)-(\nx)}
+{\fy=\ny pt \fx=\nx pt \advance\slope by -\fx \advance\slope by \fy}{5pt}
+\end{verbatim}
+and
+\begin{verbatim}
+\vecfldnew{\nx=-3.00+0.4}{\ny=-3.00+0.4}{15}{15}{0.35}{(\nx)*(2-(\ny))}
+{\fy=\ny pt \fx=\nx pt \advance\slope by -\decimal\fx\fy
+\advance\slope by 2\fx}{6pt}
+\end{verbatim}
+\begin{figure}[htbp]
+\centering\includegraphics[width=6.2cm]{vecb3}
+\hskip1cm\includegraphics[width=6.2cm]{vecb4}
+\caption{The vector fields of the equation $y'=y-x$ (the left) and $y'=x(2-y)$ (the right).}\label{Fig11}
+\end{figure}
+
+Finally, we consider two more examples on vector fields of differential equations $y'=f(x,y)$ containing trigonometric or rational functions on their right side. The calling sequences
+\begin{verbatim}
+\vecfldnew{\nx=-3.00+0.4}{\ny=-3.00+0.4}{15}{15}{0.35}{sin(\nx)*cos(\ny)}
+{\SIN{\nx}{\tmpa}\COS{\ny}{\tmpb}\MULTIPLY{\tmpa}{\tmpb}{\tmpc}
+\slope=\tmpc pt}{0.6pt}
+\end{verbatim}
+and
+\begin{verbatim}
+\vecfldnew{\nx=-3.00+0.3}{\ny=-3.00+0.3}{20}{20}{0.3}{2*(\nx)*(\ny)/(1+(\ny)^2)}
+{\SUMfunction{\ONEfunction}{\SQUAREfunction}{\Fncty}\Fncty{\ny}{\soly}{\Dsoly}
+\DIVIDE{\Dsoly}{\soly}{\tempa}\MULTIPLY{\nx}{\tempa}{\tempb}
+\slope=\tempb pt}{2.5pt}
+\end{verbatim}
+respectively result in the vector fields on the left and on the right in Figure \ref{Fig12}.
+
+\begin{figure}[htbp]
+\centering\includegraphics[width=6.2cm]{vecb1}
+\hskip1cm\includegraphics[width=6.2cm]{vecb2}
+\caption{The vector fields of the equation $y'=\sin(x)\cos(y)$ (the left) and $y'=2xy/(1+y^2)$ (the right).}\label{Fig12}
+\end{figure}
+\section{Drawing partitions of a simply connected plane domain}
+\subsection{Description}
+B\'{e}zier curves have been used in many different aspects, but mostly in computer graphics to model smooth curves designed by computer
+programs. We just recall here the vector function of a B\'{e}zier curve of degree $n$ with $n+1$ control points whose position
+vectors are $\mathbf{r}_0$, $\mathbf{r}_1$, \dots, $\mathbf{r}_n$. It is the vector function $\mathbf{r}(t)$ in a real variable $t\in[0,1]$ that
+is defined as
+\begin{equation}\label{eqn9}
+\mathbf{r}(t)=\sum_{i=0}^n\binom{n}{i}t^i(1-t)^{n-i}\mathbf{r}_i.
+\end{equation}
+Since $\mathbf{r}(0)=\mathbf{r}_0$, $\mathbf{r}(1)=\mathbf{r}_n$ and $\mathbf{r}'(0)=n(\mathbf{r}_1-\mathbf{r}_0)$, $\mathbf{r}'(1)=n(\mathbf{r}_n-\mathbf{r}_{n-1})$,
+we can take a curve such that it is closed and tangent to a line $(\Delta)$ at the point whose position vector is $\mathbf{r}_0$, by
+letting $\mathbf{r}_n=\mathbf{r}_0$ and the points whose position vectors are $\mathbf{r}_0$, $\mathbf{r}_1$ and $\mathbf{r}_{n-1}$
+all be on the line $(\Delta)$.
+
+Taking a closed B\'{e}zier curve to be the boundary of a plane domain has the great advantage. That is because coordinates of points
+on the curve are evaluated by polynomials, and the curve has necessary smoothness, beautiful enough for graphic illustrations.
+\texttt{PSTricks} has the procedure \verb!\parametricplot! to draw such a curve. But, an important problem here is how to control
+the coordinates of its points to construct a procedure for drawing a partition of a simply connected plane domain and coloring
+(or marking) its cells having common points with the boundary of the domain. We particularly need such a procedure for illustrations
+of essential notions in measure theory or double integral definition. Because of the limitation in accuracy imposed
+by the \TeX\ arithmetic, we should mention about $2$-dimension vector functions of a B\'{e}zier curve of small degree (in fact, as small as possible).
+According to the above requirements for the closed boundary of a simply connected domain, we will design a family of closed B\'{e}zier curves of
+degree $6$, although we may extend their degree to $12$.
+
+From the expression of $\mathbf{r}(t)$ in (\ref{eqn9}), we will construct the following functions and procedures:
+\begin{itemize}
+\item The factorial function \texttt{FACTORIAL}.
+\item The binomial function \texttt{BINOMIAL}.
+\item Polynomials $t^m(1-t)^n$.
+\item A procedure to compute a sum of $7$ terms: values of $\mathbf{r}(t)$ as linear combinations
+of the Bernstein polynomials
+$$\binom{6}{k}t^k(1-t)^{6-k},\quad k=0,\ldots,6.$$
+\end{itemize}
+These functions and procedures are macros given by definitions with or without parameters. In the following subsections we will construct them step by step and
+show how to make connections between them.
+\subsubsection{Factorial functions and binomial coefficients}
+To obtain the factorial function, a procedure for multiplying consecutively an integer $n$ with its diminished values will be constructed. For the declared
+integer variables \verb!\Fa! and \verb!\Fct!, the latter will hold values of the function, and the former will hold factors that are multiplied consecutively
+and reduced by $1$. Namely, if \verb!\Fa! is $0$ or $1$ then \verb!\Fct! takes $1$; else if $\texttt{\symbol{92}Fa}>1$ then \verb!\Fct! takes
+the initial value of \verb!\Fa! to begin a loop: diminishing \verb!\Fa! by $1$ and updating \verb!\Fct! by multiplying its old value with the new value of \verb!\Fa!.
+The loop is defined by the control sequence \verb!\Factor! and is ended when \verb!\Fa! is diminished to $1$; then, the factorial function obtains its value from
+the one given back after calling \verb!\FACTORIAL! with one parameter.
+\begin{verbatim}
+\newcount\Fa\newcount\Fct
+\newcount\tempA
+\def\Factor{\ifnum\Fa=1\relax\else\advance\Fa by -1\multiply\Fct by \Fa\Factor\fi}
+\def\FACTORIAL#1{\Fa=#1 \ifnum\Fa=0 \Fct=1\relax\else\Fct=\Fa \Factor\fi%
+\global\tempA=\Fct}
+\end{verbatim}
+Since \TeX\ limits the largest integer number to $2^{30}-1$, we can evaluate only to
+$$\textmtt{\symbol{92}FACTORIAL\{$12$\}}=12!=479001600.$$
+Besides, the last value of \verb!\Fct!, which is right the one obtained from calling the function, is assigned to a global integer variable \verb!\tempA! for use
+in other procedures. Finally, make the calling sequence
+$$\textmtt{\symbol{92}FACTORIAL\{k\}\symbol{92}the\symbol{92}Fct}$$
+to obtain and show up the value of $k!$. From these values we derive binomial coefficients by the formula
+$$\binom{m}{n}=\frac{m!}{n!(m-n)!}.$$
+A simple procedure that makes division of $m!$ by $n!$, then of the result by $(m-n)!$ can be performed by the control sequence
+\verb!\BINOMIAL! with two parameters as follows
+\begin{verbatim}
+\newcount\BINOM
+\newcount\temp\newcount\tmp
+\def\BINOMIAL#1#2{%
+\temp=#1\advance\temp by -#2
+\FACTORIAL{#1}
+\tmp=\tempA
+\FACTORIAL{\temp}
+\temp=\tempA
+\divide\tmp by \temp
+\FACTORIAL{#2}
+\temp=\tempA
+\divide\tmp by \temp\global\BINOM=\tmp}
+\end{verbatim}
+Again, the last value of \verb!\tmp! is assigned to a global integer variable \verb!\BINOM! for later use. Because the vector function of a B\'{e}zier
+curve of degree $6$ is only needed, so are the binomial coefficients \verb!\BINOMIAL{!$6$\verb!}{!$k$\verb!}!, $k=0,1,\ldots,6$.
+\subsubsection{Bernstein polynomials}
+The construction of Bernstein functions is based on an iterative multiplication of the same value $t$ by a given number $m$ of times,
+then the process is repeated with the value $1-t$ by a given number $n$ of times. The last result is multiplied by a variable that holds
+the value of $\binom{m+n}{m}$. We will use an integer variable \verb!\kc! to count times of multiplication for the same factor $t$ or $1-t$.
+The procedure of iterative multiplication \verb!\xmult! with one parameter $m$ or $n$ is a recursive one that is performed
+iteratively until \verb!\kc! reaches the value $m$ or $n$.
+\begin{verbatim}
+\newdimen\Xa\newdimen\Yb\newcount\kc
+\def\xmult#1{\ifnum\kc<#1\advance\kc by 1\Yb=\decimal\Xa\Yb\xmult{#1}
+ \else\relax\fi}
+\end{verbatim}
+Finally, the value of $t^m(1-t)^n$ that is hold by the variable \verb!\Yb! is multiplied by \verb!\BINOM!, the value $\binom{6}{m}$.
+Thus, Bernstein polynomials are given by the following macro \verb!\BERNSTEIN! with three parameters that hold values of
+$m$, $n$ and $t$, respectively.
+\begin{verbatim}
+\newdimen\BSTemp
+\def\BERNSTEIN#1#2#3{\Xa=#3pt\kc=0\Yb=1pt\xmult{#1}\kc=0\Xa=-\Xa
+\advance\Xa by 1pt\xmult{#2}\BINOMIAL{6}{#1}\global\BSTemp=\BINOM\Yb}
+\end{verbatim}
+Also, values of \verb!\BERNSTEIN! are assigned to a global variable.
+\subsubsection{Vector functions of a plane B\'{e}zier curve of degree $6$}
+We will construct here the vector function of a plane and closed B\'{e}zier curve with the control points
+$M_0(x_0,y_0)$, $M_1(x_1,y_1)$, \dots, $M_6(x_6,y_6)$ that is chosen in such a way that the curve is tangent to
+a line $(\Delta)$ at its initial point $M_0$. According to the mentioned properties of a B\'{e}zier curve, the requirements
+for the curve are satisfied when $M_6=M_0$ and $M_0$, $M_1$, $M_5$ are all on the line $(\Delta)$.
+\begin{figure}[htbp]
+\centering\includegraphics[height=4.3cm]{Fig13}
+\caption{A B\'{e}zier curve of degree $6$ with the required control points.}\label{Fig13}
+\end{figure}
+In case $n=6$, from (\ref{eqn9}) we derive the vector function $\mathbf{r}(t)$ with the two components
+\begin{equation}\label{eqn10}
+X(t)=\sum_{i=0}^6\binom{6}{i}t^i(1-t)^{6-i}x_i,\quad Y(t)=\sum_{i=0}^6\binom{6}{i}t^i(1-t)^{6-i}y_i.
+\end{equation}
+We first evaluate values of $X(t)$ by the procedures that just have been constructed, with a choice of $x_i$, $i=1,\ldots,6$, from a given $x_0$
+and the requirements of the B\'{e}zier curve as in Figure \ref{Fig13}. For example, we may take
+$$x_1=x_0-1.5,\quad x_2=x_0+2,\quad x_3=x_0+6,\quad x_4=x_0+5,\quad x_5=x_0+1.5,\quad x_6=x_0.$$
+Moreover, we may change the shape of the curve by taking a factor $\alpha$ for $X(t)$. In short, we will make a procedure to evaluate the sum of terms
+$\binom{6}{i}t^i(1-t)^{6-i}(\alpha x_i)$, $i=0,1,\ldots,6$. In fact, it is a procedure to add up values into a global variable \verb!\XBST! that is called
+by a macro \verb!\XBC! with three declaring parameters for $x_i$, $t$ and $\alpha$. The value of $\alpha$ is used last when being multiplied by a
+variable that holds $X(t)$. Such a procedure is suggested to be the following macro
+\begin{verbatim}
+\newdimen\Xrf\newdimen\Yrf
+\newdimen\XBST\newdimen\YBST
+\def\XBC#1#2#3{%
+\BERNSTEIN{0}{6}{#2}
+\Xrf=#1pt
+\XBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{1}{5}{#2}
+\Xrf=#1pt\advance\Xrf by -1.5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{2}{4}{#2}
+\Xrf=#1pt\advance\Xrf by 2pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{3}{3}{#2}
+\Xrf=#1pt\advance\Xrf by 6pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{4}{2}{#2}
+\Xrf=#1pt\advance\Xrf by 5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{5}{1}{#2}
+\Xrf=#1pt\advance\Xrf by 1.5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{6}{0}{#2}
+\Xrf=#1pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\global\XBST=#3\XBST}
+\end{verbatim}
+In the macro, a control sequence of the form \verb!\decimal\Xdim! is for obtaining the decimal value of a variable \verb!\Xdim! without units
+(\verb!pt!, by default). This can be defined by
+\begin{verbatim}
+\def\xch{\catcode`\p=12 \catcode`\t=12}\def\ych{\catcode`\p=11 \catcode`\t=11}
+\xch \def\dec#1pt{#1}\ych \gdef\decimal#1{\expandafter\dec \the#1}
+\end{verbatim}
+Besides, the last line in the definition of \verb!\XBC! (\verb!\global\XBST=#3\XBST!) signifies \verb!\XBST! is adjusted for multiplication by
+$\alpha$ when holding the current value of the sum $X(t)$. In Table \ref{bc-Table1}, some values
+of \verb!\XBC! are compared with those of a simpler procedure in Maple\footnote{\footnotesize Maple
+is a computer algebra system. It was first developed in 1980 by the Symbolic Computation Group at the University of
+Waterloo in Waterloo, Ontario, Canada. Maple supports numeric and symbolic computations
+and can be used as a programming language, which resembles Pascal.}.
+\begin{table}[htbp]
+\centering\begin{tabular}{|c|c|c|c|c|c|}\hline
+&$(-2.4,0.23,1.5)$&$(4.2,0.45,1.1)$&$(-3.4,0.7,1.24)$&$(-0.89,0.4,1.5)$&$(5.21,0.5,2.15)$\\ \hline
+\texttt{\symbol{92}XBC}&$\XBC{-2.4}{0.23}{1.5}\decimal\XBST$&$\XBC{4.2}{0.45}{1.1}\decimal\XBST$&$\XBC{-3.4}{0.7}{1.24}\decimal\XBST$&$\XBC{-0.89}{0.4}{1.5}\decimal\XBST$&$\XBC{5.21}{0.5}{2.15}\decimal\XBST$\\ \hline
+Maple&$-2.41044$&$8.13235$&$-0.13696$&$2.78628$&$18.76008$\\ \hline
+\end{tabular}
+\caption{A comparison between some values of \textmtt{\symbol{92}XBC} and those of a procedure in Maple.}\label{bc-Table1}
+\end{table}
+
+Likewise, from a given $y_0$, we may have a choice of $y_i$, $i=1,\ldots,6$, as follows
+$$y_1=y_0+2,\quad y_2=y_0+5,\quad y_3=y_0+3,\quad y_4=y_0-1,\quad y_5=y_0-2,\quad y_6=y_0.$$
+The macro \verb!\YBC! is constructed in a quite analogous way as for \verb!\XBC! to evaluate values of $Y(t)$ in (\ref{eqn10}),
+and the value $\beta Y(t)$ ($\beta$ is again an adjustment factor) is hold by a global variable \verb!\YBST!.
+
+\subsubsection{Partition of a simply connected plane domain by a rectangular grid}
+
+We consider here a simply connected plane domain $D$ surrounded by a B\'{e}zier curve of degree $6$ that will be depicted by
+the procedure \verb!\NetDraw!. This is called together with its five parameters whose values are assigned to the five local variables
+with their following meaning:
+\begin{align*}
+\texttt{\symbol{92}CellNum:}&\text{ The number of horizontal and vertical cells of the grid.}\\
+\texttt{\symbol{92}Xref:}&\text{ The value of $x_0$.}\\
+\texttt{\symbol{92}Yref:}&\text{ The value of $y_0$.}\\
+\texttt{\symbol{92}Xfact:}&\text{ The value of $\alpha$.}\\
+\texttt{\symbol{92}Yfact:}&\text{ The value of $\beta$.}
+\end{align*}
+We denote by $R$ a rectangular domain containing $D$ and having edges parallel to the coordinate axes.
+A grid of rectangular cells will be depicted on $R$. According to the given values of $x_0$, $y_0$, $\alpha$ and $\beta$, the vertices of $R$
+can be chosen as the points $(\verb!\XMin!,\verb!\YMax!)$, $(\verb!\XMax!,\verb!\YMax!)$, $(\verb!\XMax!,\verb!\YMin!)$, $(\verb!\XMin!,\verb!\YMin!)$, where
+\begin{align*}
+\textmtt{\symbol{92}XMin}&=\alpha(\textmtt{\symbol{92}Xref}-1.5),&&\textmtt{\symbol{92}XMax}=\alpha(\textmtt{\symbol{92}Xref}+6),\\
+\textmtt{\symbol{92}YMin}&=\beta(\textmtt{\symbol{92}Yref}-2),&&\textmtt{\symbol{92}YMax}=\beta(\texttt{\symbol{92}Yref}+5).
+\end{align*}
+Then, the horizontal step size \verb!\Xsize! and the vertical step
+size \verb!\Ysize! may be taken as
+$$\mtt\\\texttt{Xsize}=\frac{\mtt\\\texttt{XMax}-\mtt\\\texttt{XMin}}{\mtt\\\texttt{CellNum}},\quad
+\mtt\\\texttt{Ysize}=\frac{\mtt\\\texttt{YMax}-\mtt\\\texttt{YMin}}{\mtt\\\texttt{CellNum}}.$$
+
+At first, the grid is made by using the structure \verb!\multido! to draw vertical and horizontal lines whose equations are
+$$x=\texttt{\symbol{92}XMin}+i\texttt{\symbol{92}Xsize},\quad
+y=\texttt{\symbol{92}YMin}+i\texttt{\symbol{92}Ysize},\quad i=0,\ldots,\texttt{\symbol{92}CellNum}.$$
+Next, the B\'{e}zier curve is depicted by the command
+$$\textmtt{\symbol{92}parametricplot[algebraic,fillstyle=solid]\{$0$\}\{$1$\}\{$\alpha X(t)$|$\beta Y(t)$\}}$$
+and it is approximated by the sequence of points $(X_i,Y_i)$, $i=1,\ldots,N$, where $X_i$ and $Y_i$ are given from
+the calling sequences
+$$\textmtt{\symbol{92}XBC\{\symbol{92}XRef\}\{$t_i$\}\{\symbol{92}Xfact\}},\quad
+\textmtt{\symbol{92}YBC\{\symbol{92}YRef\}\{$t_i$\}\{\symbol{92}Yfact\}}.$$
+
+Finally, the most important algorithm is to determine cells that have points in common with the B\'{e}zier curve,
+and to color them. The chosen ``filter'' method here can be described as follows: for each point $(X_i,Y_i)$ of the approximate sequence,
+$i=1,\ldots, N$, we examine cells from left to right in horizontal direction, and from below to above in vertical direction. As soon as
+being found, the cell containing $(X_i,Y_i)$ is specifically colored by the command \textmtt{\mtt\\pspolygon[fillstyle=solid,$\ldots$]} passing its four
+vertices; then, we examine the next point $(X_{i+1},Y_{i+1})$, and so on. Actually, a structure of three nested \verb!\multido! loops
+is used to perform this filter method, and the loop for counting points $(X_i,Y_i)$ is the most outer one. The algorithm to examine if
+a cell contains $(X_i,Y_i)$ may have the form of
+\begin{verbatim}
+ \ifdim\YBST<y\relax\else\advance y by \Ysize
+ \ifdim\YBST>y\relax\else
+ \ifdim\XBST<x\relax\else\advance x by \Xsize
+ \ifdim\XBST>x\relax\else
+ \pspolygon[fillstyle=solid,fillcolor=red]
+ (x,y)(x+\Xsize,y)(x+\Xsize,y+\Ysize)(x,y+\Ysize)(x,y)\relax
+ \fi\fi\fi\fi
+\end{verbatim}
+The single characters ``\verb!x!'', ``\verb!y!'' and the opertation ``\verb!+!'' will be replaced appropriately in the procedure \verb!\NetDraw! below.
+For increasingly chosen values of $N$, we may know if the set of cells having points in common with the curve can cover the curve itself?
+On the other hand, to increase the number of approximate points is corresponding to reduce the increment in the most outer loop \verb!\multido!.
+For instance, if we take $N=100$, then the variable \verb!\nz! in the loop should be declared as $\texttt{\mtt\\nz}=0.00+0.01$ because
+$t_i\in[0,1]$.
+
+In summary, to illustrate a partition of a simply connected plane domain, we can apply the following procedure \verb!\NetDraw!. As mentioned above,
+step by step, \verb!\NetDraw! can: draw the boundary of a plane domain $D$ by a B\'{e}zier curve of degree $6$, draw a partition of a rectangle $R$ containing $D$
+by a grid of rectangular cells, and color cells having points in common with the boundary of $D$.
+\bigskip
+%\vskip2ex
+\hrule
+\begin{verbatim}
+\def\NetDraw#1#2#3#4#5{%
+\newcount\CellNum
+\newdimen\XRef
+\newdimen\YRef
+\newdimen\Xfact
+\newdimen\Yfact
+\newdimen\XMin
+\newdimen\XMax
+\newdimen\YMin
+\newdimen\YMax
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\CellNum=#1
+\XRef=#2pt
+\YRef=#3pt
+\Xfact=#4pt
+\Yfact=#5pt
+\XMin=\decimal\Xfact\XRef \advance\XMin by -1.50\Xfact
+\XMax=\decimal\Xfact\XRef \advance\XMax by 6.00\Xfact
+\YMin=\decimal\Yfact\YRef \advance\YMin by -2.00\Yfact
+\YMax=\decimal\Yfact\YRef \advance\YMax by 5.00\Yfact
+\Xsize=\XMax \advance\Xsize by -\XMin \divide\Xsize by \CellNum
+\Ysize=\YMax \advance\Ysize by -\YMin \divide\Ysize by \CellNum
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!80,plotpoints=200,
+linewidth=0.5pt]{0}{1}{\XBsix{\decimal\XRef}{\decimal\Xfact}|
+\YBsix{\decimal\YRef}{\decimal\Yfact}}
+\multido{\nz=0.00+0.005}{200}{\XBC{\decimal\XRef}{\nz}{\decimal\Xfact}
+\YBC{\decimal\YRef}{\nz}{\decimal\Yfact}
+\multido{\nx=\decimal\XMin+\decimal\Xsize}{\the\CellNum}
+{\tempx=\nx pt\multido{\ny=\decimal\YMin+\decimal\Ysize}{\the\CellNum}
+{\tempy=\ny pt\ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize%
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else
+ \pspolygon[fillstyle=solid,fillcolor=blue!90,linecolor=black,
+ linewidth=0.2pt]
+ (\nx,\ny)(\decimal\tempx,\ny)(\decimal\tempx,\decimal\tempy)
+ (\nx,\decimal\tempy)(\nx,\ny)\relax\fi\fi\fi\fi}
+}}
+\advance\CellNum by 1
+\multido{\nx=\decimal\XMin+\decimal\Xsize}{\the\CellNum}
+{\psline[linewidth=0.2pt](\nx,\decimal\YMax)(\nx,\decimal\YMin)}
+\multido{\ny=\decimal\YMin+\decimal\Ysize}{\the\CellNum}
+{\psline[linewidth=0.2pt](\decimal\XMin,\ny)(\decimal\XMax,\ny)}
+\parametricplot[algebraic,linecolor=white,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XBsix{\decimal\XRef}{\decimal\Xfact}|\YBsix{\decimal\YRef}{\decimal\Yfact}}}
+\end{verbatim}\hrule\bigskip
+
+In the definition of \verb!\NetDraw!, the expressions $\alpha X(t)$, $\beta Y(t)$ are declared in the \verb!algebraic! form by the macros \verb!\XBsix!,
+\verb!\YBsix! with two parameters that hold values of $x_0,\alpha$ and $y_0,\beta$, respectively. These macros are given by
+the following definitions:
+\begin{verbatim}
+\def\XBsix#1#2{%
+(1-t)^6*(#1)*(#2)+6*t*(1-t)^5*(#1-1.5)*(#2)+15*t^2*(1-t)^4*(#1+2)*(#2)+
+20*t^3*(1-t)^3*(#1+6)*(#2)+15*t^4*(1-t)^2*(#1+5)*(#2)+
+6*t^5*(1-t)*(#1+1.5)*(#2)+t^6*(#1)*(#2)}
+\def\YBsix#1#2{%
+(1-t)^6*(#1)*(#2)+6*t*(1-t)^5*(#1+2)*(#2)+15*t^2*(1-t)^4*(#1+5)*(#2)+
+20*t^3*(1-t)^3*(#1+3)*(#2)+15*t^4*(1-t)^2*(#1-1)*(#2)+
+6*t^5*(1-t)*(#1-2)*(#2)+t^6*(#1)*(#2)}
+\end{verbatim}
+\subsection{Examples}
+Firstly, let us see the effect of change for the shape of a domain when adjusting its boundary by taking different values of $\alpha$ and $\beta$. The
+calling sequence for this purpose may have the form of
+\begin{align*}
+&\textmtt{\mtt\\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]\{$0$\}\{$1$\}}\\
+&\textmtt{\mtt\{XBsix\{$x_0$\}\{$\alpha$\}|\mtt\\YBsix\{$y_0$\}\{$\beta$\}\mtt\}}
+\end{align*}
+and its result is given in Figure \ref{Fig14}.
+\begin{figure}[htbp]
+\centering\includegraphics[height=3cm]{Fig14}
+\caption{From left to right, corresponding to the couple of values:
+$\alpha=2,\,\beta=2$; $\alpha=2.5,\,\beta=2$; $\alpha=2,\,\beta=2.5$.}\label{Fig14}
+\end{figure}
+
+The Table \ref{bc-table2} below provides three partitions of a domain $D$ with cells that decrease in size. In each case, \verb!\NetDraw! can
+determine the cells that have points in common with the boundary curve and color them. The calling sequence here
+takes a simple form
+$$\textmtt{\mtt\\NetDraw\{$c$\}\{$x_0$\}\{$y_0$\}\{$\alpha$\}\{$\beta$\}}$$
+The numerical argument $c$ is assigned to the local variable \verb!\CellNum!. The number of approximate points $(X_i,Y_i)$ for the boundary curve
+is chosen to be $200$, by default, corresponding to the increment $\Delta\mtt{z}=0.005$. The number $N$ can be made larger and the filter procedure
+for determining required cells may be more exact. In Table \ref{bc-table2}, the B\'{e}zier curves are depicted with the choice
+$x_0=y_0=\alpha=\beta=2$.
+\begin{table}[htbp]
+\centering\begin{tabular}{cc}
+\includegraphics[width=6cm]{b6of1}&\includegraphics[width=6cm]{b6of2}\\
+\includegraphics[width=6cm]{b6of3}&\includegraphics[width=6cm]{b6of4}
+\end{tabular}
+\caption{The partitions of $D$ with $c=18$, $c=36$ and $c=63$.}\label{bc-table2}
+\end{table}
+
+\acknw
+I am very grateful to
+\begin{itemize}
+\item Timothy Van Zandt, Herbert Vo\ss, Dominique Rodriguez and Michael Sharpe for helping me with
+their great works on \texttt{PSTricks}.
+\item H\`an Th\hantt\rlap\accentcircflx\ Th\`anh for helping me with his pdf\hskip.03em\LaTeX\ program.
+\item Robert Fuster for his very useful package \texttt{calculator}.
+\end{itemize}
+\begin{thebibliography}{10}
+\bibitem{one} Dominique Rodriguez, Michael Sharpe \&\ Herbert Vo\ss. \textsl{\texttt{pstricks-add}: Additional Macros for PSTricks\/}.
+Version 3.60,
+\url{http://ctan.org/tex-archive/graphics/pstricks/contrib}, 2013
+\bibitem{two} Timothy Van Zandt, Michael Sharpe \&\ Herbert Vo\ss. \textsl{\texttt{pst-node}: Nodes and node connections}.
+Version 1.29,
+\url{http://ctan.org/tex-archive/graphics/pstricks/contrib}, 2013
+\bibitem{three} Helmut Kopka \&\ Patrick W. Daly. \textsl{Guide to \LaTeX \/}.
+Addison-Wesley, Fourth Edition, 2004, ISBN 0321173856
+\bibitem{four} Timothy Van Zandt. \textsl{User's Guide\/}. Version 1.5,\\
+\url{http://ctan.org/tex-archive/graphics/pstricks/base}, 2007
+\bibitem{five}Eitan M. Gurari. \textsl{Writing With \TeX \/}, McGraw-Hill, Inc., 1994, ISBN 0-07-025207-6
+\bibitem{six} Robert Fuster. \textsl{\texttt{calculator-calculus}: Scientific Calculations With \LaTeX \/}. Version 1.0a,
+\url{http://ctan.org/tex-archive/macros/latex/contrib/calculator}, 2012
+\end{thebibliography}
+
+\end{document}
+\begin{thebibliography}{10}
+\bibitem{one} Dominique Rodriguez, Michael Sharpe \&\ Herbert Vo\ss. \textsl{\texttt{pstricks-add}: Additional Macros for PSTricks\/}.
+Version 3.60,
+\url{http://ctan.org/tex-archive/graphics/pstricks/contrib}, 2013
+\bibitem{two} Timothy Van Zandt, Michael Sharpe \&\ Herbert Vo\ss. \textsl{\texttt{pst-node}: Nodes and node connections}.
+Version 1.29,
+\url{http://ctan.org/tex-archive/graphics/pstricks/contrib}, 2013
+\bibitem{three} Helmut Kopka \&\ Patrick W. Daly. \textsl{Guide to \LaTeX \/}.
+Addison-Wesley, Fourth Edition, 2004, ISBN 0321173856
+\bibitem{four} Timothy Van Zandt. \textsl{User's Guide\/}. Version 1.5,\\
+\url{http://ctan.org/tex-archive/graphics/pstricks/base}, 2007
+\bibitem{five}Eitan M. Gurari. \textsl{Writing With \TeX \/}, McGraw-Hill, Inc., 1994, ISBN 0-07-025207-6
+\bibitem{six} Robert Fuster. \textsl{\texttt{calculator-calculus}: Scientific Calculations With \LaTeX \/}. Version 1.0a,
+\url{http://ctan.org/tex-archive/macros/latex/contrib/calculator}, 2012
+\end{thebibliography}
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@@ -0,0 +1,551 @@
+\documentclass[11pt,a4paper,oneside]{article}
+\usepackage{multirow}
+\usepackage{longtable}
+\usepackage{amsthm}
+\usepackage{amsmath}
+\usepackage{url}
+\usepackage{cmtt}
+\usepackage[dvips]{geometry}
+\usepackage{pstricks}
+\usepackage{graphicx}
+\usepackage{graphics}
+\usepackage{pst-plot}
+\usepackage{pst-node}
+\usepackage{multido}
+\usepackage{pst-xkey}
+\usepackage{pst-func}
+\usepackage{pstricks-add}
+\usepackage[dvips,colorlinks,linktocpage]{hyperref}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\hantt{\^e}\def\accentcircflx{\hskip-.3em\raisebox{0.32ex}{\'{}}}
+\DeclareRobustCommand{\cs}[1]{\textmtt{\char`\\#1}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcount\Fa\newcount\Fct\newcount\tempA
+\def\Factor{\ifnum\Fa=1\relax\else\advance\Fa by -1\multiply\Fct by \Fa\Factor\fi}
+\def\FACTORIAL#1{\Fa=#1 \ifnum\Fa=0 \Fct=1\relax\else\Fct=\Fa \Factor\fi\global\tempA=\Fct}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcount\BINOM
+\newcount\temp
+\newcount\tmp
+\def\BINOMIAL#1#2{%
+\temp=#1\advance\temp by -#2
+\FACTORIAL{#1}
+\tmp=\tempA
+\FACTORIAL{\temp}
+\temp=\tempA
+\divide\tmp by \temp
+\FACTORIAL{#2}
+\temp=\tempA
+\divide\tmp by \temp\global\BINOM=\tmp}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\xch{\catcode`\p=12 \catcode`\t=12}\def\ych{\catcode`\p=11 \catcode`\t=11}
+\xch \def\dec#1pt{#1}\ych \def\decimal#1{\expandafter\dec \the#1}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newdimen\Xa\newdimen\Yb\newcount\kc
+\newdimen\BSTemp
+\def\xmult#1{\ifnum\kc<#1\advance\kc by 1\Yb=\decimal\Xa\Yb\xmult{#1}\else\relax\fi}
+\def\BERNSTEIN#1#2#3{\Xa=#3pt\kc=0\Yb=1pt\xmult{#1}\kc=0\Xa=-\Xa\advance\Xa by 1pt\xmult{#2}
+\BINOMIAL{5}{#1}\global\BSTemp=\BINOM\Yb}
+
+\newdimen\Xrf
+\newdimen\Yrf
+\newdimen\XoneBST\newdimen\YoneBST
+\newdimen\XtwoBST\newdimen\YtwoBST
+\newdimen\XBST\newdimen\YBST
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XoneBC#1{%
+\BERNSTEIN{2}{3}{#1}
+\Xrf=1.5pt
+\XoneBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{3}{2}{#1}
+\Xrf=3pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{4}{1}{#1}
+\Xrf=5pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{5}{0}{#1}
+\Xrf=5pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\global\XBST=\XoneBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XtwoBC#1{%
+\BERNSTEIN{0}{5}{#1}
+\Xrf=5pt
+\XtwoBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{1}{4}{#1}
+\Xrf=5pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{2}{3}{#1}
+\Xrf=3.5pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{3}{2}{#1}
+\Xrf=2pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\global\XBST=\XtwoBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\YoneBC#1#2#3{%
+\BERNSTEIN{1}{4}{#1}
+\Yrf=1.5pt
+\YoneBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{2}{3}{#1}
+\Yrf=1pt
+\Yrf=#2\Yrf
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{2}{#1}
+\Yrf=2pt
+\Yrf=#3\Yrf
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{1}{#1}
+\Yrf=1.5pt
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\global\YBST=\YoneBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\YtwoBC#1#2#3{%
+\BERNSTEIN{1}{4}{#1}
+\Yrf=-1.5pt
+\YtwoBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{2}{3}{#1}
+\Yrf=-1pt
+\Yrf=#2\Yrf
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{2}{#1}
+\Yrf=-2pt
+\Yrf=#3\Yrf
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{1}{#1}
+\Yrf=-1.5pt
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\global\YBST=\YtwoBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XoneFive{15*t^2*(1-t)^3+30*t^3*(1-t)^2+25*t^4*(1-t)+5*t^5}
+\def\YoneFive#1#2{7.5*t*(1-t)^4+(#1)*10*t^2*(1-t)^3+(#2)*20*t^3*(1-t)^2+7.5*t^4*(1-t)}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XtwoFive{5*(1-t)^5+25*t*(1-t)^4+35*t^2*(1-t)^3+20*t^3*(1-t)^2}
+\def\YtwoFive#1#2{(-7.5)*t*(1-t)^4+(#1)*(-10)*t^2*(1-t)^3+(#2)*(-20)*t^3*(1-t)^2+(-7.5)*t^4*(1-t)}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\NetDrawOne#1#2#3{%
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\Xsize=7pt \divide\Xsize by #1
+\Ysize=6pt \divide\Ysize by #1
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!85,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XoneFive|\YoneFive{#2}{#3}}
+\multido{\nz=0.00+0.005}{200}{\XoneBC{\nz}\YoneBC{\nz}{#2}{#3}
+\multido{\nx=-1.00+\decimal\Xsize}{#1}
+{\tempx=\nx pt\multido{\ny=-3.00+\decimal\Ysize}{#1}
+{\tempy=\ny pt\ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else\pspolygon[fillstyle=solid,fillcolor=blue!70,linecolor=black,linewidth=0.2pt]
+ (\nx,\ny)(\decimal\tempx,\ny)(\decimal\tempx,\decimal\tempy)(\nx,\decimal\tempy)(\nx,\ny)\fi\fi\fi\fi}
+}}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\NetDrawTwo#1#2#3{%
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\Xsize=7pt \divide\Xsize by #1
+\Ysize=6pt \divide\Ysize by #1
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!85,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XtwoFive|\YtwoFive{#2}{#3}}
+\multido{\nz=0.00+0.005}{200}{\XtwoBC{\nz}\YtwoBC{\nz}{#2}{#3}
+\multido{\nx=-1.00+\decimal\Xsize}{#1}
+{\tempx=\nx pt\multido{\ny=-3.00+\decimal\Ysize}{#1}
+{\tempy=\ny pt\ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else\pspolygon[fillstyle=solid,fillcolor=blue!70,linecolor=black,linewidth=0.2pt]
+ (\nx,\ny)(\decimal\tempx,\ny)(\decimal\tempx,\decimal\tempy)(\nx,\decimal\tempy)(\nx,\ny)\fi\fi\fi\fi}
+}}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagestyle{headings}
+\topmargin=-0.6cm
+\textwidth=16.7cm
+\textheight=23cm
+\headheight=2.5ex
+\headsep=0.6cm
+\oddsidemargin=.cm
+\evensidemargin=-.4cm
+\parskip=0.7ex plus0.5ex minus 0.5ex
+\baselineskip=17pt plus2pt minus2pt
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\catcode`\@=11
+\gdef\@seccntformat#1{\csname the#1\endcsname.\hskip.6em}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\renewcommand\sectionmark[1]{\markright{\thesection. #1}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\title{Drawing partitions of a simply connected plane domain}
+\author{Le Phuong Quan\\
+\small{(Cantho University)}\\
+\small{\texttt{lpquan@ctu.edu.vn}}}
+\begin{document}
+\maketitle
+
+This drawing procedure takes shape from the macros \verb+\psline+, \verb+\pspolygon+, \verb+\multido+
+and \verb+\parametricplot+ in PSTricks\footnote{\footnotesize PSTricks is the original work of Timothy Van Zandt (email address: \texttt{tvz@econ.insead.fr}).
+It is currently edited by Herbert Vo\ss\ (\texttt{hvoss@tug.org}).}. The \TeX\ arithmetic gives the pointwise parametrization of curves.
+\section{How to make a boundary using B\'{e}zier curves}
+We can make the closed boundary of a plane domain by joining B\'{e}zier curves. This can produce various boundaries. We consider here
+two B\'{e}zier curves of degree $5$ whose vector functions are
+$$\mathbf{r}_a(t)=\sum_{i=0}^5\binom{5}{i}t^i(1-t)^{5-i}\mathbf{a}_i,\quad \mathbf{r}_b(t)=\sum_{i=0}^5\binom{5}{i}t^i(1-t)^{5-i}\mathbf{b}_i,$$
+where $\mathbf{a}_i$ and $\mathbf{b}_i$ are the position vectors of control points $M_i$, $N_i$ of the two curves, respectively, $i=0,\ldots,5$.
+Here we choose:
+$M_0=(0,0)$, $M_1=(0,1.5)$, $M_2=(1.5,1)$, $M_3=(3,2)$, $M_4=(5,1.5)$, $M_5=(5,0)$, and
+$N_0=(5,0)$, $N_1=(5,-1.5)$, $N_2=(3.5,-1)$, $N_3=(2,-2)$, $N_4=(0,-1.5)$, $N_5=(0,0)$. The two curves and
+their control points are shown in Figure \ref{BZ-1} and the picture in it gives us an obvious explanation of how to combine two B\'{e}zier curves to make a closed and smooth boundary.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(-1,-2)(6,2)
+\rput[rt](0,0){$N_5=M_0\,$}\psdot(0,0)\psdot(5,0)
+\rput[rt](0,-1.5){$N_4$}\rput[rt](2,-2){$N_3$}\rput[rt](3.5,-1){$N_2$}\rput[rt](5,-1.5){$N_1$}\rput[lt](5,0){$\,M_5=N_0$}
+\psdots(5,0)(5,-1.5)(3.5,-1)(2,-2)(0,-1.5)(0,0)
+\psdots(0,1.5)(1.5,1)(3,2)(5,1.5)
+\rput[rt](0,1.5){$M_1$}\rput[rt](1.5,1){$M_2$}\rput[rt](3,2){$M_3$}\rput[rt](5,1.5){$M_4$}
+\psline[linestyle=dotted](0,1.5)(0,-1.5)\psline[linestyle=dotted](5,1.5)(5,-1.5)
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XoneFive|\YoneFive{1}{1}}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XtwoFive|\YtwoFive{1}{1}}
+\end{pspicture}
+\caption{A B\'{e}zier-spline boundary.}\label{BZ-1}
+\end{figure}
+To change the shape of the boundary, we take one couple of multipliers for the second coordinates of $M_2$, $M_3$ and another one for those of $N_2$, $N_3$. To
+draw the curves $\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$ we need their parametrization $(X_a(t),Y_a(t))$ and $(X_b(t),Y_b(t))$, $t\in[0,1]$. From
+their control points and the given couple of multipliers $\alpha_M,\beta_M$, we derive
+\begin{align*}
+X_a(t)&=15t^2(1-t)^3+30t^3(1-t)^2+25t^4(1-t)+5t^5,\\
+Y_a(t)&=7.5t(1-t)^4+10\alpha_M t^2(1-t)^3+20\beta_M t^3(1-t)^2+7.5t^4(1-t).
+\end{align*}
+Similarly, we have
+\begin{align*}
+X_b(t)&=5(1-t)^5+25t(1-t)^4+35t^2(1-t)^3+20t^3(1-t)^2,\\
+Y_b(t)&=-7.5t(1-t)^4-10\alpha_N t^2(1-t)^3-20\beta_N t^3(1-t)^2-7.5t^4(1-t),
+\end{align*}
+where $\alpha_N$, $\beta_N$ are multipliers. Then, these curves will be depicted by the macro \verb+\parametricplot+
+with the corresponding declarations in the \texttt{algebraic} form:
+\begin{verbatim}
+\def\XoneFive{15*t^2*(1-t)^3+30*t^3*(1-t)^2+25*t^4*(1-t)+5*t^5}
+\def\YoneFive#1#2%
+{7.5*t*(1-t)^4+(#1)*10*t^2*(1-t)^3+(#2)*20*t^3*(1-t)^2+7.5*t^4*(1-t)}
+\def\XtwoFive{5*(1-t)^5+25*t*(1-t)^4+35*t^2*(1-t)^3+20*t^3*(1-t)^2}
+\def\YtwoFive#1#2%
+{(-7.5)*t*(1-t)^4+(#1)*(-10)*t^2*(1-t)^3+(#2)*(-20)*t^3*(1-t)^2+(-7.5)*t^4*(1-t)}
+\end{verbatim}
+where \verb+#1+, \verb+#2+ stand for $\alpha_M$ and $\beta_M$ in the definition of \verb+\YoneFive+ and
+for $\alpha_N$ and $\beta_N$ in that of \verb+\YtwoFive+, respectively.
+In Figure \ref{BZ-2}, the boundaries are drawn by using together the commands
+\begin{verbatim}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XoneFive|\YoneFive{alphaM}{betaM}}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XtwoFive|\YtwoFive{alphaN}{betaN}}
+\end{verbatim}
+where, \verb+alphaM+, \verb+betaM+, \verb+alphaN+ and \verb+betaN+ are chosen values of $\alpha_M$, $\beta_M$,
+$\alpha_N$ and $\beta_N$, respectively.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(0,-1.5)(4.5,1.5)
+\psset{unit=24pt}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XoneFive|\YoneFive{-0.5}{2.1}}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XtwoFive|\YtwoFive{2.4}{-0.4}}
+\end{pspicture}
+\begin{pspicture}(0,-1.5)(4.5,1.5)
+\psset{unit=24pt}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XoneFive|\YoneFive{1.1}{1.4}}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XtwoFive|\YtwoFive{1.2}{1.5}}
+\end{pspicture}
+\begin{pspicture}(0,-1.5)(4.5,1.5)
+\psset{unit=24pt}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XoneFive|\YoneFive{1.7}{0.2}}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XtwoFive|\YtwoFive{0.1}{1.8}}
+\end{pspicture}
+\caption{From left to right, corresponding to the couple of values: $\alpha_M=-0.5$, $\beta_M=2.1$, $\alpha_N=2.4$, $\beta_N=-0.4$;
+$\alpha_M=1.1$, $\beta_M=1.4$, $\alpha_N=1.2$, $\beta_N=1.5$; $\alpha_M=1.7$, $\beta_M=0.2$, $\alpha_N=0.1$, $\beta_N=1.8$}\label{BZ-2}
+\end{figure}
+\section{How to draw a partition of a plane domain}
+To draw a partition of a plane domain whose boundary is made by the way that has just been described, we need the two
+procedures \verb+\NetDrawOne+ and \verb+\NetDrawTwo+, corresponding to $\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$. Their calling sequences take three arguments in order: one for $c$ (the number of cells) and
+the others for $\alpha_M$ and $\beta_M$ or $\alpha_N$ and $\beta_N$.
+Both of \verb+\NetDrawOne+ and \verb+\NetDrawTwo+ are used here to find cells in a given grid that have points in common with
+$\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$, and to color those cells. To obtain the definition of these procedures, we first state the
+problem that we are considering here.
+
+A grid of rectangular cells will be put on a rectangle $R$ containing a domain $D$ whose boundary consist of $\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$, including
+the given values of $c$, $\alpha_M$, $\beta_M$, $\alpha_N$ and $\beta_N$. Then, the steps for drawing a partition of $D$ can be listed as follows:
+\begin{itemize}
+\item Coloring cells that have points in common with the boundary of $D$.
+This is the result of calling \textmtt{\mtt\\NetDrawOne\{$c$\}\{$\alpha_M$\}\{$\beta_M$\}} and \textmtt{\mtt\\NetDrawTwo\{$c$\}\{$\alpha_N$\}\{$\beta_N$\}} together.
+\item Drawing the grid on $R$, which has been chosen as $R=\{(x,y)\colon -1\le x\le 6,\,-3\le y\le 3\}$.
+\item Drawing the two curves $\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$.
+\end{itemize}
+
+In practice, a partition of $D$ can be given by a calling sequence that has the following structure inside the \verb+\begin{pspicture}+ \ldots \verb+\end{pspicture}+
+environment:
+\begin{center}\begin{tabular}{l|l}\hline
+\textbf{Commands}&\textbf{Result}\\ \hline
+\textmtt{\mtt\\NetDrawOne\{$c$\}\{$\alpha_M$\}\{$\beta_M$\}}\textmtt{\mtt\\NetDrawTwo\{$c$\}\{$\alpha_N$\}\{$\beta_N$\}}&Coloring cells\\ \hline
+\textmtt{\mtt\\multido\{\mtt\\nx=-1.00+\mtt\\decimal\mtt\\Xsize\}\{$c+1$\}}\\
+\textmtt{\mtt\\psline[linewidth=0.2pt](\mtt\\nx,-3)(\mtt\\nx,3)}\\
+\textmtt{\mtt\\multido\{\mtt\\ny=-3.00+\mtt\\decimal\mtt\\Ysize\}\{$c+1$\}}\\
+\textmtt{\mtt\\psline[linewidth=0.2pt](-1,\mtt\\ny)(6,\mtt\\ny)}&Drawing the grid on $R$ \\ \hline
+\textmtt{\mtt\\parametricplot[algebraic,plotpoints=200,linecolor=white,}\\
+\textmtt{linewidth=0.5pt]\{0\}\{1\}\{\mtt\\XoneBFive|\mtt\\YoneBFive\{$\alpha_M$\}\{$\beta_M$\}\}}\\
+\textmtt{\mtt\\parametricplot[algebraic,plotpoints=200,linecolor=white,}\\
+\textmtt{linewidth=0.5pt]\{0\}\{1\}\{\mtt\\XtwoFive|\mtt\\YtwoFive\{$\alpha_N$\}\{$\beta_N$\}\}}&Drawing $\mathbf{r}_a(t)$, $\mathbf{r}_b(t)$\\ \hline
+\end{tabular}
+\end{center}
+
+In the following, beside the definitions of \verb+\XoneFive+, \verb+\YoneFive+, \verb+\XtwoFive+ and \verb+\YtwoFive+,
+we list all the remaining macros by their control sequences only and the results derived from running them. They form the whole drawing package, and of course they are also put in the preamble or in
+a single \TeX\ file to be loaded when running the package.
+\begin{itemize}
+\item \verb+\def\xch+: Setting \verb+\catcode'\p=12+, \verb+\catcode'\t=12+.
+\item \verb+\def\ych+: Setting \verb+\catcode'\p=11+, \verb+\catcode'\t=11+.
+\item \verb+\def\decimal#1+: Getting the numeric value of \verb+#1+ without unit.
+\item \verb+\def\FACTORIAL#1+: The factorial function. Ex: $\textmtt{\mtt\\FACTORIAL\{3\}}=6$.
+\item \verb+\def\BINOMIAL#1#2+: Binomial coefficients. Ex: $\textmtt{\mtt\\BINOMIAL\{5\}\{2\}}=10$.
+\item \verb+\def\BERNSTEIN#1#2#3+: Bernstein's functions. Ex: $\textmtt{\mtt\\BERNSTEIN\{3\}\{2\}\{t\}}=\displaystyle\binom{5}{3}t^3(1-t)^2$.
+\item \verb+\def\XoneBC#1+, \verb+\def\XtwoBC#1+: The values of $X_a(t)$, $X_b(t)$. Ex: $\textmtt{\mtt\\XoneBC\{0.5\}}=X_a(0.5)$.
+\item \verb+\def\YoneBC#1#2#3+, \verb+\def\YtwoBC#1#2#3+:
+The value of $Y_a(t)$ with given values of $\alpha_M$, $\beta_M$, and the value of $Y_b(t)$ with given values of $\alpha_N$, $\beta_N$.
+Ex: $\textmtt{\mtt\\YoneBC\{0.5\}\{1.8\}\{1.2\}}=Y_a(0.5)$, with $\alpha_M=1.8$, $\beta_M=1.2$.
+\end{itemize}
+
+We recall here the main idea for this drawing procedure. We have already the expressions of $\mathbf{r}_a(t)$ and $\mathbf{r}_b(t)$ to draw
+these B\'{ezier} curves by the macro \verb+\parametricplot+. But, we need to have in hand their points' coordinates to determine
+cells of a grid containing points in common with these curves. Fortunately, we may use the \TeX\ arithmetic
+to design expressions of $X_a(t)$, $Y_a(t)$, $X_b(t)$ and $Y_b(t)$, hence we can evaluate their values at each given $t\in[0,1]$.
+For instance, the macro \verb+\def\XoneBC#1+ is destined for evaluating the value of $X_a(t)$, and since it is a linear combination of Bernstein's functions,
+we need binomial coefficients. We do not take directly numeric values of those coefficients, and we have had the macro \verb+\def\BINOMIAL#1#2+ do that instead.
+It might be possible to use this macro in other problems later.
+In Appendix \ref{appendixA}, we list the replacement texts of the above macros and all the local and global variables they need.
+
+From the listed macros, \verb+\NetDrawOne+ may now have its definition as
+\begin{verbatim}
+==================================================================================
+\def\NetDrawOne#1#2#3{%
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\Xsize=7pt \divide\Xsize by #1
+\Ysize=6pt \divide\Ysize by #1
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!80,plotpoints=200,
+linewidth=0.5pt]{0}{1}{\XoneFive|\YoneFive{#2}{#3}}
+\multido{\nz=0.00+0.005}{200}{\XoneBC{\nz}\YoneBC{\nz}{#2}{#3}
+\multido{\nx=-1.00+\decimal\Xsize}{#1}
+{\tempx=\nx pt\multido{\ny=-3.00+\decimal\Ysize}{#1}
+{\tempy=\ny pt
+ \ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else\pspolygon[fillstyle=solid,fillcolor=blue!70,
+linecolor=black,linewidth=0.2pt](\nx,\ny)(\decimal\tempx,\ny)
+(\decimal\tempx,\decimal\tempy)(\nx,\decimal\tempy)(\nx,\ny)\relax\fi\fi\fi\fi}}}}
+==================================================================================
+\end{verbatim}
+To obtain the definition of \verb+\NetDrawTwo+, we just replace by \verb+\XtwoFive+,
+\verb+\Ytwofive+, \verb+\XtwoBC+ and \verb+\YtwoBC+ for \verb+\XoneFive+,
+\verb+\YoneFive+, \verb+\XoneBC+ and \verb+\YoneBC+ in that of \verb+\NetDrawaOne+, respectively.
+
+Because of its inevitable shortcoming, \TeX\ often gives approximate results of calculations on dimensions.
+In the following table, let us see a slight difference between results obtained from the same expression (by declaration of
+operations) in Maple and in the \TeX\ arithmetic:
+\begin{table}[htbp]
+\centering\begin{tabular}{c||c|c|c|c|c}
+$t$&$0.12$&$0.33$&$0.54$&$0.74$&$0.97$\\ \hline
+\textmtt{\mtt\\XoneBC\{$t$\}}&$\XoneBC{0.12}\decimal\XBST$&$\XoneBC{0.33}\decimal\XBST$&$\XoneBC{0.54}\decimal\XBST$&$\XoneBC{0.74}\decimal\XBST$&$\XoneBC{0.97}\decimal\XBST$\\ \hline
+Maple&$0.19203$&$1.1935$&$2.6328$&$4.02479$&$4.98266$
+\end{tabular}
+\end{table}
+
+Actually, calculations in determining if a point of the two curves belongs a cell almost give the desired result.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(0,0)(4,4)
+\pspolygon[linewidth=0.5pt,fillstyle=solid,fillcolor=gray!30](1,1)(4,1)(4,3)(1,3)(1,1)
+\rput(0.8,0.8){$C$}
+\psline[linewidth=0.5pt,linestyle=dashed](1,0)(1,1)
+\psline[linewidth=0.5pt,linestyle=dashed](1,3)(1,4)
+\psline[linewidth=0.5pt,linestyle=dashed](4,0)(4,1)
+\psline[linewidth=0.5pt,linestyle=dashed](4,3)(4,4)
+\psline[linewidth=0.5pt,linestyle=dashed](0,1)(1,1)
+\psline[linewidth=0.5pt,linestyle=dashed](4,1)(5,1)
+\psline[linewidth=0.5pt,linestyle=dashed](0,3)(1,3)
+\psline[linewidth=0.5pt,linestyle=dashed](4,3)(5,3)
+\rput[rt](1,0){$d_1$}\rput[lt](4,0){$d_2$}
+\rput[lt](5,1){$d_3$}\rput[lb](5,3){$d_4$}
+\pcline[offset=3pt,linewidth=0.4pt]{<->}(1,0.5)(4,0.5)
+\ncput*{\small\textmtt{xsize}}
+\pcline[offset=3pt,linewidth=0.4pt]{<->}(4.7,1)(4.7,3)
+\ncput*{\small\textmtt{ysize}}
+\end{pspicture}
+\caption{A typical cell.}\label{BZ-3}
+\end{figure}
+
+Before taking some examples, we give an explanation about what the main algorithm in the procedure \verb+\NetDrawOne+ (or \verb+\NetDrawTwo+) is. Let us take an approximate sequence of points
+for the curve $\mathbf{r}_a(t)$, say $P_i(\textmtt{\mtt\\XoneBC\{$t_i$\}},\textmtt{\mtt\\YoneBC\{$t_i$\}\{$\alpha_M$\}\{$\beta_M$\}})$, $i=1,\ldots,200$. Then, each $P_i$ is examined whether to be in a cell that has the reference point $C=(x,y)$ by the instruction that: do nothing if
+$P_i$ is
+
+\begin{figure}[htbp]
+\centering\includegraphics[width=6cm]{BZ6}\hskip1cm\includegraphics[width=6cm]{BZ7}
+\caption{From left to right: $c=25$ and $c=45$.}\label{BZ-4}
+\end{figure}
+
+\begin{itemize}
+\item below $d_3$, or
+\item above $d_4$, or
+\item on the left side of $d_1$, or
+\item on the right side of $d_2$;
+\end{itemize}
+otherwise, color the cell. This algorithm can be expressed in the form of
+\begin{center}
+\begin{tabular}{llll}
+\multicolumn{4}{l}{\textmtt{\mtt\\ifdim\mtt\\YBST<$y$ \mtt\\relax\mtt\\else\mtt\\advance $y$ by ysize}}\\
+&\multicolumn{3}{l}{\textmtt{\mtt\\ifdim\mtt\\YBST>$y$ \mtt\\relax\mtt\\else}}\\
+&&\multicolumn{2}{l}{\textmtt{\mtt\\ifdim\mtt\\XBST<$x$ \mtt\\relax\mtt\\else\mtt\\advance $x$ by xsize}}\\
+&&&\textmtt{\mtt\\ifdim\mtt\\XBST>$x$ \mtt\\relax\mtt\\else\mtt\\pspolygon[fillstyle=solid,$\ldots$]}
+\end{tabular}
+\end{center}
+where \verb+\XBST+ and \verb+\YBST+ hold the values of \textmtt{\mtt\\XoneBC\{$t_i$\}} and \textmtt{\mtt\\YoneBC\{$t_i$\}\{$\alpha_M$\}\{$\beta_M$\}}, respectively.
+This structure is almost the same as that in the procedure \verb+\NetDrawOne+ (or \verb+\NetDrawTwo+), but the variables here are declared according to the gloss in
+Figure \ref{BZ-3}.
+
+Finally, let us take two examples where we just give values of $c$ for the caption of figures. In Figure \ref{BZ-4}, we take the
+same couples $\alpha_M=1.7$, $\beta_M=0.2$, $\alpha_N=0.1$ and $\beta_N=1.8$ for its two pictures. In Figure \ref{BZ-5}, we take the
+same couples $\alpha_M=-0.5$, $\beta_M=2.1$, $\alpha_N=2.4$ and $\beta_N=-0.4$ for its three pictures.
+\begin{figure}[htbp]
+\centering\includegraphics[width=5cm]{BZ8}\hskip0.5cm\includegraphics[width=5cm]{BZ9}\hskip0.5cm\includegraphics[width=5cm]{BZ10}
+\caption{From left to right: $c=25$, $c=45$ and $c=63$.}\label{BZ-5}
+\end{figure}
+\appendix
+\section{Appendix: detailed definitions}\label{appendixA}
+The following is the list of all the detailed definitions needed for the procedure, except those of \verb+\XoneFive+, \verb+\YoneFive+, \verb+\XtwoFive+, \verb+\YtwoFive+,
+\verb+\NetDrawOne+ and \verb+\NetDrawTwo+.
+
+\begin{verbatim}
+----------------------------------------------------------------------------------
+\def\xch{\catcode`\p=12 \catcode`\t=12}
+\def\ych{\catcode`\p=11 \catcode`\t=11}\xch
+\def\dec#1pt{#1}\ych
+\def\decimal#1{\expandafter\dec \the#1}
+\newcount\Fa\newcount\Fct\newcount\tempA
+
+\def\Factor{\ifnum\Fa=1\relax\else\advance\Fa by -1\multiply\Fct by \Fa\Factor\fi}
+\def\FACTORIAL#1{\Fa=#1 \ifnum\Fa=0 \Fct=1\relax\else\Fct=\Fa
+\Factor\fi\global\tempA=\Fct}
+----------------------------------------------------------------------------------
+\newcount\BINOM
+\newcount\temp
+\newcount\tmp
+
+\def\BINOMIAL#1#2{%
+\temp=#1\advance\temp by -#2
+\FACTORIAL{#1}
+\tmp=\tempA
+\FACTORIAL{\temp}
+\temp=\tempA
+\divide\tmp by \temp
+\FACTORIAL{#2}
+\temp=\tempA
+\divide\tmp by \temp\global\BINOM=\tmp}
+----------------------------------------------------------------------------------
+\newdimen\Xa\newdimen\Yb\newcount\kc
+\newdimen\BSTemp
+
+\def\xmult#1{\ifnum\kc<#1\advance\kc by 1\Yb=\decimal\Xa\Yb\xmult{#1}
+\else\relax\fi}
+\def\BERNSTEIN#1#2#3{\Xa=#3pt\kc=0\Yb=1pt\xmult{#1}\kc=0\Xa=-\Xa\advance\Xa
+by 1pt\xmult{#2}\BINOMIAL{5}{#1}\global\BSTemp=\BINOM\Yb}
+----------------------------------------------------------------------------------
+\newdimen\Xrf
+\newdimen\Yrf
+\newdimen\XoneBST\newdimen\YoneBST
+\newdimen\XtwoBST\newdimen\YtwoBST
+\newdimen\XBST\newdimen\YBST
+
+\def\XoneBC#1{%
+\BERNSTEIN{2}{3}{#1}
+\Xrf=1.5pt
+\XoneBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{3}{2}{#1}
+\Xrf=3pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{4}{1}{#1}
+\Xrf=5pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{5}{0}{#1}
+\Xrf=5pt
+\advance\XoneBST by \decimal\BSTemp\Xrf
+\global\XBST=\XoneBST}
+----------------------------------------------------------------------------------
+\def\XtwoBC#1{%
+\BERNSTEIN{0}{5}{#1}
+\Xrf=5pt
+\XtwoBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{1}{4}{#1}
+\Xrf=5pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{2}{3}{#1}
+\Xrf=3.5pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{3}{2}{#1}
+\Xrf=2pt
+\advance\XtwoBST by \decimal\BSTemp\Xrf
+\global\XBST=\XtwoBST}
+----------------------------------------------------------------------------------
+\def\YoneBC#1#2#3{%
+\BERNSTEIN{1}{4}{#1}
+\Yrf=1.5pt
+\YoneBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{2}{3}{#1}
+\Yrf=1pt
+\Yrf=#2\Yrf
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{2}{#1}
+\Yrf=2pt
+\Yrf=#3\Yrf
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{1}{#1}
+\Yrf=1.5pt
+\advance\YoneBST by \decimal\BSTemp\Yrf
+\global\YBST=\YoneBST}
+----------------------------------------------------------------------------------
+\def\YtwoBC#1#2#3{%
+\BERNSTEIN{1}{4}{#1}
+\Yrf=-1.5pt
+\YtwoBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{2}{3}{#1}
+\Yrf=-1pt
+\Yrf=#2\Yrf
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{2}{#1}
+\Yrf=-2pt
+\Yrf=#3\Yrf
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{1}{#1}
+\Yrf=-1.5pt
+\advance\YtwoBST by \decimal\BSTemp\Yrf
+\global\YBST=\YtwoBST}
+----------------------------------------------------------------------------------
+\end{verbatim}
+
+\begin{thebibliography}{10}
+\bibitem{one} Dominique Rodriguez, Michael Sharpe \&\ Herbert Vo\ss. \textsl{\texttt{pstricks-add}: Additional Macros for PSTricks\/}.
+Version 3.60,
+\url{http://ctan.org/tex-archive/graphics/pstricks/contrib}, 2013
+\bibitem{two}Eitan M. Gurari. \textsl{Writing With \TeX \/}, McGraw-Hill, Inc., 1994, ISBN 0-07-025207-6
+\bibitem{three} Helmut Kopka \&\ Patrick W. Daly. \textsl{Guide to \LaTeX \/}.
+Addison-Wesley, Fourth Edition, 2004, ISBN 0321173856
+\bibitem{four} Timothy Van Zandt. \textsl{User's Guide\/}. Version 1.5,\\
+\url{http://ctan.org/tex-archive/graphics/pstricks/base}, 2007
+\end{thebibliography}
+\end{document}
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+imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
+exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
+fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
+delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
+B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
+p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
+rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end
+
+%%EndProcSet
+%%BeginProcSet: pstricks.pro 0 0
+% $Id: pstricks.pro 755 2013-03-09 08:48:58Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 1.15, 2012/10/18
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+% Define the follwing gs-functions if not known, eg when using distiller
+%
+systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if
+systemdict /.setblendmode known not {/.setblendmode { pop } def } if
+systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
+%
+/tx@Dict 200 dict def % the main PSTricks dictionary
+tx@Dict begin
+/ADict 25 dict def % The arrow dictionaray
+/CM { matrix currentmatrix } bind def
+/SLW /setlinewidth load def
+/CLW /currentlinewidth load def
+/CP /currentpoint load def
+/ED { exch def } bind def
+/L /lineto load def
+/T /translate load def
+/TMatrix { } def
+/RAngle { 0 } def
+/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments
+/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known
+/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter)
+/Div { dup 0 eq { pop } { div } ifelse } def % control the division
+/tan { dup cos abs 1.e-10 lt
+ { pop 1.e10 } % return 1.e10 as infinit
+ { dup sin exch cos div } ifelse % default sin/cos
+} def
+/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees
+/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root
+ pop pop 0 }{ sqrt exch atan} ifelse } def
+/NET { neg exch neg exch T } def % change coordinate system to the negative one
+/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter
+/Pyth2 { % Pythagoras, xA yA xB yB
+ 3 -1 roll % xA xB yB yA
+ sub % xA xB yB-yA
+ 3 1 roll % yB-yA xA xB
+ sub % yB-yA xA-xB
+ Pyth } def
+/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian
+/Rand { rand 4294967295 div } def % a real random number
+%----------------- hv added 20050516 ---------------
+/PiDiv2 1.57079632680 def
+/Pi 3.14159265359 def
+/TwoPi 6.28318530718 def
+/Euler 2.71828182846 def
+%/e Euler bind def
+%
+/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees
+/DegtoRad { Pi mul 180 div } bind def % viceversa
+%----------------- hv end---------------------------
+/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def
+%
+/PathLength {
+ flattenpath /z 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def }
+ { /y ED /x ED PathLength@ }
+ {}
+ { /y y2 def /x x2 def PathLength@ }
+ /pathforall load stopped { pop pop pop pop } if
+ z
+} def
+%
+/STP { .996264 dup scale } def % BP/PT scaling
+/STV { SDict begin normalscale end STP } def %
+%
+/DashLine {
+ dup 0 gt
+ { /a .5 def PathLength exch div }
+ { pop /a 1 def PathLength } ifelse
+ /b ED % pattern should fit evenly in b
+ dup /X ED % pattern array
+ 0 get /y ED % length of first black segment
+ /z 0 X {add} forall def % length of the full pattern
+ %% Computation of the scaling factor as described by van Zandt:
+ b a .5 sub 2 mul y mul sub z Div round
+ z mul a .5 sub 2 mul y mul add b exch Div
+ %%%% scaling factor on stack.
+ /z ED %% now, z is the scaling factor
+ false % for the length test below
+ X { z mul } forall X astore %% modification TN 04-08-07
+ %%% Checking whether at least one dash in X has positive length:
+ {0 gt or} forall
+ { X 1 a sub y mul }
+ { [ 1 0 ] 0 }
+ ifelse
+ setdash stroke
+} def
+%
+/DotLine {
+ /b PathLength def
+ /a ED /z ED /y CLW def
+ /z y z add def
+ a 0 gt {
+ /b b a div def
+ }{
+ a 0 eq {
+ /b b y sub def
+ }{ a -3 eq {
+ /b b y add def } if
+ } ifelse
+ } ifelse
+ [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
+ a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
+ setdash 1 setlinecap stroke
+} def
+%
+/SymbolLine { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt
+ { %XYLength SymStep div abs cvi
+ /nSym SymStep abs cvi def }
+ { /nSym XYLength SymStep div cvi def }
+ ifelse
+ 0.5 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ /deltaX XLength nSym div def
+ /deltaY YLength nSym div def
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ nSym {
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ currentpoint translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+ /YA YB def /XA XB def
+ } repeat
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ XA YA translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ pop % delete the mark symbol
+} def
+%
+/LineFill { % hv ------------ patch 7 -------------
+ gsave
+ abs /hatchWidthInc ED
+ abs /hatchSepInc ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clipType % must be defined in pstricks.tex: clip -- eoclip
+ newpath
+ 2 setlinecap
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ x2 x1 sub 1 add {
+ x1 a mul y1 moveto 0 y2 rlineto stroke
+ /x1 x1 1 add
+ hatchWidthInc 0 gt { CLW add } if
+ def
+ hatchSepInc 0 gt hatchWidthInc 0 gt or {
+ /a a hatchSepInc add def
+ CLW hatchWidthInc add SLW
+ } if
+ } repeat
+ grestore
+ pop pop } def
+%
+/DotFill {% on stack: dot radius
+ /dotRadius ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform
+ pathbbox % llx lly urx ury of smallest bounding box
+ /y2 ED /x2 ED /y1 ED /x1 ED
+ y2 y1 sub a div 2 add cvi /Ny ED
+ x2 x1 sub a div 2 add cvi /Nx ED
+ clipType % must be defined in pstricks.tex: clip -- eoclip
+ newpath
+ /yA y1 dotRadius add CLW add def
+ /xA0 x1 dotRadius add CLW add def
+ Ny {
+ /xA xA0 def
+ Nx {
+ newpath
+ xA yA dotRadius 0 360 arc
+ SolidDot { gsave fill grestore } if
+ stroke
+ xA a add /xA ED
+ } repeat
+ yA a add /yA ED
+ } repeat
+ grestore
+} def
+%
+/PenroseFill {% on stack: scaling factor
+ /Scale ED
+% 1 exch div round /penroseFactor ED
+% a 0 dtransform round exch round exch
+% 2 copy idtransform
+% exch Atan rotate
+% idtransform pop /a ED
+% .25 .25 itransform pathbbox
+% /y2 ED
+% a Div ceiling cvi /x2 ED /y1 ED
+% a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+gsave
+ 220 150 translate
+ Scale dup scale
+ systemdict /setstrokeadjust known { true setstrokeadjust } if
+ /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
+ { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
+ [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
+ i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
+ mul j l + S rmoveto}F i L j L stroke }F}F}F}F
+ grestore
+% pop pop
+} def
+%
+/PenroseFillA {% on stack: scaling factor, border color, kite color, dart color
+ /Scale ED
+ Scale dup scale
+ /border_colour ED
+ /kite_colour ED
+ /dart_colour ED
+ clip
+
+ newpath
+ gsave
+ 100 100 translate
+ 6
+ Scale 1 lt { 1 Scale dup add div mul cvi } if %%%% Number of iterations
+ 10 %%%% Long side length in millimeters
+ /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
+ /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
+ /f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio
+ /l{L f mul}bind def %%%% Short side length l = L*f
+ /Ll{L l add}bind def %%%% Ll = L + l
+ /c{36 cos L mul}bind def %%%% c = L*cos(36)
+ /s{36 sin L mul}bind def %%%% s = L*sin(36)
+ /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
+ 0 setlinewidth stroke grestore border_colour stroke } bind def
+ /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
+ Ll 0 translate 144 rotate kite grestore }
+ { kite_colour L draw_tile }ifelse
+ pop } bind def
+ /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
+ -144 rotate Ll neg 0 translate half_dart grestore }
+ { dart_colour l draw_tile }ifelse
+ pop } bind def
+ /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
+ border_width setlinewidth 1 setlinejoin 1 setlinecap
+% 450 0 translate
+ dup f exch neg exp dup scale
+ 5 {kite 72 rotate } repeat stroke
+ grestore
+} def
+%
+%
+/TruchetFill { % on stack: scaling factor
+ 10 dict begin
+ dup dup scale
+ 1 exch div round /penroseFactor ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ /ma a neg def
+ /ha a 2 div def
+ /mha ha neg def
+ /tile {
+ rand dup 2 idiv 2 mul eq { 90 rotate } if
+ mha mha moveto ha mha lineto
+ ha ha lineto mha ha lineto
+% closepath .1 setlinewidth stroke
+ contents
+ } def
+ /contents{
+ 0 ha moveto ha 0 lineto
+ 0 mha moveto mha 0 lineto
+% 1 setlinewidth stroke
+ } def
+ /dotiling {
+ f ma mul a f a mul {
+ /i exch def
+ f ma mul a f a mul {
+ /j exch def
+ gsave i j translate
+ tile stroke grestore
+ } for
+ } for
+ } def
+%
+ /f 3 def
+ 5 srand dotiling
+ end % local user dict
+} def
+%
+/BeginArrow {
+ ADict begin % hold it local, for end see EndArrow
+ /@mtrx CM def
+ gsave
+ 2 copy T
+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
+%
+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
+%
+/Arrow {
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
+%
+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
+ gsave fill grestore
+} def
+%
+/Tbar {
+ CLW mul add /z ED
+ z -2 div CLW 2 div moveto
+ z 0 rlineto stroke
+ 0 CLW moveto
+} def
+%
+/Bracket {
+ CLW mul add dup CLW sub 2 div
+ /x ED mul CLW add /y ED /z CLW 2 div def
+ x neg y moveto
+ x neg CLW 2 div L x CLW 2 div L x y L stroke
+ 0 CLW moveto
+} def
+%
+/RoundBracket {
+ CLW mul add dup 2 div
+ /x ED mul /y ED /mtrx CM def
+ 0 CLW 2 div T x y mul 0 ne { x y scale } if
+ 1 1 moveto
+ .85 .5 .35 0 0 0 curveto
+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
+ /b ED % the color definition
+ 0 z DS SD
+ b { 0 z DS CLW sub SD } if
+ 0 DS z add CLW 4 div sub
+ moveto
+} def
+%
+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+ load } if ] cvx newpath 3 1 roll T exec } def
+%
+/NArray { % holds the coordinates and on top of stack the showpoints boolean
+ /showpoints ED
+ counttomark 2 div dup cvi /n ED % n 2 div on stack
+ n eq not { exch pop } if % even numbers of points? delete one
+ ] aload /Points ED
+ showpoints not { Points aload pop } if
+% { ] aload /Points ED }
+% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
+} def
+%
+/Line {
+ NArray n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
+ n { Lineto } repeat
+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
+%
+/LineToYAxis {
+ /Ox ED % Save the x origin value
+ NArray % all x-y pairs on stack
+ n { 2 copy moveto % go to current point
+ Ox exch Lineto % line to y-axis
+ pop % delete old x-value
+ } repeat
+} def
+%
+/LineToXAxis{
+ /Oy ED % Save the y origin value
+ NArray % all x-y pairs on stack
+ n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if
+ ArrowA
+ /n n 2 sub def
+ CP 2 copy moveto pop Oy Lineto
+ n { 2 copy moveto pop Oy Lineto } repeat
+ CP
+ 4 2 roll
+ ArrowB
+ 2 copy moveto pop Oy
+ L
+ pop pop } if
+} def
+%
+/Arcto {
+ /a [ 6 -2 roll ] cvx def
+ a r
+ /arcto load stopped { 5 } { 4 } ifelse { pop } repeat
+ a
+} def
+%
+/CheckClosed {
+ dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
+ and { pop pop /n n 1 sub def } if
+} def
+%
+/Polygon {
+ NArray n 2 eq { 0 0 /n 3 def } if
+ n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ n 2 mul -2 roll
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ n { Lineto } repeat
+ x1 y1 x0 y0 6 4 roll Lineto
+ Lineto pop pop closepath } ifelse
+} def
+%
+/SymbolPolygon { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 add /m ED
+ 2 copy m 2 roll % copy last two
+ m 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+ /nSym XYLength SymStep Div cvi def
+ /Shift Symbol stringwidth pop 2 Div def
+ /deltaX XLength nSym Div def
+ /deltaY YLength nSym Div def
+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
+%
+/Simpson { % on stack must be a b M --- simple version ---
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+%
+/LogGamma { 5 dict begin % z on stack
+ /z ED
+ /sum 0 def
+ /k 1 def
+ {
+ z k div dup 1 add ln sub dup
+ abs eps8 lt { pop exit } if
+ sum add /sum exch def
+ /k k 1 add def
+ } loop
+ sum z ln sub CEuler z mul sub
+ end
+} def
+%
+/ChebyshevT { 5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 2 k mul MoverN mul
+ add
+ } for
+ end
+} def
+%
+/ChebyshevU {5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 1 add 2 k mul 1 add MoverN mul
+ add
+ } for
+ end
+} def
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+% $Id: pstricks.pro 755 2013-03-09 08:48:58Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 1.15, 2012/10/18
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+% Define the follwing gs-functions if not known, eg when using distiller
+%
+systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if
+systemdict /.setblendmode known not {/.setblendmode { pop } def } if
+systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
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+/CLW /currentlinewidth load def
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+ 3 1 roll % yB-yA xA xB
+ sub % yB-yA xA-xB
+ Pyth } def
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+/Rand { rand 4294967295 div } def % a real random number
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+} def
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+ z mul a .5 sub 2 mul y mul add b exch Div
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+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
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+ /setstrokeadjust known { true setstrokeadjust } if
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+ /y2 ED /x2 ED /y1 ED /x1 ED
+ y2 y1 sub a div 2 add cvi /Ny ED
+ x2 x1 sub a div 2 add cvi /Nx ED
+ clipType % must be defined in pstricks.tex: clip -- eoclip
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+ /xA xA0 def
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+% a Div cvi /x1 ED /y2 y2 y1 sub def
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+ newpath
+gsave
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+ Scale dup scale
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+ /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
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+ [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
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+ grestore
+% pop pop
+} def
+%
+/PenroseFillA {% on stack: scaling factor, border color, kite color, dart color
+ /Scale ED
+ Scale dup scale
+ /border_colour ED
+ /kite_colour ED
+ /dart_colour ED
+ clip
+
+ newpath
+ gsave
+ 100 100 translate
+ 6
+ Scale 1 lt { 1 Scale dup add div mul cvi } if %%%% Number of iterations
+ 10 %%%% Long side length in millimeters
+ /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
+ /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
+ /f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio
+ /l{L f mul}bind def %%%% Short side length l = L*f
+ /Ll{L l add}bind def %%%% Ll = L + l
+ /c{36 cos L mul}bind def %%%% c = L*cos(36)
+ /s{36 sin L mul}bind def %%%% s = L*sin(36)
+ /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
+ 0 setlinewidth stroke grestore border_colour stroke } bind def
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+ Ll 0 translate 144 rotate kite grestore }
+ { kite_colour L draw_tile }ifelse
+ pop } bind def
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+ { dart_colour l draw_tile }ifelse
+ pop } bind def
+ /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
+ border_width setlinewidth 1 setlinejoin 1 setlinecap
+% 450 0 translate
+ dup f exch neg exp dup scale
+ 5 {kite 72 rotate } repeat stroke
+ grestore
+} def
+%
+%
+/TruchetFill { % on stack: scaling factor
+ 10 dict begin
+ dup dup scale
+ 1 exch div round /penroseFactor ED
+ a 0 dtransform round exch round exch
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+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
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+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
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+ /mha ha neg def
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+ mha mha moveto ha mha lineto
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+% closepath .1 setlinewidth stroke
+ contents
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+ /j exch def
+ gsave i j translate
+ tile stroke grestore
+ } for
+ } for
+ } def
+%
+ /f 3 def
+ 5 srand dotiling
+ end % local user dict
+} def
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+ ADict begin % hold it local, for end see EndArrow
+ /@mtrx CM def
+ gsave
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+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
+%
+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
+%
+/Arrow {
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+ 2 div /w ED
+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
+%
+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
+ gsave fill grestore
+} def
+%
+/Tbar {
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+ z 0 rlineto stroke
+ 0 CLW moveto
+} def
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+ x neg y moveto
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+ 0 CLW moveto
+} def
+%
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+ /x ED mul /y ED /mtrx CM def
+ 0 CLW 2 div T x y mul 0 ne { x y scale } if
+ 1 1 moveto
+ .85 .5 .35 0 0 0 curveto
+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
+ /b ED % the color definition
+ 0 z DS SD
+ b { 0 z DS CLW sub SD } if
+ 0 DS z add CLW 4 div sub
+ moveto
+} def
+%
+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+ load } if ] cvx newpath 3 1 roll T exec } def
+%
+/NArray { % holds the coordinates and on top of stack the showpoints boolean
+ /showpoints ED
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+ n eq not { exch pop } if % even numbers of points? delete one
+ ] aload /Points ED
+ showpoints not { Points aload pop } if
+% { ] aload /Points ED }
+% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
+} def
+%
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+ NArray n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
+ n { Lineto } repeat
+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
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+ NArray % all x-y pairs on stack
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+ Ox exch Lineto % line to y-axis
+ pop % delete old x-value
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+} def
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+ NArray % all x-y pairs on stack
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+ { n 1 eq { 0 0 /n 2 def } if
+ ArrowA
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+ n { 2 copy moveto pop Oy Lineto } repeat
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+% DG/SR modification end
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+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
+%
+/Simpson { % on stack must be a b M --- simple version ---
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+%
+/LogGamma { 5 dict begin % z on stack
+ /z ED
+ /sum 0 def
+ /k 1 def
+ {
+ z k div dup 1 add ln sub dup
+ abs eps8 lt { pop exit } if
+ sum add /sum exch def
+ /k k 1 add def
+ } loop
+ sum z ln sub CEuler z mul sub
+ end
+} def
+%
+/ChebyshevT { 5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 2 k mul MoverN mul
+ add
+ } for
+ end
+} def
+%
+/ChebyshevU {5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 1 add 2 k mul 1 add MoverN mul
+ add
+ } for
+ end
+} def
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+stroke grestore end
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+stroke grestore end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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diff --git a/info/pstricks_calcnotes/For_Ps_Output/BZ7.eps b/info/pstricks_calcnotes/For_Ps_Output/BZ7.eps
new file mode 100644
index 0000000000..68ca61d1e5
--- /dev/null
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+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
+%
+/LineToYAxis {
+ /Ox ED % Save the x origin value
+ NArray % all x-y pairs on stack
+ n { 2 copy moveto % go to current point
+ Ox exch Lineto % line to y-axis
+ pop % delete old x-value
+ } repeat
+} def
+%
+/LineToXAxis{
+ /Oy ED % Save the y origin value
+ NArray % all x-y pairs on stack
+ n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if
+ ArrowA
+ /n n 2 sub def
+ CP 2 copy moveto pop Oy Lineto
+ n { 2 copy moveto pop Oy Lineto } repeat
+ CP
+ 4 2 roll
+ ArrowB
+ 2 copy moveto pop Oy
+ L
+ pop pop } if
+} def
+%
+/Arcto {
+ /a [ 6 -2 roll ] cvx def
+ a r
+ /arcto load stopped { 5 } { 4 } ifelse { pop } repeat
+ a
+} def
+%
+/CheckClosed {
+ dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
+ and { pop pop /n n 1 sub def } if
+} def
+%
+/Polygon {
+ NArray n 2 eq { 0 0 /n 3 def } if
+ n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ n 2 mul -2 roll
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ n { Lineto } repeat
+ x1 y1 x0 y0 6 4 roll Lineto
+ Lineto pop pop closepath } ifelse
+} def
+%
+/SymbolPolygon { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 add /m ED
+ 2 copy m 2 roll % copy last two
+ m 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+ /nSym XYLength SymStep Div cvi def
+ /Shift Symbol stringwidth pop 2 Div def
+ /deltaX XLength nSym Div def
+ /deltaY YLength nSym Div def
+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
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+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
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+ y0 F sub /Phi exch def
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+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
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+ y0 % the returned value ist the zero point
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+ mul add exch
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+} def
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+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
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+ Horner
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+ /pstZeros [] def
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+ } repeat
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+ array astore
+ /pstZeros exch def
+ } for
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+ end
+} def
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+ end
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+%
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+ exch 0 get % b a
+ neg exch neg % -a -b
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+} def
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+} def
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+ dup mul % a b^2
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+} def
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+ cxnorm2 sqrt
+} def
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+} def
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+ 4 -1 roll exch div % b n2 a/n2
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+ neg 2 array astore
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+/cxmake2 { 2 array astore } def % dito, both given
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+ cxrmul
+} def
+%
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ -12.80054 72.0 -12.80054 -72.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 5.8656 72.0 5.8656 -72.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+{ } def /ArrowInside { } def [ 46.93066 72.0 46.93066 -72.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+stroke grestore end
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+stroke grestore end
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+stroke grestore end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+% $Id: pstricks.pro 755 2013-03-09 08:48:58Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 1.15, 2012/10/18
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+% Define the follwing gs-functions if not known, eg when using distiller
+%
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+systemdict /.setblendmode known not {/.setblendmode { pop } def } if
+systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
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+ sub % yB-yA xA-xB
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+ z mul a .5 sub 2 mul y mul add b exch Div
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+ x2 x1 sub a div 2 add cvi /Nx ED
+ clipType % must be defined in pstricks.tex: clip -- eoclip
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+ /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
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+% pop pop
+} def
+%
+/PenroseFillA {% on stack: scaling factor, border color, kite color, dart color
+ /Scale ED
+ Scale dup scale
+ /border_colour ED
+ /kite_colour ED
+ /dart_colour ED
+ clip
+
+ newpath
+ gsave
+ 100 100 translate
+ 6
+ Scale 1 lt { 1 Scale dup add div mul cvi } if %%%% Number of iterations
+ 10 %%%% Long side length in millimeters
+ /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
+ /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
+ /f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio
+ /l{L f mul}bind def %%%% Short side length l = L*f
+ /Ll{L l add}bind def %%%% Ll = L + l
+ /c{36 cos L mul}bind def %%%% c = L*cos(36)
+ /s{36 sin L mul}bind def %%%% s = L*sin(36)
+ /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
+ 0 setlinewidth stroke grestore border_colour stroke } bind def
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+ { dart_colour l draw_tile }ifelse
+ pop } bind def
+ /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
+ border_width setlinewidth 1 setlinejoin 1 setlinecap
+% 450 0 translate
+ dup f exch neg exp dup scale
+ 5 {kite 72 rotate } repeat stroke
+ grestore
+} def
+%
+%
+/TruchetFill { % on stack: scaling factor
+ 10 dict begin
+ dup dup scale
+ 1 exch div round /penroseFactor ED
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+ a Div cvi /x1 ED /y2 y2 y1 sub def
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+ tile stroke grestore
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+ } for
+ } def
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+} def
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+ /@mtrx CM def
+ gsave
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+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
+%
+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
+%
+/Arrow {
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+ 2 div /w ED
+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
+%
+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
+ gsave fill grestore
+} def
+%
+/Tbar {
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+ z 0 rlineto stroke
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+} def
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+ 0 CLW moveto
+} def
+%
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+ /x ED mul /y ED /mtrx CM def
+ 0 CLW 2 div T x y mul 0 ne { x y scale } if
+ 1 1 moveto
+ .85 .5 .35 0 0 0 curveto
+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
+ /b ED % the color definition
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+ b { 0 z DS CLW sub SD } if
+ 0 DS z add CLW 4 div sub
+ moveto
+} def
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+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+ load } if ] cvx newpath 3 1 roll T exec } def
+%
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+ n eq not { exch pop } if % even numbers of points? delete one
+ ] aload /Points ED
+ showpoints not { Points aload pop } if
+% { ] aload /Points ED }
+% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
+} def
+%
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+ n { Lineto } repeat
+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
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+ pop % delete old x-value
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+} def
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+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
+%
+/Simpson { % on stack must be a b M --- simple version ---
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+%
+/LogGamma { 5 dict begin % z on stack
+ /z ED
+ /sum 0 def
+ /k 1 def
+ {
+ z k div dup 1 add ln sub dup
+ abs eps8 lt { pop exit } if
+ sum add /sum exch def
+ /k k 1 add def
+ } loop
+ sum z ln sub CEuler z mul sub
+ end
+} def
+%
+/ChebyshevT { 5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 2 k mul MoverN mul
+ add
+ } for
+ end
+} def
+%
+/ChebyshevU {5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 1 add 2 k mul 1 add MoverN mul
+ add
+ } for
+ end
+} def
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 23.04016 72.0 23.04016 -72.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+0.2 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap
+stroke grestore end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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diff --git a/info/pstricks_calcnotes/For_Ps_Output/BZ9.eps b/info/pstricks_calcnotes/For_Ps_Output/BZ9.eps
new file mode 100644
index 0000000000..81852feb3d
--- /dev/null
+++ b/info/pstricks_calcnotes/For_Ps_Output/BZ9.eps
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+ /y0 ED /x0 ED /y1 ED /x1 ED
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ n { Lineto } repeat
+ x1 y1 x0 y0 6 4 roll Lineto
+ Lineto pop pop closepath } ifelse
+} def
+%
+/SymbolPolygon { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 add /m ED
+ 2 copy m 2 roll % copy last two
+ m 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+ /nSym XYLength SymStep Div cvi def
+ /Shift Symbol stringwidth pop 2 Div def
+ /deltaX XLength nSym Div def
+ /deltaY YLength nSym Div def
+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
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+ Horner
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+ /pstZeros [] def
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+} def
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+} def
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+} def
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+/cxmake2 { 2 array astore } def % dito, both given
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+0.2 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap
+stroke grestore end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
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+0.2 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap
+stroke grestore end
+
+@endspecial @beginspecial
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
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+0.2 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap
+stroke grestore end
+
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 144.0 1.59814 -24.0 1.59814 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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diff --git a/info/pstricks_calcnotes/For_Ps_Output/ThreeAppsPS.tex b/info/pstricks_calcnotes/For_Ps_Output/ThreeAppsPS.tex
new file mode 100644
index 0000000000..b1cfddca66
--- /dev/null
+++ b/info/pstricks_calcnotes/For_Ps_Output/ThreeAppsPS.tex
@@ -0,0 +1,1165 @@
+\documentclass[11pt,a4paper,oneside]{article}
+\usepackage{calculator}
+\usepackage{calculus}
+\usepackage{amsthm}
+\usepackage{amsmath}
+\usepackage{cmtt}
+\usepackage[dvips]{geometry}
+\usepackage{pstricks}
+\usepackage{graphicx}
+\usepackage{graphics}
+\usepackage{pst-plot}
+\usepackage{pst-node}
+\usepackage{multido}
+\usepackage{pst-xkey}
+\usepackage{pst-func}
+\usepackage{pstricks-add}
+\usepackage[dvips,colorlinks,linktocpage]{hyperref}
+\def\hantt{\^e}\def\accentcircflx{\hskip-.3em\raisebox{0.32ex}{\'{}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\RiemannSum#1#2#3#4#5#6#7#8#9{%
+\psplot[linecolor=blue]{#1}{#2}{#3}
+\pscustom[linecolor=red]{%
+\psline{-}(#1,0)(#1,0)
+\multido{\ni=#5,\ne=#6}{#4}
+{\psline(*{\ni} {#8})(*{\ne} {#9})}}
+\multido{\ne=#6,\nc=#7}{#4}
+{\psdot(*{\nc} {#3})
+\psline[linestyle=dotted,dotsep=1.5pt](\nc,0)(*{\nc} {#3})
+\psline[linecolor=red](\ne,0)(*{\ne} {#9})}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcount\Fa\newcount\Fct\newcount\tempA
+\def\Factor{\ifnum\Fa=1\relax\else\advance\Fa by -1\multiply\Fct by \Fa\Factor\fi}
+\def\FACTORIAL#1{\Fa=#1 \ifnum\Fa=0 \Fct=1\relax\else\Fct=\Fa \Factor\fi\global\tempA=\Fct}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcount\BINOM
+\newcount\temp
+\newcount\tmp
+\def\BINOMIAL#1#2{%
+\temp=#1\advance\temp by -#2
+\FACTORIAL{#1}
+\tmp=\tempA
+\FACTORIAL{\temp}
+\temp=\tempA
+\divide\tmp by \temp
+\FACTORIAL{#2}
+\temp=\tempA
+\divide\tmp by \temp\global\BINOM=\tmp}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newdimen\Xa\newdimen\Yb\newcount\kc
+\newdimen\BSTemp
+\def\xmult#1{\ifnum\kc<#1\advance\kc by 1\Yb=\decimal\Xa\Yb\xmult{#1}\else\relax\fi}
+\def\BERNSTEIN#1#2#3{\Xa=#3pt\kc=0\Yb=1pt\xmult{#1}\kc=0\Xa=-\Xa\advance\Xa by 1pt\xmult{#2}
+\BINOMIAL{6}{#1}\global\BSTemp=\BINOM\Yb}
+\newdimen\Xrf\newdimen\Yrf
+\newdimen\XBST\newdimen\YBST
+\def\XBC#1#2#3{%
+\BERNSTEIN{0}{6}{#2}
+\Xrf=#1pt
+\XBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{1}{5}{#2}
+\Xrf=#1pt\advance\Xrf by -1.5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{2}{4}{#2}
+\Xrf=#1pt\advance\Xrf by 2pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{3}{3}{#2}
+\Xrf=#1pt\advance\Xrf by 6pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{4}{2}{#2}
+\Xrf=#1pt\advance\Xrf by 5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{5}{1}{#2}
+\Xrf=#1pt\advance\Xrf by 1.5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{6}{0}{#2}
+\Xrf=#1pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\global\XBST=#3\XBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\YBC#1#2#3{%
+\BERNSTEIN{0}{6}{#2}
+\Yrf=#1pt
+\YBST=\decimal\BSTemp\Yrf
+\BERNSTEIN{1}{5}{#2}
+\Yrf=#1pt\advance\Yrf by 2pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{2}{4}{#2}
+\Yrf=#1pt\advance\Yrf by 5pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{3}{3}{#2}
+\Yrf=#1pt\advance\Yrf by 3pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{4}{2}{#2}
+\Yrf=#1pt\advance\Yrf by -1pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{5}{1}{#2}
+\Yrf=#1pt\advance\Yrf by -2pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\BERNSTEIN{6}{0}{#2}
+\Yrf=#1pt
+\advance\YBST by \decimal\BSTemp\Yrf
+\global\YBST=#3\YBST}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\XBsix#1#2{%
+(1-t)^6*(#1)*(#2)+6*t*(1-t)^5*(#1-1.5)*(#2)+15*t^2*(1-t)^4*(#1+2)*(#2)+
+20*t^3*(1-t)^3*(#1+6)*(#2)+15*t^4*(1-t)^2*(#1+5)*(#2)+6*t^5*(1-t)*(#1+1.5)*(#2)+t^6*(#1)*(#2)}
+\def\YBsix#1#2{%
+(1-t)^6*(#1)*(#2)+6*t*(1-t)^5*(#1+2)*(#2)+15*t^2*(1-t)^4*(#1+5)*(#2)+
+20*t^3*(1-t)^3*(#1+3)*(#2)+15*t^4*(1-t)^2*(#1-1)*(#2)+6*t^5*(1-t)*(#1-2)*(#2)+t^6*(#1)*(#2)}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\NetDraw#1#2#3#4#5{%
+\newcount\CellNum
+\newdimen\XRef
+\newdimen\YRef
+\newdimen\Xfact
+\newdimen\Yfact
+\newdimen\XMin
+\newdimen\XMax
+\newdimen\YMin
+\newdimen\YMax
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\CellNum=#1
+\XRef=#2pt
+\YRef=#3pt
+\Xfact=#4pt
+\Yfact=#5pt
+\XMin=\decimal\Xfact\XRef \advance\XMin by -1.50\Xfact
+\XMax=\decimal\Xfact\XRef \advance\XMax by 5.00\Xfact
+\YMin=\decimal\Yfact\YRef \advance\YMin by -6.00\Yfact
+\YMax=\decimal\Yfact\YRef \advance\YMax by \Yfact
+\Xsize=\XMax \advance\Xsize by -\XMin \divide\Xsize by \CellNum
+\Ysize=\YMax \advance\Ysize by -\YMin \divide\Ysize by \CellNum
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!30,plotpoints=200,linewidth=0.5pt]{0}{0.5}
+{\XBeight{\decimal\XRef}{\decimal\Xfact}|\YBeight{\decimal\YRef}{\decimal\Yfact}}
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!30,plotpoints=200,linewidth=0.5pt]{0.5}{1}
+{\XBeight{\decimal\XRef}{\decimal\Xfact}|\YBeight{\decimal\YRef}{\decimal\Yfact}}
+\multido{\nz=0.00+0.05}{200}{\XBC{\decimal\XRef}{\nz}{\decimal\Xfact}\YBC{\decimal\YRef}{\nz}{\decimal\Yfact}
+\multido{\nx=\decimal\XMin+\decimal\Xsize}{\the\CellNum}
+{\tempx=\nx pt\multido{\ny=\decimal\YMin+\decimal\Ysize}{\the\CellNum}
+{\tempy=\ny pt\ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize%
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else
+ \pspolygon[fillstyle=solid,fillcolor=red!90,linecolor=black,linewidth=0.2pt]
+ (\nx,\ny)(\decimal\tempx,\ny)(\decimal\tempx,\decimal\tempy)(\nx,\decimal\tempy)(\nx,\ny)\relax\fi\fi\fi\fi}
+}}
+\advance\CellNum by 1
+\multido{\nx=\decimal\XMin+\decimal\Xsize}{\the\CellNum}
+{\psline[linewidth=0.2pt](\nx,\decimal\YMax)(\nx,\decimal\YMin)}
+\multido{\ny=\decimal\YMin+\decimal\Ysize}{\the\CellNum}
+{\psline[linewidth=0.2pt](\decimal\XMin,\ny)(\decimal\XMax,\ny)}
+\parametricplot[algebraic,linecolor=white,plotpoints=200,linewidth=0.5pt]{0}{0.5}
+{\XBeight{\decimal\XRef}{\decimal\Xfact}|\YBeight{\decimal\YRef}{\decimal\Yfact}}
+\parametricplot[algebraic,linecolor=white,plotpoints=200,linewidth=0.5pt]{0.5}{1}
+{\XBeight{\decimal\XRef}{\decimal\Xfact}|\YBeight{\decimal\YRef}{\decimal\Yfact}}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\avecfld#1#2#3#4#5#6{%
+\multido{#2}{#4}
+{\multido{#1}{#3}
+{\parametricplot[algebraic,arrows=->,linecolor=red]{0}{1}
+{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\anothervecfld#1#2#3#4#5#6{%
+\multido{#2}{#4}
+{\multido{#1}{#3}
+{\curvepnodes[algebraic,plotpoints=2]{0}{1}
+{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}{P}
+\psline[linewidth=0.7pt,linecolor=red]{->}(P0)(P1)}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\xch{\catcode`\p=12 \catcode`\t=12}\def\ych{\catcode`\p=11 \catcode`\t=11}
+\xch \def\dec#1pt{#1}\ych \def\decimal#1{\expandafter\dec \the#1}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\vecfldnew#1#2#3#4#5#6#7#8{%
+\newcount\intg \newdimen\fx \newdimen\fy \newdimen\slope \newdimen\interm
+\def\fintg{\interm=#8 \interm=\intg\interm \ifdim\ifdim\slope<0pt-\fi\slope<\interm\advance\intg by -1\relax\else\advance\intg by 1\fintg\fi}
+\multido{#2}{#4}
+{\multido{#1}{#3}
+{\curvepnodes[algebraic,plotpoints=2]{0}{1}{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}{P}
+#7 \slope=10\slope\fintg
+\ifnum\intg>10\psline[linecolor=red]{->}(P0)(P1)\else\ifnum\intg=0\psline[linecolor=red!5]{->}(P0)(P1)\else\multiply\intg by 10
+\psline[linecolor=red!\the\intg]{->}(P0)(P1)\fi\fi
+\intg=0\slope=0pt
+}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\pagestyle{headings}
+\topmargin=-0.6cm
+\textwidth=16.7cm
+\textheight=23cm
+\headheight=2.5ex
+\headsep=0.6cm
+\oddsidemargin=.cm
+\evensidemargin=-.4cm
+\parskip=0.7ex plus0.5ex minus 0.5ex
+\baselineskip=17pt plus2pt minus2pt
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\catcode`@=11
+\renewcommand\section{\@startsection {section}{1}{\z@}%
+ {-3.5ex \@plus -1ex \@minus -.2ex}%
+ {2.3ex \@plus.2ex}%
+ {\normalfont\large\bfseries}}
+\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
+ {-3.25ex\@plus -1ex \@minus -.2ex}%
+ {1.5ex \@plus .2ex}%
+ {\normalfont\normalsize\bfseries}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\gdef\acknw{\section*{%
+{\acknwname}\markright{\protect\textsl{\acknwname}}}%
+\addcontentsline{toc}{section}{\acknwname}}
+\gdef\acknwname{Acknowledgment}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\renewcommand\sectionmark[1]{\markright{\thesection. #1}}
+\newcounter{lk}
+\newenvironment{listof}{\begin{list}{\rm(\roman{lk})}{\usecounter{lk}%
+\setlength{\topsep}{0ex plus0.1ex}%
+\setlength{\labelwidth}{1cm}%
+\setlength{\itemsep}{0ex plus0.1ex}%
+\setlength{\itemindent}{0.5cm}%
+}}{\end{list}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\title{Three applications of macros in \texttt{PSTricks}\thanks{PSTricks is the original work of Timothy Van Zandt (email address: \texttt{tvz@econ.insead.fr}).
+It is currently edited by Herbert Vo\ss\ (\texttt{hvoss@tug.org}).}}
+\author{Le Phuong Quan\\
+\small{(Cantho University, Vietnam)}\\
+\small{\texttt{lpquan@ctu.edu.vn}}}
+\begin{document}
+\maketitle
+\tableofcontents
+\section{Drawing approximations to the area under a graph by rectangles}
+\subsection{Description}
+
+We recall here an operation in Calculus. Let $f(x)$ be a function, defined and bounded on
+an interval $[a,b]$. If $f$ is integrable (in Riemann sense) on $[a,b]$, then its definite integral over this interval
+is
+$$\int_a^bf(x)dx=\lim_{\|P\|\to 0}\sum_{i=1}^nf(\xi_i)\Delta x_i,$$
+where $P\colon a=x_0<x_1<\cdots<x_n=b$, $\Delta x_i=x_i-x_{i-1}$ is a partition of $[a,b]$, $\xi_i\in[x_{i-1},x_i]$, $i=1,2,\ldots,n$,
+and $\|P\|=\max\{\Delta x_i\colon i=1,2,\ldots,n\}$. Hence, when $\|P\|$ is small enough, we may have an
+approximation
+\begin{equation}\label{eqn1}
+I=\int_a^bf(x)dx\approx\sum_{i=1}^nf(\xi_i)\Delta x_i.
+\end{equation}
+Because $I$ is independent to the choice of $P$ and $\xi_i$, we may
+divide $[a,b]$ into $n$ subintervals with equal length and choose $\xi_i=(x_i+x_{i-1})/2$.
+Then, $I$ can be approximately seen as the sum of areas of the rectangles with sides
+$f(\xi_i)$ and $\Delta x_i$.
+
+We will make a drawing procedure to illustrate the approximation (\ref{eqn1}). Firstly, we establish
+commands to draw the ``sum'' of rectangles, like the area under piecewise-constant functions
+(called \textsl{step shape\/}, for brevity). The chosen procedure here
+obviously includes a combination of the macros \texttt{\symbol{92}pscustom} (to \textsl{join\/} horizontal segments, automatically)
+and \texttt{\symbol{92}multido}. In particular, horizontal segments are depicted within the loop
+\texttt{\symbol{92}multido} by
+$$\textmtt{\symbol{92}psplot[{\it settings}]\{$x_{i-1}$\}\{$x_i$\}\{$f(\xi_i)$\}}$$
+Then, \texttt{\symbol{92}pscustom} will join these segments altogether with the ending points
+$(a,0)$, $(b,0)$ to make the boundary of the step shape. Next, we draw the points $(\xi_i,f(\xi_i))$, $i=1,2,\ldots,n$,
+and the dotted segments between these points and the points $(\xi_i,0)$, $i=1,2,\ldots,n$, by
+\begin{align*}
+&\textmtt{\symbol{92}psdot[algebraic,\dots](*\{$\xi_i$\} \{$f(x)$\})}\\
+&\textmtt{\symbol{92}psline[algebraic,linestyle=dotted,\dots]($\xi_i$,$0$)(*\{$\xi_i$\} \{$f(x)$\})}
+\end{align*}
+where we use the structure \textmtt{(*\{{\it value}\} \{$f(x)$\})} to obtain $(\xi_i,f(\xi_i))$. Finally, we draw
+vertical segments to split the step shape into rectangular cells by
+$$\textmtt{\symbol{92}psline[algebraic,\dots]($x_i$,$0$)(*\{$x_i$\} \{$f(x-\Delta x_i/2)$\})}$$
+The process of approximation is depicted in Figure \ref{Fig1}.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(-2,-2)(3,3.5)
+\psset{yunit=0.2}
+\psaxes[labelFontSize=$\footnotesize$,Dy=2,ticksize=2.2pt,labelsep=4pt]{->}(0,0)(-2.5,-10)(3.5,15.5)
+\psplot[plotpoints=500,algebraic,linecolor=red]{-2}{3}{x^3-2*x^2+6}
+\pscustom{
+\psline{-}(-2,0)(-2,0)
+\multido{\nx=-2.000+0.500,\ny=-1.750+0.500,\ni=-1.500+0.500}{10}
+{\psplot[algebraic]{\nx}{\ni}{(\ny)^3-2*(\ny)^2+6}}
+\psline{-}(3,0)}
+\end{pspicture}
+\hskip3em
+\begin{pspicture}(-2,-2)(3,3.5)
+\psset{yunit=0.2}
+\psaxes[labelFontSize=$\footnotesize$,Dy=2,ticksize=2.2pt,labelsep=4pt]{->}(0,0)(-2.5,-10)(3.5,15.5)
+\psplot[plotpoints=500,algebraic,linecolor=red]{-2}{3}{x^3-2*x^2+6}
+\pscustom{
+\psline{-}(-2,0)(-2,0)
+\multido{\nx=-2.000+0.500,\ny=-1.750+0.500,\ni=-1.500+0.500}{10}
+{\psplot[algebraic]{\nx}{\ni}{(\ny)^3-2*(\ny)^2+6}}
+\psline{-}(3,0)}
+\multido{\nx=-2.000+0.500,\ny=-1.750+0.500,\ni=-1.500+0.500}{10}
+{\psline[linestyle=dotted,dotsep=1.5pt,dotstyle=o,linecolor=gray](\ny,0)(*{\ny} {x^3-2*x^2+6})
+\psdot[dotsize=1.2pt 1,dotstyle=Bo](*{\ny} {x^3-2*x^2+6})}
+\end{pspicture}\\[3ex]
+\centering\begin{pspicture}(-2,-2)(3,3)
+\psset{yunit=0.2}
+\psaxes[labelFontSize=$\footnotesize$,Dy=2,ticksize=2.2pt,labelsep=4pt]{->}(0,0)(-2.5,-10)(3.5,15.5)
+\psplot[plotpoints=500,algebraic,linecolor=red]{-2}{3}{x^3-2*x^2+6}
+\pscustom{
+\psline{-}(-2,0)(-2,0)
+\multido{\nx=-2.000+0.500,\ny=-1.750+0.500,\ni=-1.500+0.500}{10}
+{\psplot[algebraic]{\nx}{\ni}{(\ny)^3-2*(\ny)^2+6}}
+\psline{-}(3,0)}
+\multido{\nx=-2.000+0.500,\ny=-1.750+0.500,\ni=-1.500+0.500}{10}
+{\psline[linestyle=dotted,dotsep=1.5pt,dotstyle=o,linecolor=gray](\ny,0)(*{\ny} {x^3-2*x^2+6})
+\psdot[dotsize=1.2pt 1,dotstyle=Bo](*{\ny} {x^3-2*x^2+6})}
+\multido{\nx=-2.000+0.500,\ny=-1.750+0.500,\ni=-1.500+0.500}{9}
+{\psline(\ni,0)(*{\ni} {(x-0.25)^3-2*(x-0.25)^2+6})}
+\end{pspicture}
+\caption{Steps to make the drawing procedure.}\label{Fig1}
+\end{figure}
+
+We now combine the above steps to make a procedure whose calling sequence consists of main parameters
+$a$, $b$, $f$ and $n$, and dependent parameters $x_{i-1}$, $x_i$, $\xi_i$, $f(\xi_i)$ and
+$f(x\pm\Delta x_i/2)$. For instance, let us consider approximations to the integral of $f(x)=\sin x-\cos x$
+over $[-2,3]$ in cases of $n=5$ and $n=20$. They are given in Figure \ref{Fig2}.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(-2.5,-3)(3.5,3.01)
+\psset{plotpoints=500,algebraic,dotsize=1pt 2,yunit=2}
+\psaxes[labelFontSize=$\footnotesize$,Dy=1]{->}(0,0)(-2.5,-1.5)(3.5,1.5)
+\RiemannSum{-2}{3}{sin(x)-cos(x)}{5}
+{-2.0+1.0}{-1.0+1.0}{-1.5+1.0}
+{sin(x+0.5)-cos(x+0.5)}{sin(x-0.5)-cos(x-0.5)}
+\end{pspicture}
+\hskip4em
+\begin{pspicture}(-2.5,-3)(3.5,3.01)
+\psset{plotpoints=500,algebraic,dotsize=1pt 2,yunit=2}
+\psaxes[labelFontSize=$\footnotesize$,Dy=1]{->}(0,0)(-2.5,-1.5)(3.5,1.5)
+\RiemannSum{-2}{3}{sin(x)-cos(x)}{20}
+{-2.000+0.250}{-1.750+0.250}{-1.875+0.250}
+{sin(x+0.125)-cos(x+0.125)}{sin(x-0.125)-cos(x-0.125)}
+\end{pspicture}
+\caption{Approximations to the integral of $f(x)=\sin x-\cos x$ over $[-2,3]$.}\label{Fig2}
+\end{figure}
+
+In summary, we can make a procedure to illustrate the approximation (\ref{eqn1}), say \texttt{RiemannSum}, whose calling sequence has the form of
+$$\textmtt{\symbol{92}RiemannSum\{$a$\}\{$b$\}\{$f(x)$\}\{$n$\}\{$x_{\rm ini}$\}\{$x_{\rm end}$\}\{$x_{\rm choice}$\}\{$f(x+\Delta x_i/2)$\}\{$f(x-\Delta x_i/2)$\}},$$
+where $x_0=a$ and for each $i=1,2\ldots,n$:
+\begin{align*}
+x_i&=a+\dfrac{b-a}{n}i,\quad\Delta x_i=x_i-x_{i-1}=\dfrac{b-a}{n},\\
+x_{\rm ini}&=x_0+\Delta x_i,\quad x_{\rm end}=x_1+\Delta x_i,\quad x_{\rm choice}=\dfrac{x_{\rm ini}+x_{\rm end}}{2}=\dfrac{x_0+x_1}{2}+\Delta x_i.
+\end{align*}
+Note that $x_{\rm ini}$, $x_{\rm end}$ and $x_{\rm choice}$ are given in such forms to be
+suitable to variable declaration in \texttt{\symbol{92}multido}. They are nothing but
+$x_{i-1}$, $x_i$ and $\xi_i$, respectively, at the step $i$-th in the loop.
+
+Tentatively, in \texttt{PSTricks} language, the definition of \texttt{RiemannSum} is suggested to be
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\def\RiemannSum#1#2#3#4#5#6#7#8#9{%!\\
+\verb!\psplot[linecolor=blue]{#1}{#2}{#3}!\\
+\verb!\pscustom[linecolor=red]{%!\\
+\verb!\psline{-}(#1,0)(#1,0)!\\
+\verb!\multido{\ni=#5,\ne=#6}{#4}!\\
+\verb!{\psline(*{\ni} {#8})(*{\ne} {#9})}}!\\
+\verb!\multido{\ne=#6,\nc=#7}{#4}!\\
+\verb!{\psdot(*{\nc} {#3})!\\
+\verb!\psline[linestyle=dotted,dotsep=1.5pt](\nc,0)(*{\nc} {#3})!\\
+\verb!\psline[linecolor=red](\ne,0)(*{\ne} {#9})}}!
+\end{tabular}\hrule
+\subsection{Examples}
+We give here two more examples just to see that using the drawing procedure is very easy. In the first example, we approximate
+the area under the graph of the function $f(x)=x-(x/2)\cos x+2$ on the interval $[0,8]$. To draw the approximation, we try
+the case $n=16$; thus $x_0=0$ and for each $i=1,\ldots,16$, we have
+$x_i=0.5\,i$, $\Delta x_i=0.5$, $x_{\rm ini}=0.00+0.50$, $x_{\rm end}=0.50+0.50$ and $x_{\rm choice}=0.25+0.50$.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(0,0)(5.1,6.6)
+\psset{plotpoints=500,algebraic,dotsize=1pt 2,unit=0.6}
+\RiemannSum{0}{8}{x-(x/2)*cos(x)+2}{16}{0.00+0.50}{0.50+0.50}{0.25+0.50}
+{x+0.25-((x+0.25)/2)*cos(x+0.25)+2}{x-0.25-((x-0.25)/2)*cos(x-0.25)+2}
+\psaxes[labelFontSize=$\footnotesize$,Dy=1,ticksize=2.2pt,labelsep=4pt]{->}(0,0)(8.5,11)
+\end{pspicture}
+\vskip0.5ex
+\caption{An approximation to the area under the graph of $f(x)=x-(x/2)\cos x+2$ on $[0,8]$.}\label{Fig3}
+\end{figure}
+
+To get Figure \ref{Fig3}, we have used the following \LaTeX\ code:
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\begin{pspicture}(0,0)(4.125,5.5)!\\
+\verb!\psset{plotpoints=500,algebraic,dotsize=2.5pt,unit=0.5}!\\
+\verb!\RiemannSum{0}{8}{x-(x/2)*cos(x)+2}{16}{0.00+0.50}{0.50+0.50}{0.25+0.50}!\\
+\verb!{x+0.25-((x+0.25)/2)*cos(x+0.25)+2}{x-0.25-((x-0.25)/2)*cos(x-0.25)+2}!\\
+\verb!\psaxes[ticksize=2.2pt,labelsep=4pt]{->}(0,0)(8.5,11)!\\
+\verb!\end{pspicture}!
+\end{tabular}\hrule\bigskip
+
+In the second example below, we will draw an approximation to the integral of $f(x)=x\sin x$ over $[1,9]$.
+Choosing $n=10$ and computing parameters needed, we get Figure \ref{Fig4}, mainly by
+the command
+\begin{align*}
+&\textmtt{\symbol{92}RiemannSum\{$1$\}\{$9$\}\{$x\sin x$\}\{$10$\}\{$1.00+0.80$\}\{$1.80+0.80$\}\{$1.40+0.80$\}}\\
+&\textmtt{\{$(x+0.4)\sin(x+0.4)$\}\{$(x-0.4)\sin(x-0.4)$\}}
+\end{align*}
+in the drawing procedure.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(0,-2.5)(4.75,4.25)
+\psset{plotpoints=500,algebraic,dotsize=1pt 2,unit=0.5}
+\RiemannSum{1}{9}{x*sin(x)}{10}%
+{1.00+0.80}{1.80+0.80}{1.40+0.80}%
+{(x+0.4)*sin(x+0.4)}{(x-0.4)*sin(x-0.4)}
+\psaxes[labelFontSize=$\footnotesize$,Dy=1,ticksize=2.2pt,labelsep=4pt]{->}(0,0)(0,-5)(9.5,8.5)
+\end{pspicture}
+\caption{An approximation to the integral of $f(x)=x\sin x$ over $[1,9]$.}\label{Fig4}
+\end{figure}
+\section{Drawing the vector field of an ordinary differential equation of order one}
+\subsection{Description}\label{sect1}
+
+Let us consider the differential equation
+\begin{equation}\label{eqn2}
+\frac{dy}{dx}=f(x,y).
+\end{equation}
+At each point $(x_0,y_0)$ in the domain $D$ of $f$, we will put a vector $\mathbf{v}$ with slope
+$k=f(x_0,y_0)$. If $y(x_0)=y_0$, then $k$ is the slope of the tangent to the solution curve $y=y(x)$
+of (\ref{eqn2}) at $(x_0,y_0)$. The $\mathbf{v}$'s make a \textsl{vector field\/} and the picture
+of this field would give us information about the shape of solution curves of (\ref{eqn2}), even
+we have not found yet any solution of (\ref{eqn2}).
+
+The vector field of (\ref{eqn2}) will be depicted on a finite grid of points in $D$. This grid is made of
+lines, paralell to the axes $Ox$ and $Oy$. The intersectional points of those lines are called \textsl{grid points\/}
+and often indexed by $(x_i,y_j)$, $i=0,\ldots,N_x$, $j=0,\ldots,N_y$. For convenience, we will use
+polar coordinates to locate the terminal point $(x,y)$ of a field vector, with the initial point at
+grid point $(x_i,y_j)$. Then, we can write
+\begin{align*}
+x&=x_i+r\cos\varphi,\\
+y&=y_j+r\sin\varphi.
+\end{align*}
+Because $k=f(x_i,y_j)=\tan\varphi$ is finite, we may take $-\pi/2<\varphi<\pi/2$.
+From $\sin^2\varphi+\cos^2\varphi=1$ and $\sin\varphi=k\cos\varphi$, we derive
+$$\cos\varphi=\frac{1}{\sqrt{1+k^2}},\quad\sin\varphi=\frac{k}{\sqrt{1+k^2}}.$$
+\begin{figure}[htbp]
+\centering\begin{pspicture}(0,0)(5,5)
+\psset{unit=2}
+\psaxes[labelFontSize=$\footnotesize$,Dx=0.5,Dy=0.5,labels=none,ticksize=2pt,labelsep=2pt,linewidth=0.5pt]
+{->}(0,0)(2.5,2.5)
+\psdots[dotstyle=*,dotsize=3pt,linecolor=red](1,1)(1.5,1)(1,1.5)
+\psline[linewidth=0.3pt](1.5,0.5)(1.5,2)(1,2)(1,0.5)(2,0.5)(2,1.5)
+\psline[linewidth=0.3pt](1,1.5)(2,1.5)\psline[linewidth=0.3pt](1,1)(2,1)
+\psarc[linewidth=0.5pt,linestyle=dotted,dotsep=1.5pt](1,1){0.5}{-90}{90}
+\psarc[linewidth=0.5pt,linestyle=dotted,dotsep=1.5pt](1.5,1){0.5}{-90}{90}
+\psarc[linewidth=0.5pt,linestyle=dotted,dotsep=1.5pt](1,1.5){0.5}{-90}{90}
+\psline[linewidth=0.8pt,linecolor=red]{->}(1,1.5)(1.27,1.92)
+\psline[linewidth=0.8pt,linecolor=red]{->}(1,1)(1.382,1.322)
+\psline[linewidth=0.8pt,linecolor=red]{->}(1.5,1)(1.977,1.147)
+\rput(1,-0.1){$x_i$}\rput(1.5,-0.1){$x_{i+1}$}\rput(-0.1,1){$y_j$}\rput(-0.2,1.5){$y_{j+1}$}
+\end{pspicture}
+\caption{Field vectors on a grid.}\label{Fig5}
+\end{figure}
+The field vectors should all have the same magnitude and we choose here that length to be
+$1/2$, that means $r=1/2$. Thus, vectors on the grid have their initial and terminal points as
+$$(x_i,y_j),\quad \Big(x_i+\frac{1}{2}\cos\varphi,y_j+\frac{1}{2}\sin\varphi\Big),$$
+respectively. Hence, we easily get the parametrization of a vector at grid point
+$(x_i,y_j)$:
+\begin{align*}
+x&=x_i+\frac{t}{2}\cos\varphi=x_i+\frac{t}{2\sqrt{1+k^2}},\\
+y&=y_j+\frac{t}{2}\sin\varphi=y_j+\frac{tk}{2\sqrt{1+k^2}},
+\end{align*}
+where $t$ goes from $0$ to $1$, as along the direction of the vector.
+
+Of macros in \texttt{PSTricks} to draw lines from their parametrization, we select \texttt{\symbol{92}parametricplot}\footnote{\footnotesize
+This macro is of ones, often added and updated in the package \texttt{pstricks-add}, the authors:
+Dominique Rodriguez (\texttt{dominique.rodriguez@waika9.com}), Herbert Vo\ss\ (\texttt{voss@pstricks.de}).}
+for its fitness. The macro has the syntax
+$$\textmtt{\symbol{92}parametricplot[{\it settings}]\{$t_{\rm min}$\}\{$t_{\rm max}$\}\{$x(t)$|$y(t)$\}},$$
+where we may use the option \texttt{algebraic} to make the declaration of $x(t)$ and $y(t)$ simpler
+in \texttt{ASCII} code.
+
+From the above description of one field vector, we now construct the vector field
+on a grid within a domain $R=\{(x,y)\colon a\le x\le b,\,c\le y\le d\}$. To determine the grid, we confine grid points to the range
+\begin{equation}\label{eqn3}
+a\le x_i\le b,\quad c\le y_j\le d.
+\end{equation}
+We start with initial values $x_0=a$ and $y_0=c$ to have points $(x_i,y_j)$ with increments $\Delta x=\Delta y=\delta$, corresponding to the length of vectors and the distance
+between grid points as indicated in Figure \ref{Fig5}. Thus, to draw vectors at grid points
+$(x_i,y_j)$, we need two loops for indices $i$ and $j$, with $0\le i\le\lfloor m/\delta\rfloor$, $0\le j\le\lfloor n/\delta\rfloor$, where
+$m=b-a$, $n=d-c$. Apparently, these two loops are nested \texttt{\symbol{92}multido}s, with variable declaration
+for each loop as follows
+\begin{align*}
+\texttt{\symbol{92}nx}&=\text{initial value}+\text{increment}=x_0+\Delta x,\\
+\texttt{\symbol{92}ny}&=\text{initial value}+\text{increment}=y_0+\Delta y.
+\end{align*}
+Finally, we will replace \texttt{\symbol{92}nx}, \texttt{\symbol{92}ny} by $x_i$, $y_j$ in the
+below calling sequence for simplicity.
+
+Thus, the main command to draw the vector field of the equation (\ref{eqn2}) on the grid (\ref{eqn3})
+is
+\begin{align*}
+&\textmtt{\symbol{92}multido\big\{$y_j=y_0+\Delta y$\big\}\big\{$\lfloor n/\delta\rfloor$\big\}}\textmtt{\bigg\{\symbol{92}multido\big\{$x_i=x_0+\Delta x$\big\}\big\{$\lfloor m/\delta\rfloor$\big\}}\\
+&\quad\textmtt{\Big\{\symbol{92}parametricplot[{\it settings}]\{$0$\}\{$1$\}\Big\{$x_i+\frac{t}{2\sqrt{1+\big[f(x_i,y_j)\big]^2}}$\Big|
+$y_j+\frac{tf(x_i,y_j)}{2\sqrt{1+\big[f(x_i,y_j)\big]^2}}$\Big\}\bigg\}}
+\end{align*}
+where we at least use \texttt{arrows=->} and \texttt{algebraic} for \textit{settings}.
+
+We can combine the steps mentioned above to define a drawing procedure, say \texttt{\symbol{92}avecfld},
+that consists of $6$ parameters in the order as
+\texttt{\symbol{92}nx=}$x_0+\Delta x$, \texttt{\symbol{92}ny=}$y_0+\Delta y$, $\lfloor m/\delta\rfloor$, $\lfloor n/\delta\rfloor$, $\delta$
+and $f(\texttt{\symbol{92}nx},\texttt{\symbol{92}ny})$. We may change these values to modify
+the vector field or to avoid the vector intersection. Such a procedure is suggested to be
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\def\avecfld#1#2#3#4#5#6{%!\\
+\verb!\multido{#2}{#4}{\multido{#1}{#3}!\\
+\verb!{\parametricplot[algebraic,arrows=->,linecolor=red]{0}{1}!\\
+\verb!{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}}}}!
+\end{tabular}\hrule\bigskip
+
+Actually, the procedure \texttt{\symbol{92}parametricplot} is used here only to draw a vector by its parametrization $(x(t),y(t))$, so we can use the structure \texttt{\symbol{92}curvepnodes} in the package \texttt{pst-node}\footnote{\footnotesize
+Package authors: Timothy Van Zandt (\texttt{tvz@econ.insead.fr}), Michael Sharpe (\texttt{msharpe@euclid.ucsd.edu}) and Herbert Vo\ss\ (\texttt{hvoss@tug.org}).} to
+extract the two ending points of the curve $(x(t),y(t))$ by the command
+$$\textmtt{\symbol{92}curvepnodes[algebraic,plotpoints=2]\{0\}\{1\}\{$x(t)$|$y(t)$\}\{P\}},$$
+where \texttt{P} is a name of the root of nodes and we just get the two nodes \texttt{P0}, \texttt{P1} when executing this command. Then, the corresponding
+vector is drawn by the command
+$$\textmtt{\symbol{92}psline[linecolor={\it settings}]\{->\}(P0)(P1)}$$
+
+Therefore, another procedure to draw a vector field may be defined as
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\def\anothervecfld#1#2#3#4#5#6{%!\\
+\verb!\multido{#2}{#4}{\multido{#1}{#3}!\\
+\verb!{\curvepnodes[algebraic,plotpoints=2]{0}{1}!\\
+\verb!{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}{P}!\\
+\verb!\psline[linecolor=red]{->}(P0)(P1)}}}!
+\end{tabular}\hrule
+\subsection{Examples}
+Firstly, we consider the equation that describes an object falling in a resistive medium:
+\begin{equation}\label{eqn4}
+\frac{dv}{dt}=9.8-\frac{v}{5},
+\end{equation}
+where $v=v(t)$ is the speed of the object in time $t$. In Figure \ref{Fig6}, the vector field of (\ref{eqn4}) is given
+on the grid $R=\{(t,y)\colon 0\le t\le 9,\,46\le v\le 52\}$, together with the graph of the equilibrium solution
+$v=49$.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(0,41.4)(8.55,47.25)
+\psset{xunit=0.9,yunit=0.9}
+\multido{\ny=46.25+0.50}{13}
+{\multido{\nx=0.25+0.50}{18}
+{\curvepnodes[algebraic,plotpoints=2]{0}{1}{\nx+(t/2)*(1/sqrt(1+(9.8-0.2*(\ny))^2))|\ny+(t/2)*(1/sqrt(1+(9.8-(0.2)*(\ny))^2))*(9.8-(0.2)*(\ny))}{P}
+\psline[linewidth=0.7pt,linecolor=red]{->}(P0)(P1)}}
+\psplot[algebraic,linewidth=1.2pt]{0}{9.25}{49}
+\psaxes[labelFontSize=$\footnotesize$,ticksize=2.2pt,labelsep=4pt,Dy=1,Dx=1,Oy=46,linewidth=0.7pt]{->}(0,46)(0,46)(9.5,52.5)
+\rput(9.5,45.8){$t$}\rput(-0.2,52.5){$y$}
+\end{pspicture}
+\caption{The vector field of (\ref{eqn4}).}\label{Fig6}
+\end{figure}
+
+Figure \ref{Fig6} is made of the following \LaTeX\ code:
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\begin{pspicture}(0,46)(9.5,52.5)!\\
+\verb!\anothervecfld{\nx=0.25+0.50}{\ny=46.25+0.50}{18}{12}{0.5}{9.8-0.2*\ny}!\\
+\verb!\psplot[algebraic,linewidth=1.2pt]{0}{9}{49}!\\
+\verb!\psaxes[Dy=1,Dx=1,Oy=46]{->}(0,46)(0,46)(9.5,52.5)!\\
+\verb!\rput(9.5,45.8){$t$}\rput(-0.2,52.5){$y$}!\\
+\verb!\end{pspicture}!
+\end{tabular}\hrule\bigskip
+
+Let us next consider the problem
+\begin{equation}\label{eqn5}
+\frac{dy}{dx}=x+y,\quad y(0)=0.
+\end{equation}
+It is easy to check that $y=e^x-x-1$ is the unique solution to (\ref{eqn5}). We now draw
+the vector field of (\ref{eqn5}) and the solution curve\footnote{\footnotesize
+We have used ${\rm ch}(1)+{\rm sh}(1)$ for the declaration of $e$, natural base of logarithmic function.} on the grid $R=\{(x,y)\colon 0\le x\le 3,\,0\le y\le 5\}$ in
+Figure \ref{Fig7}.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(0,0)(3.25,5.5)
+\psset{unit=1}
+\multido{\ny=0.25+0.50}{10}
+{\multido{\nx=0.25+0.50}{6}
+{\curvepnodes[algebraic,plotpoints=2]{0}{1}{\nx+(t/2)*(1/sqrt(1+(\nx+\ny)^2))|\ny+(t/2)*(1/sqrt(1+(\nx+\ny)^2))*(\nx+\ny)}{P}
+\psline[linewidth=0.7pt,linecolor=red]{->}(P0)(P1)}}
+\psplot[algebraic,linewidth=1.2pt]{0}{2.15}{(sh(1)+ch(1))^x-x-1}
+\psaxes[labelFontSize=$\footnotesize$,Dy=1,Dx=1,ticksize=2.2pt,labelsep=4pt,linewidth=0.7pt]{->}(0,0)(3.5,5.5)
+\rput(3.5,-0.2){$x$}\rput(-0.25,5.5){$y$}
+\end{pspicture}
+\caption{The vector field of (\ref{eqn5}).}\label{Fig7}
+\end{figure}
+
+We then go to the logistic equation, which is chosen to be a model for the dependence
+of the population size $P$ on time $t$ in Biology:
+\begin{equation}\label{eqn6}
+\frac{dP}{dt}=kP\Big(1-\frac{P}{M}\Big),
+\end{equation}
+where $k$ and $M$ are constants, respectively various to selected species and environment.
+For specification, we take, for instance, $k=0.5$ and $M=100$. The right hand side of
+(\ref{eqn6}) then becomes $f(t,P)=0.5\,P(1-0.01\,P)$. In Figure \ref{Fig8}, we draw the vector field
+of (\ref{eqn6}) on the grid $R=\{(t,P)\colon 0\le t\le 10,\,95\le P\le 100\}$ and the equilibrium
+solution curve $P=100$. Furthermore, with the initial condition $P(0)=95$, the equation (\ref{eqn6})
+has the unique solution $P=1900(e^{-0.5t}+19)^{-1}$. This solution curve is also given in Figure \ref{Fig8}.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(0,76)(8.4,80.4)
+\psset{xunit=0.8,yunit=0.8}
+\multido{\ny=95.25+0.50}{10}
+{\multido{\nx=0.25+0.50}{20}
+{\curvepnodes[algebraic,plotpoints=2]{0}{1}{\nx+(t/2)*(1/sqrt(1+((0.5)*(\ny)*(1-(0.01)*(\ny)))^2))|\ny+(t/2)*(1/sqrt(1+((0.5)*(\ny)*(1-(0.01)*(\ny)))^2))*((0.5)*(\ny)*(1-(0.01)*(\ny)))}{P}
+\psline[linewidth=0.7pt,linecolor=red]{->}(P0)(P1)}}
+\psplot[algebraic,linewidth=1.2pt]{0}{10.25}{100}
+\psplot[algebraic,linewidth=1.2pt]{0}{10.25}{1900/((ch(1)+sh(1))^(-0.5*x)+19)}
+\psaxes[labelFontSize=$\footnotesize$,Dy=1,Dx=1,Oy=95,ticksize=2pt,labelsep=4pt,linewidth=0.7pt]{->}(0,95)(0,95)(10.5,100.5)
+\rput(10.5,94.8){$t$}\rput(-0.25,100.5){$P$}
+\end{pspicture}
+\caption{The vector field of (\ref{eqn6}) with $k=0.5$ and $M=100$.}\label{Fig8}
+\end{figure}
+
+The previous differential equations are all of seperated variable or linear cases that
+can be solved for closed-form solutions by some simple integration formulas. We will consider one more
+equation of the non-linear case whose solution can only be approximated by numerical methods.
+The vector field of such an equation is so useful and we will use the Runge-Kutta curves (of order $4$)
+to add more information about the behaviour of solution curves. Here, those Runge-Kutta curves are depicted by the procedure
+\texttt{\symbol{92}psplotDiffEqn}, also updated from the package \texttt{pstricks-add}.
+
+The vector field of the non-linear differential equation
+\begin{equation}\label{eqn7}
+\frac{dy}{dx}=y^2-xy+1
+\end{equation}
+will be depicted on the grid $R=\{(x,y)\colon -3\le x\le 3,\,-3\le y\le 3\}$ and the solutions
+of Cauchy problems for (\ref{eqn7}), corresponding to initial conditions
+\begin{listof}
+\item $y(-3)=-1$,
+\item $y(-2)=-3$,
+\item $y(-3)=-0.4$,
+\end{listof}
+will be approximated by the method of Runge-Kutta, with the grid size $h=0.2$. It is very easy
+to recognize approximate curves, respective to (i), (ii) and (iii) in Figure \ref{Fig9} below.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(-3.6,-3.6)(4.2,4.2)
+\psset{unit=1.2,dotsize=2.6pt}
+\anothervecfld{\nx=-3.00+0.4}{\ny=-3.00+0.4}{16}{16}{0.35}{(\ny)^2-(\nx)*(\ny)+1}
+\psplotDiffEqn[linewidth=1.2pt,algebraic,showpoints=true,plotpoints=24,method=rk4]{-3}{1.9}{-1}{(y[0])^2-x*y[0]+1}
+\psplotDiffEqn[linewidth=1.2pt,algebraic,showpoints=true,plotpoints=25,method=rk4]{-2}{3}{-3}{(y[0])^2-x*y[0]+1}
+\psplotDiffEqn[linewidth=1.2pt,algebraic,showpoints=true,plotpoints=10,method=rk4]{-3}{-0.96}{-0.4}{(y[0])^2-x*y[0]+1}
+\psaxes[labelFontSize=$\footnotesize$,Dy=1,Dx=1,ticksize=2.2pt,labelsep=4pt,linewidth=0.7pt]{->}(0,0)(-3,-3)(3.5,3.5)
+\rput(3.5,-0.2){$x$}\rput(-0.25,3.5){$y$}
+\end{pspicture}
+\caption{The vector field of (\ref{eqn7}) and the Runge-Kutta curves.}\label{Fig9}
+\end{figure}
+\subsection{Remarks on how to color arrows properly for a vector field}
+There remains a problem in drawing a vector field. That is coloring arrows.
+Obviously, their color shade should vary according to their slope and this would give us the picture of domains containing
+increase or decrease solutions of a differential equation. In some cases, we even know how large the rate of change of those
+solutions is in a specific domain.
+
+In Subsection \ref{sect1}, we know for the equation (\ref{eqn2}) that $f(x_i,y_j)$ is right the slope of
+field vectors at grid points $(x_i,y_j)$, and we will divide these slopes into some number of scales, corresponding to the
+degree of color shades. Here, we confine our interest to a continuous function $f(x,y)$ in two independent variables on a domain
+$R=\{(x,y)\colon a\le x\le b,\,c\le y\le d\}$ and choose the scale of $10$ degrees. This number of degrees can be changed to any positive integer.
+
+According to the input data from the differential equation (\ref{eqn2}), the set $R$ and the grid points on it and the value $M=\max\{|f(x_i,y_j)|\colon
+0\le i\le\lfloor m/\Delta x\rfloor,\,0\le j\le\lfloor n/\Delta y\rfloor\}$, where $m=b-a$ and $n=d-c$,
+we can now define the degree of color shade for each arrow in our vector field. It should be an integer $n_{ij}$ such that
+$n_{ij}=\lfloor 10|f(x_i,y_j)|/M\rfloor$, that is
+\begin{equation}\label{eqn8}n_{ij}M\le 10|f(x_i,y_j)|<(n_{ij}+1)M.\end{equation}
+For finding such an integer, in \TeX\ codes, we need one \texttt{\symbol{92}newcount} for it and two \texttt{\symbol{92}newdimen} for
+$f(x_i,y_j)$ and intermediate values to be compared with $|f(x_i,y_j)|$. For more explanation, let us begin with settings
+\texttt{\symbol{92}newcount\symbol{92}intg} (referring (ref.) to ``integer''), \texttt{\symbol{92}newdimen\symbol{92}slope} (ref. to ``slope'') and \texttt{\symbol{92}newdimen\symbol{92}interm}
+(ref. to ``intermediate values''). Then, the integer $n_{ij}$ at stage $(i,j)$ within the two \texttt{\symbol{92}multido} loops can be defined by the recursive macro \texttt{\symbol{92}fintg} (ref. to ``find the integer'') as follows
+\begin{verbatim}
+ \def\fintg{\interm=Mpt \interm=\intg\interm%
+ \ifdim\ifdim\slope<0pt -\fi\slope<\interm\advance\intg by -1\relax
+ \else\advance\intg by 1\fintg\fi}
+\end{verbatim}
+where \texttt{M} and \texttt{\symbol{92}slope} are holding the values $M$ and $f(x_i,y_j)$, respectively. Note that, before running our macro, \verb!\slope! should be multiplied
+by $10$ with the assignment \texttt{\symbol{92}slope=10\symbol{92}slope}, as defined in (\ref{eqn8}). Besides, by simulating the expression of $f(x,y)$, the calculation of $f(x_i,y_j)$
+should be declared with operations on \texttt{\symbol{92}newcount}s and \texttt{\symbol{92}newdimen}s. Then, the integer $n_{ij}$, which is found at stage $(i,j)$, should take its
+degree, say $k$, from $0$ to $10$ by its value, suitably associated to the command \textmtt{\symbol{92}psline[linecolor=red!case-k]\{->\}(P0)(P1)}.
+Here, we choose \texttt{red} for the main color (it can be changed, of course), and \texttt{case-k} will be replaced with an appropriate percentage of \texttt{red}. Finally,
+such a color scale is local and relative, so we can use one more parameter in the procedure to adjust color shades.
+The old procedures take $6$ parameters and the new one will take two more parameters: one for declaration of computing $f(x_i,y_j)$ and the other
+for adjusting color shades.
+
+Let us take some examples on how to compute $f(x_i,y_j)$ by \TeX\ codes or by commands from the package \texttt{calculator}\footnote{\footnotesize
+Package author: Robert Fuster (\texttt{rfuster@mat.upv.es}).}. For a simple polynomial $f(x,y)$,
+computing $f(x_i,y_j)$ by \TeX\ codes might be facile. Because \verb!\nx! and \verb!\ny! are respectively holding values of
+$x_i$ and $y_j$, we need the two corresponding variables \verb!\newdimen\fx! and \verb!\newdimen\fy! to take these values. By assigning \verb!\fx=\nx pt\fy=\ny pt!,
+we compute $f(\verb!\nx!,\verb!\ny!)$ and assign its value to \verb!\slope!. The declaration of calculations for some cases of $f(x,y)$ is given in the following table.
+
+\begin{table}[htbp]
+\centering\begin{tabular}{c|l}
+$f(x,y)$&\multicolumn{1}{c}{\TeX\ codes for computing $f(\texttt{\symbol{92}nx},\texttt{\symbol{92}ny})$} \\ \hline
+$x+y$&\verb!\advance\slope by \fx \advance\slope by \fy!\\ \hline
+$1-xy$&\verb!\advance\slope by -\decimal\fx\fy \advance\slope by 1pt!\\ \hline
+$y(3-y)$&\verb!\advance\slope by -\decimal\fy\fy \advance\slope by 3\fy!\\ \hline
+$y^2-xy$&\verb!\advance\slope by \decimal\fy\fy \advance\slope by -\decimal\fx\fy!\\ \hline
+\end{tabular}
+\end{table}
+In the table, the command \verb!\decimal!, which is quotative from \cite{five} for producing decimal numbers from dimensions, is put in the preamble using a definition as
+\begin{verbatim}
+ \def\xch{\catcode`\p=12 \catcode`\t=12}\def\ych{\catcode`\p=11 \catcode`\t=11}
+ \xch \def\dec#1pt{#1}\ych \def\decimal#1{\expandafter\dec \the#1}
+\end{verbatim}
+
+For a transcendental or rational function $f(x,y)$, we may use the package \texttt{calculator} for
+computing $f(x_i,y_j)$. The following table shows how to perform calculations.
+\begin{table}[htbp]
+\centering\begin{tabular}{c|l}
+$f(x,y)$&\multicolumn{1}{c}{The commands from the package \texttt{calculator} for computing $f(\texttt{\symbol{92}nx},\texttt{\symbol{92}ny})$} \\ \hline
+$\sin(y-x)$&\verb!\SUBTRACT{\ny}{\nx}{\sola}\SIN{\sola}{\solb}\slope=\solb pt!\\ \hline
+\raisebox{-2ex}[0pt][0pt]{$2xy/(1+y^2)$}&\verb!\SUMfunction{\ONEfunction}{\SQUAREfunction}{\Fncty}!\\
+&\verb!\Fncty{\ny}{\soly}{\Dsoly}\DIVIDE{\Dsoly}{\soly}{\tempa}!\\
+&\verb!\MULTIPLY{\nx}{\tempa}{\tempb}\slope=\tempb pt!\\ \hline
+\end{tabular}
+\end{table}
+
+From the old macros \verb!\avecfld! or \verb!\anothervecfld!, we will construct the new one \verb!\vecfldnew! by adding up to the former the two parameters as described above. According to
+the description of new parameters and of known ones, the calling sequence of \verb!\vecfldnew! may have the form of
+$$\textmtt{\symbol{92}vecfldnew\{\symbol{92}nx$=x_0+\Delta x$\}\{\symbol{92}ny$=y_0+\Delta y$\}\{$n_x$\}\{$n_y$\}\{$\ell$\}\{$f(\texttt{\symbol{92}nx},\texttt{\symbol{92}ny})$\}\{{\rm\TeX\ codes}\}\{$n_a$\}}$$
+where $n_a$ is an estimate value for $M$ and can be adjusted to be greater or less than $M$. This flexible mechanism might be to increase or decrease the degree of
+color shades. Finally, \verb!\intg! and \verb!\slope! should be reset to
+zero at the end of each stage. Now, all materials to make the new macro are ready, and its definition is suggested to be
+\bigskip\hrule
+\noindent\begin{tabular}{@{}l}
+\verb!\def\vecfldnew#1#2#3#4#5#6#7#8{%!\\
+\verb!\newcount\intg \newdimen\slope \newdimen\interm \newdimen\fx \newdimen\fy!\\
+\verb!\def\fintg{\interm=#8 \interm=\intg\interm%!\\
+\verb! \ifdim\ifdim\slope<0pt -\fi\slope>\interm \advance\intg by 1\fintg\fi}!\\
+\verb!\multido{#2}{#4}!\\
+\verb!{\multido{#1}{#3}!\\
+\verb!{\curvepnodes[algebraic,plotpoints=2]{0}{1}!\\
+\verb!{\nx+((#5)*t)*(1/sqrt(1+(#6)^2))|\ny+((#5)*t)*(1/sqrt(1+(#6)^2))*(#6)}{P}!\\
+\verb!#7\slope=10\slope \fintg \ifnum\intg>10\psline[linecolor=red]{->}(P0)(P1)!\\
+\verb+\else\ifnum\intg=0\psline[linecolor=red!5]{->}(P0)(P1)+\\
+\verb+\else\multiply\intg by 10\psline[linecolor=red!\the\intg]{->}(P0)(P1)\fi\fi+\\
+\verb+\intg=0\slope=0pt+\\
+\verb+}}}+
+\end{tabular}\hrule\bigskip
+
+If we predefine some scale of degrees, instead of the code $\verb!\ifnum\intg>10!\ldots\verb!\fi\fi!$, the structure \verb!\ifcase! can be used as
+$$\begin{array}{c}
+\verb!\ifcase\intg!\\
+\verb+\psline[linecolor=red!5]{->}(P0)(P1)\or+\\
+\verb+\psline[linecolor=red!10]{->}(P0)(P1)\or+\\
+\vdots\\
+\verb!\psline[linecolor=red]{->}(P0)(P1)\fi!
+\end{array}$$
+
+The first example is given with two values of $n_a$ to see how different the color shades are between the two cases. The left vector field in Figure \ref{Fig10}
+is made of the calling sequence
+\begin{verbatim}
+\vecfldnew{\nx=-2.00+0.3}{\ny=-2.00+0.3}{14}{14}{0.3}{(\nx)-2*(\ny)}
+{\fy=\ny pt \fx=\nx pt \advance\slope by -2\fy \advance\slope by \fx}{7pt}
+\end{verbatim}
+\begin{figure}[htbp]
+\centering\includegraphics[width=4.6cm]{vecb5}
+\hskip1cm\includegraphics[width=4.6cm]{vecb6}
+\caption{The vector fields of the equation $y'=x-2y$ with $n_a=\texttt{7pt}$ (the left) and $n_a=\texttt{4pt}$ (the right)}\label{Fig10}
+\end{figure}
+
+In Figure \ref{Fig11}, the vector fields of the equations $y'=y-x$ and $y'=x(2-y)$ are respectively drawn by the calling sequences
+\begin{verbatim}
+\vecfldnew{\nx=-3.00+0.4}{\ny=-3.00+0.4}{15}{15}{0.35}{(\ny)-(\nx)}
+{\fy=\ny pt \fx=\nx pt \advance\slope by -\fx \advance\slope by \fy}{5pt}
+\end{verbatim}
+and
+\begin{verbatim}
+\vecfldnew{\nx=-3.00+0.4}{\ny=-3.00+0.4}{15}{15}{0.35}{(\nx)*(2-(\ny))}
+{\fy=\ny pt \fx=\nx pt \advance\slope by -\decimal\fx\fy
+\advance\slope by 2\fx}{6pt}
+\end{verbatim}
+\begin{figure}[htbp]
+\centering\includegraphics[width=6.2cm]{vecb3}
+\hskip1cm\includegraphics[width=6.2cm]{vecb4}
+\caption{The vector fields of the equation $y'=y-x$ (the left) and $y'=x(2-y)$ (the right).}\label{Fig11}
+\end{figure}
+
+Finally, we consider two more examples on vector fields of differential equations $y'=f(x,y)$ containing trigonometric or rational functions on their right side. The calling sequences
+\begin{verbatim}
+\vecfldnew{\nx=-3.00+0.4}{\ny=-3.00+0.4}{15}{15}{0.35}{sin(\nx)*cos(\ny)}
+{\SIN{\nx}{\tmpa}\COS{\ny}{\tmpb}\MULTIPLY{\tmpa}{\tmpb}{\tmpc}
+\slope=\tmpc pt}{0.6pt}
+\end{verbatim}
+and
+\begin{verbatim}
+\vecfldnew{\nx=-3.00+0.3}{\ny=-3.00+0.3}{20}{20}{0.3}{2*(\nx)*(\ny)/(1+(\ny)^2)}
+{\SUMfunction{\ONEfunction}{\SQUAREfunction}{\Fncty}\Fncty{\ny}{\soly}{\Dsoly}
+\DIVIDE{\Dsoly}{\soly}{\tempa}\MULTIPLY{\nx}{\tempa}{\tempb}
+\slope=\tempb pt}{2.5pt}
+\end{verbatim}
+respectively result in the vector fields on the left and on the right in Figure \ref{Fig12}.
+
+\begin{figure}[htbp]
+\centering\includegraphics[width=6.2cm]{vecb1}
+\hskip1cm\includegraphics[width=6.2cm]{vecb2}
+\caption{The vector fields of the equation $y'=\sin(x)\cos(y)$ (the left) and $y'=2xy/(1+y^2)$ (the right).}\label{Fig12}
+\end{figure}
+\section{Drawing partitions of a simply connected plane domain}
+\subsection{Description}
+B\'{e}zier curves have been used in many different aspects, but mostly in computer graphics to model smooth curves designed by computer
+programs. We just recall here the vector function of a B\'{e}zier curve of degree $n$ with $n+1$ control points whose position
+vectors are $\mathbf{r}_0$, $\mathbf{r}_1$, \dots, $\mathbf{r}_n$. It is the vector function $\mathbf{r}(t)$ in a real variable $t\in[0,1]$ that
+is defined as
+\begin{equation}\label{eqn9}
+\mathbf{r}(t)=\sum_{i=0}^n\binom{n}{i}t^i(1-t)^{n-i}\mathbf{r}_i.
+\end{equation}
+Since $\mathbf{r}(0)=\mathbf{r}_0$, $\mathbf{r}(1)=\mathbf{r}_n$ and $\mathbf{r}'(0)=n(\mathbf{r}_1-\mathbf{r}_0)$, $\mathbf{r}'(1)=n(\mathbf{r}_n-\mathbf{r}_{n-1})$,
+we can take a curve such that it is closed and tangent to a line $(\Delta)$ at the point whose position vector is $\mathbf{r}_0$, by
+letting $\mathbf{r}_n=\mathbf{r}_0$ and the points whose position vectors are $\mathbf{r}_0$, $\mathbf{r}_1$ and $\mathbf{r}_{n-1}$
+all be on the line $(\Delta)$.
+
+Taking a closed B\'{e}zier curve to be the boundary of a plane domain has the great advantage. That is because coordinates of points
+on the curve are evaluated by polynomials, and the curve has necessary smoothness, beautiful enough for graphic illustrations.
+\texttt{PSTricks} has the procedure \verb!\parametricplot! to draw such a curve. But, an important problem here is how to control
+the coordinates of its points to construct a procedure for drawing a partition of a simply connected plane domain and coloring
+(or marking) its cells having common points with the boundary of the domain. We particularly need such a procedure for illustrations
+of essential notions in measure theory or double integral definition. Because of the limitation in accuracy imposed
+by the \TeX\ arithmetic, we should mention about $2$-dimension vector functions of a B\'{e}zier curve of small degree (in fact, as small as possible).
+According to the above requirements for the closed boundary of a simply connected domain, we will design a family of closed B\'{e}zier curves of
+degree $6$, although we may extend their degree to $12$.
+
+From the expression of $\mathbf{r}(t)$ in (\ref{eqn9}), we will construct the following functions and procedures:
+\begin{itemize}
+\item The factorial function \texttt{FACTORIAL}.
+\item The binomial function \texttt{BINOMIAL}.
+\item Polynomials $t^m(1-t)^n$.
+\item A procedure to compute a sum of $7$ terms: values of $\mathbf{r}(t)$ as linear combinations
+of the Bernstein polynomials
+$$\binom{6}{k}t^k(1-t)^{6-k},\quad k=0,\ldots,6.$$
+\end{itemize}
+These functions and procedures are macros given by definitions with or without parameters. In the following subsections we will construct them step by step and
+show how to make connections between them.
+\subsubsection{Factorial functions and binomial coefficients}
+To obtain the factorial function, a procedure for multiplying consecutively an integer $n$ with its diminished values will be constructed. For the declared
+integer variables \verb!\Fa! and \verb!\Fct!, the latter will hold values of the function, and the former will hold factors that are multiplied consecutively
+and reduced by $1$. Namely, if \verb!\Fa! is $0$ or $1$ then \verb!\Fct! takes $1$; else if $\texttt{\symbol{92}Fa}>1$ then \verb!\Fct! takes
+the initial value of \verb!\Fa! to begin a loop: diminishing \verb!\Fa! by $1$ and updating \verb!\Fct! by multiplying its old value with the new value of \verb!\Fa!.
+The loop is defined by the control sequence \verb!\Factor! and is ended when \verb!\Fa! is diminished to $1$; then, the factorial function obtains its value from
+the one given back after calling \verb!\FACTORIAL! with one parameter.
+\begin{verbatim}
+\newcount\Fa\newcount\Fct
+\newcount\tempA
+\def\Factor{\ifnum\Fa=1\relax\else\advance\Fa by -1\multiply\Fct by \Fa\Factor\fi}
+\def\FACTORIAL#1{\Fa=#1 \ifnum\Fa=0 \Fct=1\relax\else\Fct=\Fa \Factor\fi%
+\global\tempA=\Fct}
+\end{verbatim}
+Since \TeX\ limits the largest integer number to $2^{30}-1$, we can evaluate only to
+$$\textmtt{\symbol{92}FACTORIAL\{$12$\}}=12!=479001600.$$
+Besides, the last value of \verb!\Fct!, which is right the one obtained from calling the function, is assigned to a global integer variable \verb!\tempA! for use
+in other procedures. Finally, make the calling sequence
+$$\textmtt{\symbol{92}FACTORIAL\{k\}\symbol{92}the\symbol{92}Fct}$$
+to obtain and show up the value of $k!$. From these values we derive binomial coefficients by the formula
+$$\binom{m}{n}=\frac{m!}{n!(m-n)!}.$$
+A simple procedure that makes division of $m!$ by $n!$, then of the result by $(m-n)!$ can be performed by the control sequence
+\verb!\BINOMIAL! with two parameters as follows
+\begin{verbatim}
+\newcount\BINOM
+\newcount\temp\newcount\tmp
+\def\BINOMIAL#1#2{%
+\temp=#1\advance\temp by -#2
+\FACTORIAL{#1}
+\tmp=\tempA
+\FACTORIAL{\temp}
+\temp=\tempA
+\divide\tmp by \temp
+\FACTORIAL{#2}
+\temp=\tempA
+\divide\tmp by \temp\global\BINOM=\tmp}
+\end{verbatim}
+Again, the last value of \verb!\tmp! is assigned to a global integer variable \verb!\BINOM! for later use. Because the vector function of a B\'{e}zier
+curve of degree $6$ is only needed, so are the binomial coefficients \verb!\BINOMIAL{!$6$\verb!}{!$k$\verb!}!, $k=0,1,\ldots,6$.
+\subsubsection{Bernstein polynomials}
+The construction of Bernstein functions is based on an iterative multiplication of the same value $t$ by a given number $m$ of times,
+then the process is repeated with the value $1-t$ by a given number $n$ of times. The last result is multiplied by a variable that holds
+the value of $\binom{m+n}{m}$. We will use an integer variable \verb!\kc! to count times of multiplication for the same factor $t$ or $1-t$.
+The procedure of iterative multiplication \verb!\xmult! with one parameter $m$ or $n$ is a recursive one that is performed
+iteratively until \verb!\kc! reaches the value $m$ or $n$.
+\begin{verbatim}
+\newdimen\Xa\newdimen\Yb\newcount\kc
+\def\xmult#1{\ifnum\kc<#1\advance\kc by 1\Yb=\decimal\Xa\Yb\xmult{#1}
+ \else\relax\fi}
+\end{verbatim}
+Finally, the value of $t^m(1-t)^n$ that is hold by the variable \verb!\Yb! is multiplied by \verb!\BINOM!, the value $\binom{6}{m}$.
+Thus, Bernstein polynomials are given by the following macro \verb!\BERNSTEIN! with three parameters that hold values of
+$m$, $n$ and $t$, respectively.
+\begin{verbatim}
+\newdimen\BSTemp
+\def\BERNSTEIN#1#2#3{\Xa=#3pt\kc=0\Yb=1pt\xmult{#1}\kc=0\Xa=-\Xa
+\advance\Xa by 1pt\xmult{#2}\BINOMIAL{6}{#1}\global\BSTemp=\BINOM\Yb}
+\end{verbatim}
+Also, values of \verb!\BERNSTEIN! are assigned to a global variable.
+\subsubsection{Vector functions of a plane B\'{e}zier curve of degree $6$}
+We will construct here the vector function of a plane and closed B\'{e}zier curve with the control points
+$M_0(x_0,y_0)$, $M_1(x_1,y_1)$, \dots, $M_6(x_6,y_6)$ that is chosen in such a way that the curve is tangent to
+a line $(\Delta)$ at its initial point $M_0$. According to the mentioned properties of a B\'{e}zier curve, the requirements
+for the curve are satisfied when $M_6=M_0$ and $M_0$, $M_1$, $M_5$ are all on the line $(\Delta)$.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(0,0)(5,4.3)
+\psset{unit=0.6cm}
+\newcount\pos\def\drawpts#1#2{\newdimen\xrp\xrp=2pt\newdimen\yrp\yrp=2pt\advance\xrp by #1pt\advance\yrp by #2pt\psdot(\decimal\xrp,\decimal\yrp)
+\rput[rt](\decimal\xrp,\decimal\yrp){$M_{\the\pos}$}\advance\pos by 1}
+\drawpts{0}{0}\drawpts{-1.5}{2}\drawpts{2}{5}\drawpts{6}{3}\drawpts{5}{-1}\drawpts{1.5}{-2}
+\parametricplot[algebraic,linewidth=0.5pt]{0}{0.5}{\XBsix{2}{1}|\YBsix{2}{1}}
+\parametricplot[algebraic,linewidth=0.5pt]{0.5}{1}{\XBsix{2}{1}|\YBsix{2}{1}}
+\psline[linewidth=0.2pt](0.5,4)(3.5,0)
+\end{pspicture}
+\caption{A B\'{e}zier curve of degree $6$ with the required control points.}\label{Fig13}
+\end{figure}
+In case $n=6$, from (\ref{eqn9}) we derive the vector function $\mathbf{r}(t)$ with the two components
+\begin{equation}\label{eqn10}
+X(t)=\sum_{i=0}^6\binom{6}{i}t^i(1-t)^{6-i}x_i,\quad Y(t)=\sum_{i=0}^6\binom{6}{i}t^i(1-t)^{6-i}y_i.
+\end{equation}
+We first evaluate values of $X(t)$ by the procedures that just have been constructed, with a choice of $x_i$, $i=1,\ldots,6$, from a given $x_0$
+and the requirements of the B\'{e}zier curve as in Figure \ref{Fig13}. For example, we may take
+$$x_1=x_0-1.5,\quad x_2=x_0+2,\quad x_3=x_0+6,\quad x_4=x_0+5,\quad x_5=x_0+1.5,\quad x_6=x_0.$$
+Moreover, we may change the shape of the curve by taking a factor $\alpha$ for $X(t)$. In short, we will make a procedure to evaluate the sum of terms
+$\binom{6}{i}t^i(1-t)^{6-i}(\alpha x_i)$, $i=0,1,\ldots,6$. In fact, it is a procedure to add up values into a global variable \verb!\XBST! that is called
+by a macro \verb!\XBC! with three declaring parameters for $x_i$, $t$ and $\alpha$. The value of $\alpha$ is used last when being multiplied by a
+variable that holds $X(t)$. Such a procedure is suggested to be the following macro
+\begin{verbatim}
+\newdimen\Xrf\newdimen\Yrf
+\newdimen\XBST\newdimen\YBST
+\def\XBC#1#2#3{%
+\BERNSTEIN{0}{6}{#2}
+\Xrf=#1pt
+\XBST=\decimal\BSTemp\Xrf
+\BERNSTEIN{1}{5}{#2}
+\Xrf=#1pt\advance\Xrf by -1.5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{2}{4}{#2}
+\Xrf=#1pt\advance\Xrf by 2pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{3}{3}{#2}
+\Xrf=#1pt\advance\Xrf by 6pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{4}{2}{#2}
+\Xrf=#1pt\advance\Xrf by 5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{5}{1}{#2}
+\Xrf=#1pt\advance\Xrf by 1.5pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\BERNSTEIN{6}{0}{#2}
+\Xrf=#1pt
+\advance\XBST by \decimal\BSTemp\Xrf
+\global\XBST=#3\XBST}
+\end{verbatim}
+In the macro, a control sequence of the form \verb!\decimal\Xdim! is for obtaining the decimal value of a variable \verb!\Xdim! without units
+(\verb!pt!, by default). This can be defined by
+\begin{verbatim}
+\def\xch{\catcode`\p=12 \catcode`\t=12}\def\ych{\catcode`\p=11 \catcode`\t=11}
+\xch \def\dec#1pt{#1}\ych \gdef\decimal#1{\expandafter\dec \the#1}
+\end{verbatim}
+Besides, the last line in the definition of \verb!\XBC! (\verb!\global\XBST=#3\XBST!) signifies \verb!\XBST! is adjusted for multiplication by
+$\alpha$ when holding the current value of the sum $X(t)$. In Table \ref{bc-Table1}, some values
+of \verb!\XBC! are compared with those of a simpler procedure in Maple\footnote{\footnotesize Maple
+is a computer algebra system. It was first developed in 1980 by the Symbolic Computation Group at the University of
+Waterloo in Waterloo, Ontario, Canada. Maple supports numeric and symbolic computations
+and can be used as a programming language, which resembles Pascal.}.
+\begin{table}[htbp]
+\centering\begin{tabular}{|c|c|c|c|c|c|}\hline
+&$(-2.4,0.23,1.5)$&$(4.2,0.45,1.1)$&$(-3.4,0.7,1.24)$&$(-0.89,0.4,1.5)$&$(5.21,0.5,2.15)$\\ \hline
+\texttt{\symbol{92}XBC}&$\XBC{-2.4}{0.23}{1.5}\decimal\XBST$&$\XBC{4.2}{0.45}{1.1}\decimal\XBST$&$\XBC{-3.4}{0.7}{1.24}\decimal\XBST$&$\XBC{-0.89}{0.4}{1.5}\decimal\XBST$&$\XBC{5.21}{0.5}{2.15}\decimal\XBST$\\ \hline
+Maple&$-2.41044$&$8.13235$&$-0.13696$&$2.78628$&$18.76008$\\ \hline
+\end{tabular}
+\caption{A comparison between some values of \textmtt{\symbol{92}XBC} and those of a procedure in Maple.}\label{bc-Table1}
+\end{table}
+
+Likewise, from a given $y_0$, we may have a choice of $y_i$, $i=1,\ldots,6$, as follows
+$$y_1=y_0+2,\quad y_2=y_0+5,\quad y_3=y_0+3,\quad y_4=y_0-1,\quad y_5=y_0-2,\quad y_6=y_0.$$
+The macro \verb!\YBC! is constructed in a quite analogous way as for \verb!\XBC! to evaluate values of $Y(t)$ in (\ref{eqn10}),
+and the value $\beta Y(t)$ ($\beta$ is again an adjustment factor) is hold by a global variable \verb!\YBST!.
+
+\subsubsection{Partition of a simply connected plane domain by a rectangular grid}
+
+We consider here a simply connected plane domain $D$ surrounded by a B\'{e}zier curve of degree $6$ that will be depicted by
+the procedure \verb!\NetDraw!. This is called together with its five parameters whose values are assigned to the five local variables
+with their following meaning:
+\begin{align*}
+\texttt{\symbol{92}CellNum:}&\text{ The number of horizontal and vertical cells of the grid.}\\
+\texttt{\symbol{92}Xref:}&\text{ The value of $x_0$.}\\
+\texttt{\symbol{92}Yref:}&\text{ The value of $y_0$.}\\
+\texttt{\symbol{92}Xfact:}&\text{ The value of $\alpha$.}\\
+\texttt{\symbol{92}Yfact:}&\text{ The value of $\beta$.}
+\end{align*}
+We denote by $R$ a rectangular domain containing $D$ and having edges parallel to the coordinate axes.
+A grid of rectangular cells will be depicted on $R$. According to the given values of $x_0$, $y_0$, $\alpha$ and $\beta$, the vertices of $R$
+can be chosen as the points $(\verb!\XMin!,\verb!\YMax!)$, $(\verb!\XMax!,\verb!\YMax!)$, $(\verb!\XMax!,\verb!\YMin!)$, $(\verb!\XMin!,\verb!\YMin!)$, where
+\begin{align*}
+\textmtt{\symbol{92}XMin}&=\alpha(\textmtt{\symbol{92}Xref}-1.5),&&\textmtt{\symbol{92}XMax}=\alpha(\textmtt{\symbol{92}Xref}+6),\\
+\textmtt{\symbol{92}YMin}&=\beta(\textmtt{\symbol{92}Yref}-2),&&\textmtt{\symbol{92}YMax}=\beta(\texttt{\symbol{92}Yref}+5).
+\end{align*}
+Then, the horizontal step size \verb!\Xsize! and the vertical step
+size \verb!\Ysize! may be taken as
+$$\mtt\\\texttt{Xsize}=\frac{\mtt\\\texttt{XMax}-\mtt\\\texttt{XMin}}{\mtt\\\texttt{CellNum}},\quad
+\mtt\\\texttt{Ysize}=\frac{\mtt\\\texttt{YMax}-\mtt\\\texttt{YMin}}{\mtt\\\texttt{CellNum}}.$$
+
+At first, the grid is made by using the structure \verb!\multido! to draw vertical and horizontal lines whose equations are
+$$x=\texttt{\symbol{92}XMin}+i\texttt{\symbol{92}Xsize},\quad
+y=\texttt{\symbol{92}YMin}+i\texttt{\symbol{92}Ysize},\quad i=0,\ldots,\texttt{\symbol{92}CellNum}.$$
+Next, the B\'{e}zier curve is depicted by the command
+$$\textmtt{\symbol{92}parametricplot[algebraic,fillstyle=solid]\{$0$\}\{$1$\}\{$\alpha X(t)$|$\beta Y(t)$\}}$$
+and it is approximated by the sequence of points $(X_i,Y_i)$, $i=1,\ldots,N$, where $X_i$ and $Y_i$ are given from
+the calling sequences
+$$\textmtt{\symbol{92}XBC\{\symbol{92}XRef\}\{$t_i$\}\{\symbol{92}Xfact\}},\quad
+\textmtt{\symbol{92}YBC\{\symbol{92}YRef\}\{$t_i$\}\{\symbol{92}Yfact\}}.$$
+
+Finally, the most important algorithm is to determine cells that have points in common with the B\'{e}zier curve,
+and to color them. The chosen ``filter'' method here can be described as follows: for each point $(X_i,Y_i)$ of the approximate sequence,
+$i=1,\ldots, N$, we examine cells from left to right in horizontal direction, and from below to above in vertical direction. As soon as
+being found, the cell containing $(X_i,Y_i)$ is specifically colored by the command \textmtt{\mtt\\pspolygon[fillstyle=solid,$\ldots$]} passing its four
+vertices; then, we examine the next point $(X_{i+1},Y_{i+1})$, and so on. Actually, a structure of three nested \verb!\multido! loops
+is used to perform this filter method, and the loop for counting points $(X_i,Y_i)$ is the most outer one. The algorithm to examine if
+a cell contains $(X_i,Y_i)$ may have the form of
+\begin{verbatim}
+ \ifdim\YBST<y\relax\else\advance y by \Ysize
+ \ifdim\YBST>y\relax\else
+ \ifdim\XBST<x\relax\else\advance x by \Xsize
+ \ifdim\XBST>x\relax\else
+ \pspolygon[fillstyle=solid,fillcolor=red]
+ (x,y)(x+\Xsize,y)(x+\Xsize,y+\Ysize)(x,y+\Ysize)(x,y)\relax
+ \fi\fi\fi\fi
+\end{verbatim}
+The single characters ``\verb!x!'', ``\verb!y!'' and the opertation ``\verb!+!'' will be replaced appropriately in the procedure \verb!\NetDraw! below.
+For increasingly chosen values of $N$, we may know if the set of cells having points in common with the curve can cover the curve itself?
+On the other hand, to increase the number of approximate points is corresponding to reduce the increment in the most outer loop \verb!\multido!.
+For instance, if we take $N=100$, then the variable \verb!\nz! in the loop should be declared as $\texttt{\mtt\\nz}=0.00+0.01$ because
+$t_i\in[0,1]$.
+
+In summary, to illustrate a partition of a simply connected plane domain, we can apply the following procedure \verb!\NetDraw!. As mentioned above,
+step by step, \verb!\NetDraw! can: draw the boundary of a plane domain $D$ by a B\'{e}zier curve of degree $6$, draw a partition of a rectangle $R$ containing $D$
+by a grid of rectangular cells, and color cells having points in common with the boundary of $D$.
+\bigskip
+%\vskip2ex
+\hrule
+\begin{verbatim}
+\def\NetDraw#1#2#3#4#5{%
+\newcount\CellNum
+\newdimen\XRef
+\newdimen\YRef
+\newdimen\Xfact
+\newdimen\Yfact
+\newdimen\XMin
+\newdimen\XMax
+\newdimen\YMin
+\newdimen\YMax
+\newdimen\Xsize
+\newdimen\Ysize
+\newdimen\tempx
+\newdimen\tempy
+\CellNum=#1
+\XRef=#2pt
+\YRef=#3pt
+\Xfact=#4pt
+\Yfact=#5pt
+\XMin=\decimal\Xfact\XRef \advance\XMin by -1.50\Xfact
+\XMax=\decimal\Xfact\XRef \advance\XMax by 6.00\Xfact
+\YMin=\decimal\Yfact\YRef \advance\YMin by -2.00\Yfact
+\YMax=\decimal\Yfact\YRef \advance\YMax by 5.00\Yfact
+\Xsize=\XMax \advance\Xsize by -\XMin \divide\Xsize by \CellNum
+\Ysize=\YMax \advance\Ysize by -\YMin \divide\Ysize by \CellNum
+\parametricplot[algebraic,fillstyle=solid,fillcolor=yellow!80,plotpoints=200,
+linewidth=0.5pt]{0}{1}{\XBsix{\decimal\XRef}{\decimal\Xfact}|
+\YBsix{\decimal\YRef}{\decimal\Yfact}}
+\multido{\nz=0.00+0.005}{200}{\XBC{\decimal\XRef}{\nz}{\decimal\Xfact}
+\YBC{\decimal\YRef}{\nz}{\decimal\Yfact}
+\multido{\nx=\decimal\XMin+\decimal\Xsize}{\the\CellNum}
+{\tempx=\nx pt\multido{\ny=\decimal\YMin+\decimal\Ysize}{\the\CellNum}
+{\tempy=\ny pt\ifdim\YBST<\tempy\relax\else\advance\tempy by \Ysize%
+ \ifdim\YBST>\tempy\relax\else
+ \ifdim\XBST<\tempx\relax\else\advance\tempx by \Xsize
+ \ifdim\XBST>\tempx\relax\else
+ \pspolygon[fillstyle=solid,fillcolor=blue!90,linecolor=black,
+ linewidth=0.2pt]
+ (\nx,\ny)(\decimal\tempx,\ny)(\decimal\tempx,\decimal\tempy)
+ (\nx,\decimal\tempy)(\nx,\ny)\relax\fi\fi\fi\fi}
+}}
+\advance\CellNum by 1
+\multido{\nx=\decimal\XMin+\decimal\Xsize}{\the\CellNum}
+{\psline[linewidth=0.2pt](\nx,\decimal\YMax)(\nx,\decimal\YMin)}
+\multido{\ny=\decimal\YMin+\decimal\Ysize}{\the\CellNum}
+{\psline[linewidth=0.2pt](\decimal\XMin,\ny)(\decimal\XMax,\ny)}
+\parametricplot[algebraic,linecolor=white,plotpoints=200,linewidth=0.5pt]{0}{1}
+{\XBsix{\decimal\XRef}{\decimal\Xfact}|\YBsix{\decimal\YRef}{\decimal\Yfact}}}
+\end{verbatim}\hrule\bigskip
+
+In the definition of \verb!\NetDraw!, the expressions $\alpha X(t)$, $\beta Y(t)$ are declared in the \verb!algebraic! form by the macros \verb!\XBsix!,
+\verb!\YBsix! with two parameters that hold values of $x_0,\alpha$ and $y_0,\beta$, respectively. These macros are given by
+the following definitions:
+\begin{verbatim}
+\def\XBsix#1#2{%
+(1-t)^6*(#1)*(#2)+6*t*(1-t)^5*(#1-1.5)*(#2)+15*t^2*(1-t)^4*(#1+2)*(#2)+
+20*t^3*(1-t)^3*(#1+6)*(#2)+15*t^4*(1-t)^2*(#1+5)*(#2)+
+6*t^5*(1-t)*(#1+1.5)*(#2)+t^6*(#1)*(#2)}
+\def\YBsix#1#2{%
+(1-t)^6*(#1)*(#2)+6*t*(1-t)^5*(#1+2)*(#2)+15*t^2*(1-t)^4*(#1+5)*(#2)+
+20*t^3*(1-t)^3*(#1+3)*(#2)+15*t^4*(1-t)^2*(#1-1)*(#2)+
+6*t^5*(1-t)*(#1-2)*(#2)+t^6*(#1)*(#2)}
+\end{verbatim}
+\subsection{Examples}
+Firstly, let us see the effect of change for the shape of a domain when adjusting its boundary by taking different values of $\alpha$ and $\beta$. The
+calling sequence for this purpose may have the form of
+\begin{align*}
+&\textmtt{\mtt\\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]\{$0$\}\{$1$\}}\\
+&\textmtt{\mtt\{XBsix\{$x_0$\}\{$\alpha$\}|\mtt\\YBsix\{$y_0$\}\{$\beta$\}\mtt\}}
+\end{align*}
+and its result is given in Figure \ref{Fig14}.
+\begin{figure}[htbp]
+\centering\begin{pspicture}(0,0.5)(3.5,3)
+\psset{unit=12pt}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}{\XBsix{2}{1.5}|\YBsix{2}{1.5}}
+\end{pspicture}
+\begin{pspicture}(0,0.5)(5,3.5)
+\psset{unit=12pt}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}{\XBsix{2}{2}|\YBsix{2}{1.5}}
+\end{pspicture}
+\begin{pspicture}(0,1)(4,3.5)
+\psset{unit=12pt}
+\parametricplot[algebraic,plotpoints=200,linewidth=0.5pt]{0}{1}{\XBsix{2}{1.5}|\YBsix{2}{2}}
+\end{pspicture}
+\caption{From left to right, corresponding to the couple of values:
+$\alpha=2,\,\beta=2$; $\alpha=2.5,\,\beta=2$; $\alpha=2,\,\beta=2.5$.}\label{Fig14}
+\end{figure}
+
+The Table \ref{bc-table2} below provides three partitions of a domain $D$ with cells that decrease in size. In each case, \verb!\NetDraw! can
+determine the cells that have points in common with the boundary curve and color them. The calling sequence here
+takes a simple form
+$$\textmtt{\mtt\\NetDraw\{$c$\}\{$x_0$\}\{$y_0$\}\{$\alpha$\}\{$\beta$\}}$$
+The numerical argument $c$ is assigned to the local variable \verb!\CellNum!. The number of approximate points $(X_i,Y_i)$ for the boundary curve
+is chosen to be $200$, by default, corresponding to the increment $\Delta\mtt{z}=0.005$. The number $N$ can be made larger and the filter procedure
+for determining required cells may be more exact. In Table \ref{bc-table2}, the B\'{e}zier curves are depicted with the choice
+$x_0=y_0=\alpha=\beta=2$.
+\begin{table}[htbp]
+\centering\begin{tabular}{cc}
+\includegraphics[width=6cm]{b6of1}&\includegraphics[width=6cm]{b6of2}\\
+\includegraphics[width=6cm]{b6of3}&\includegraphics[width=6cm]{b6of4}
+\end{tabular}
+\caption{The partitions of $D$ with $c=18$, $c=36$ and $c=63$.}\label{bc-table2}
+\end{table}
+
+\acknw
+I am very grateful to
+\begin{itemize}
+\item Timothy Van Zandt, Herbert Vo\ss, Dominique Rodriguez and Michael Sharpe for helping me with
+their great works on \texttt{PSTricks}.
+\item H\`an Th\hantt\rlap\accentcircflx\ Th\`anh for helping me with his pdf\hskip.03em\LaTeX\ program.
+\item Robert Fuster for his very useful package \texttt{calculator}.
+\end{itemize}
+\begin{thebibliography}{10}
+\bibitem{one} Dominique Rodriguez, Michael Sharpe \&\ Herbert Vo\ss. \textsl{\texttt{pstricks-add}: Additional Macros for PSTricks\/}.
+Version 3.60,
+\url{http://ctan.org/tex-archive/graphics/pstricks/contrib}, 2013
+\bibitem{two} Timothy Van Zandt, Michael Sharpe \&\ Herbert Vo\ss. \textsl{\texttt{pst-node}: Nodes and node connections}.
+Version 1.29,
+\url{http://ctan.org/tex-archive/graphics/pstricks/contrib}, 2013
+\bibitem{three} Helmut Kopka \&\ Patrick W. Daly. \textsl{Guide to \LaTeX \/}.
+Addison-Wesley, Fourth Edition, 2004, ISBN 0321173856
+\bibitem{four} Timothy Van Zandt. \textsl{User's Guide\/}. Version 1.5,\\
+\url{http://ctan.org/tex-archive/graphics/pstricks/base}, 2007
+\bibitem{five}Eitan M. Gurari. \textsl{Writing With \TeX \/}, McGraw-Hill, Inc., 1994, ISBN 0-07-025207-6
+\bibitem{six} Robert Fuster. \textsl{\texttt{calculator-calculus}: Scientific Calculations With \LaTeX \/}. Version 1.0a,
+\url{http://ctan.org/tex-archive/macros/latex/contrib/calculator}, 2012
+\end{thebibliography}
+
+\end{document}
+\begin{thebibliography}{10}
+\bibitem{one} Dominique Rodriguez, Michael Sharpe \&\ Herbert Vo\ss. \textsl{\texttt{pstricks-add}: Additional Macros for PSTricks\/}.
+Version 3.60,
+\url{http://ctan.org/tex-archive/graphics/pstricks/contrib}, 2013
+\bibitem{two} Timothy Van Zandt, Michael Sharpe \&\ Herbert Vo\ss. \textsl{\texttt{pst-node}: Nodes and node connections}.
+Version 1.29,
+\url{http://ctan.org/tex-archive/graphics/pstricks/contrib}, 2013
+\bibitem{three} Helmut Kopka \&\ Patrick W. Daly. \textsl{Guide to \LaTeX \/}.
+Addison-Wesley, Fourth Edition, 2004, ISBN 0321173856
+\bibitem{four} Timothy Van Zandt. \textsl{User's Guide\/}. Version 1.5,\\
+\url{http://ctan.org/tex-archive/graphics/pstricks/base}, 2007
+\bibitem{five}Eitan M. Gurari. \textsl{Writing With \TeX \/}, McGraw-Hill, Inc., 1994, ISBN 0-07-025207-6
+\bibitem{six} Robert Fuster. \textsl{\texttt{calculator-calculus}: Scientific Calculations With \LaTeX \/}. Version 1.0a,
+\url{http://ctan.org/tex-archive/macros/latex/contrib/calculator}, 2012
+\end{thebibliography}
diff --git a/info/pstricks_calcnotes/For_Ps_Output/b6of1.eps b/info/pstricks_calcnotes/For_Ps_Output/b6of1.eps
new file mode 100644
index 0000000000..afdba1de51
--- /dev/null
+++ b/info/pstricks_calcnotes/For_Ps_Output/b6of1.eps
@@ -0,0 +1,11111 @@
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+% $Id: pstricks.pro 801 2013-07-09 18:10:41Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 1.17, 2013/07/08
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+% Define the follwing gs-functions if not known, eg when using distiller
+%
+systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if
+systemdict /.setblendmode known not {/.setblendmode { pop } def } if
+systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
+%
+/tx@Dict 200 dict def % the main PSTricks dictionary
+tx@Dict begin
+/ADict 25 dict def % The arrow dictionary
+/CM { matrix currentmatrix } bind def
+/SLW /setlinewidth load def
+/CLW /currentlinewidth load def
+/CP /currentpoint load def
+/ED { exch def } bind def
+/L /lineto load def
+/T /translate load def
+/TMatrix { } def
+/RAngle { 0 } def
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+/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter)
+/Div { dup 0 eq { pop } { div } ifelse } def % control the division
+/tan { dup cos abs 1.e-10 lt
+ { pop 1.e10 } % return 1.e10 as infinit
+ { dup sin exch cos div } ifelse % default sin/cos
+} def
+/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees
+/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root
+ pop pop 0 }{ sqrt exch atan} ifelse } def
+/Acos2 { 2 dict begin
+ /x ED /y ED
+ y abs 1.0e-20 lt { 1.0e30 } if
+ x y div
+ dup dup mul neg 1 add dup 0 lt { % arc cos needs two values x,y
+ pop pop 0 }{ sqrt exch atan} ifelse
+ y 0 lt { 180 add } if
+} def
+/NET { neg exch neg exch T } def % change coordinate system to the negative one
+/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter
+/Pyth2 { % Pythagoras, xA yA xB yB
+ 3 -1 roll % xA xB yB yA
+ sub % xA xB yB-yA
+ 3 1 roll % yB-yA xA xB
+ sub % yB-yA xA-xB
+ Pyth } def
+/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian
+/Rand { rand 4294967295 div } def % a real random number
+%----------------- hv added 20050516 ---------------
+/PiDiv2 1.57079632680 def
+/Pi 3.14159265359 def
+/TwoPi 6.28318530718 def
+/Euler 2.71828182846 def
+%/e Euler bind def
+%
+/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees
+/DegtoRad { Pi mul 180 div } bind def % viceversa
+%
+/startGlobal { true setglobal globaldict begin } bind def
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+/pssetRGBcolor /setrgbcolor load def
+/pssetCMYKcolor /setcmykcolor load def
+/pssetGraycolor /setgray load def
+%
+%----------------- hv end---------------------------
+/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def
+%
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+ { /y ED /x ED PathLength@ }
+ {}
+ { /y y2 def /x x2 def PathLength@ }
+ /pathforall load stopped { pop pop pop pop } if
+ z
+} def
+%
+/STP { .996264 dup scale } def % BP/PT scaling
+/STV { SDict begin normalscale end STP } def %
+%
+/DashLine {
+ dup 0 gt
+ { /a .5 def PathLength exch div }
+ { pop /a 1 def PathLength } ifelse
+ /b ED % pattern should fit evenly in b
+ dup /X ED % pattern array
+ 0 get /y ED % length of first black segment
+ /z 0 X {add} forall def % length of the full pattern
+ %% Computation of the scaling factor as described by van Zandt:
+ b a .5 sub 2 mul y mul sub z Div round
+ z mul a .5 sub 2 mul y mul add b exch Div
+ %%%% scaling factor on stack.
+ /z ED %% now, z is the scaling factor
+ false % for the length test below
+ X { z mul } forall X astore %% modification TN 04-08-07
+ %%% Checking whether at least one dash in X has positive length:
+ {0 gt or} forall
+ { X 1 a sub y mul }
+ { [ 1 0 ] 0 }
+ ifelse
+ setdash stroke
+} def
+%
+/DotLine {
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+%
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+ y2 y1 sub a div 2 add cvi /Ny ED
+ x2 x1 sub a div 2 add cvi /Nx ED
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+ /kite_colour ED
+ /dart_colour ED
+ clip
+
+ newpath
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+ 6
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+ /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
+ /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
+ /f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio
+ /l{L f mul}bind def %%%% Short side length l = L*f
+ /Ll{L l add}bind def %%%% Ll = L + l
+ /c{36 cos L mul}bind def %%%% c = L*cos(36)
+ /s{36 sin L mul}bind def %%%% s = L*sin(36)
+ /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
+ 0 setlinewidth stroke grestore border_colour stroke } bind def
+ /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
+ Ll 0 translate 144 rotate kite grestore }
+ { kite_colour L draw_tile }ifelse
+ pop } bind def
+ /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
+ -144 rotate Ll neg 0 translate half_dart grestore }
+ { dart_colour l draw_tile }ifelse
+ pop } bind def
+ /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
+ border_width setlinewidth 1 setlinejoin 1 setlinecap
+% 450 0 translate
+ dup f exch neg exp dup scale
+ 5 {kite 72 rotate } repeat stroke
+ grestore
+} def
+%
+%
+/TruchetFill { % on stack: scaling factor
+ 10 dict begin
+ dup dup scale
+ 1 exch div round /penroseFactor ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ /ma a neg def
+ /ha a 2 div def
+ /mha ha neg def
+ /tile {
+ rand dup 2 idiv 2 mul eq { 90 rotate } if
+ mha mha moveto ha mha lineto
+ ha ha lineto mha ha lineto
+% closepath .1 setlinewidth stroke
+ contents
+ } def
+ /contents{
+ 0 ha moveto ha 0 lineto
+ 0 mha moveto mha 0 lineto
+% 1 setlinewidth stroke
+ } def
+ /dotiling {
+ f ma mul a f a mul {
+ /i exch def
+ f ma mul a f a mul {
+ /j exch def
+ gsave i j translate
+ tile stroke grestore
+ } for
+ } for
+ } def
+%
+ /f 3 def
+ 5 srand dotiling
+ end % local user dict
+} def
+%
+/BeginArrow {
+ ADict begin % hold it local, for end see EndArrow
+ /@mtrx CM def
+ gsave
+ 2 copy T
+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
+%
+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
+%
+/Arrow {
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
+%
+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
+ gsave fill grestore
+} def
+%
+/Tbar {
+ CLW mul add /z ED
+ z -2 div CLW 2 div moveto
+ z 0 rlineto stroke
+ 0 CLW moveto
+} def
+%
+/Bracket {
+ CLW mul add dup CLW sub 2 div
+ /x ED mul CLW add /y ED /z CLW 2 div def
+ x neg y moveto
+ x neg CLW 2 div L x CLW 2 div L x y L stroke
+ 0 CLW moveto
+} def
+%
+/RoundBracket {
+ CLW mul add dup 2 div
+ /x ED mul /y ED /mtrx CM def
+ 0 CLW 2 div T x y mul 0 ne { x y scale } if
+ 1 1 moveto
+ .85 .5 .35 0 0 0 curveto
+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
+ /b ED % the color definition
+ 0 z DS SD
+ b { 0 z DS CLW sub SD } if
+ 0 DS z add CLW 4 div sub
+ moveto
+} def
+%
+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+ load } if ] cvx newpath 3 1 roll T exec } def
+%
+/NArray { % holds the coordinates and on top of stack the showpoints boolean
+ /showpoints ED
+ counttomark 2 div dup cvi /n ED % n 2 div on stack
+ n eq not { exch pop } if % even numbers of points? delete one
+ ] aload /Points ED
+ showpoints not { Points aload pop } if
+% { ] aload /Points ED }
+% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
+} def
+%
+/Line {
+ NArray n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
+ n { Lineto } repeat
+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
+%
+/LineToYAxis {
+ /Ox ED % Save the x origin value
+ NArray % all x-y pairs on stack
+ n { 2 copy moveto % go to current point
+ Ox exch Lineto % line to y-axis
+ pop % delete old x-value
+ } repeat
+} def
+%
+/LineToXAxis{
+ /Oy ED % Save the y origin value
+ NArray % all x-y pairs on stack
+ n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if
+ ArrowA
+ /n n 2 sub def
+ CP 2 copy moveto pop Oy Lineto
+ n { 2 copy moveto pop Oy Lineto } repeat
+ CP
+ 4 2 roll
+ ArrowB
+ 2 copy moveto pop Oy
+ L
+ pop pop } if
+} def
+%
+/Arcto {
+ /a [ 6 -2 roll ] cvx def
+ a r
+ /arcto load stopped { 5 } { 4 } ifelse { pop } repeat
+ a
+} def
+%
+/CheckClosed {
+ dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
+ and { pop pop /n n 1 sub def } if
+} def
+%
+/Polygon {
+ NArray n 2 eq { 0 0 /n 3 def } if
+ n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ n 2 mul -2 roll
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ n { Lineto } repeat
+ x1 y1 x0 y0 6 4 roll Lineto
+ Lineto pop pop closepath } ifelse
+} def
+%
+/SymbolPolygon { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 add /m ED
+ 2 copy m 2 roll % copy last two
+ m 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+ /nSym XYLength SymStep Div cvi def
+ /Shift Symbol stringwidth pop 2 Div def
+ /deltaX XLength nSym Div def
+ /deltaY YLength nSym Div def
+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 801 2013-07-09 18:10:41Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
+%
+/Simpson { % on stack must be a b M --- simple version ---
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+%
+/LogGamma { 5 dict begin % z on stack
+ /z ED
+ /sum 0 def
+ /k 1 def
+ {
+ z k div dup 1 add ln sub dup
+ abs eps8 lt { pop exit } if
+ sum add /sum exch def
+ /k k 1 add def
+ } loop
+ sum z ln sub CEuler z mul sub
+ end
+} def
+%
+/ChebyshevT { 5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 2 k mul MoverN mul
+ add
+ } for
+ end
+} def
+%
+/ChebyshevU {5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 1 add 2 k mul 1 add MoverN mul
+ add
+ } for
+ end
+} def
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+%
+end
+
+%%EndProcSet
+%%BeginProcSet: pst-3dplot.pro 0 0
+%% $Id: pst-3dplot.pro 236 2009-12-31 08:59:43Z herbert $
+%%
+%% This is file `pst-3dplot.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-3dplot.tex'
+%%
+%% Herbert Voss <voss _at_ PSTricks.de>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-3dplot' is a PSTricks package to draw 3d curves and graphical objects
+%%
+%%
+%% version 0.30 / 2010-01-01 Herbert Voss <voss _at_ PSTricks.de>
+%% with contributions of Darrell Lamm <darrell.lamm _at_ gtri.gatech.edu<
+%%
+%
+/tx@3DPlotDict 200 dict def
+tx@3DPlotDict begin
+%
+/printDot { gsave 2 copy 2 0 360 arc fill stroke grestore } def
+%
+/saveCoor {
+ dzUnit mul /z ED
+ dyUnit mul /y ED
+ dxUnit mul /x ED
+} def
+%
+/ConvertTo2D {
+ RotatePoint
+ 1 { % dummy loop, will run only 1 time, allows exit
+ coorType 0 le { % the default |
+ /x2D x leftHanded not { neg } if Alpha cos mul y Alpha sin mul add def % /\ co system
+ /y2D x leftHanded { neg } if Alpha sin mul y Alpha cos mul add neg Beta sin mul z Beta cos mul add def
+ exit } if
+ coorType 1 le {
+ /x2D y x Alpha 90 sub sin mul sub def % |/_ co system, no shortened x axis
+ /y2D z x Alpha 90 sub cos mul sub def
+ exit } if
+ coorType 2 le { % coorType |/_ with a 1/sqrt(2) shortend x-axis and 135 degrees
+ /x2D y x 0.5 mul sub def
+ /y2D z x 0.5 mul sub def
+ exit } if
+ coorType 3 le { % coorType |/_ with a 1/sqrt(2) shortend x-axis and 135 degrees
+ /x2D y x -0.5 mul sub def
+ /y2D z x -0.5 mul sub def
+ exit } if
+ coorType 4 le { % Normalbild in Trimetrie Skalierung so, dass coorType2
+ /x2D x -0.5 mul y 1 mul add def
+ /y2D x -0.5 mul y -0.25 mul add z 1 mul add def
+ exit } if
+ } repeat
+} def
+%
+/Conv3D2D { /z ED /y ED /x ED ConvertTo2D x2D y2D } def
+%
+/ConvertToCartesian {
+ /latitude exch def
+ /longitude exch def
+ /Radius exch def
+ 1 { % dummy loop, will run only 1 time, allows exit
+ SphericalCoorType 0 le { % the default |
+ /z { Radius latitude sin mul } def
+ /x { Radius longitude cos mul latitude cos mul } def
+ /y { Radius longitude sin mul latitude cos mul } def
+ exit } if
+ SphericalCoorType 2 le {
+ /z { Radius longitude cos mul } def
+ /x { Radius longitude sin mul latitude cos mul} def
+ /y { Radius longitude sin mul latitude sin mul } def
+ exit } if
+ } repeat
+} def
+%
+/ConvCylToCartesian { % r phi h -> x y z
+ 3 1 roll % h r phi
+ /Phi ED
+ /Radius ED % h->z on stack
+ Radius Phi cos mul exch % x z
+ Radius Phi sin mul exch % x y z
+} def
+%
+/SphericalTo2D {
+ x y z ConvertToCartesian ConvertTo2D
+} def
+%
+/CylinderTo2D { % r phi h
+ x y z ConvCylToCartesian ConvertTo2D
+} def
+%
+/convertStackTo2D {
+ counttomark
+ /n ED /n3 n 3 div cvi def
+ n3 {
+ n -3 roll
+ SphericalCoor { ConvertToCartesian } { saveCoor } ifelse
+ ConvertTo2D
+ x2D xUnit y2D yUnit
+ /n n 1 sub def
+ } repeat
+} def
+%
+% the angle in the parameter equation for an ellipse is not proportional to the real angle!
+% phi=atan(b*tan(angle)/a)+floor(angle/180+0.5)*180
+%
+/getPhi { % on stack: vecA vecB angle
+ 3 dict begin
+ /angle exch def /vecB exch def /vecA exch def
+ angle cvi 90 mod 0 eq { angle } { vecA angle tan mul vecB atan
+ angle 180 div .5 add floor 180 mul add } ifelse
+ end
+} def
+%
+/RotSet (set ) def
+%
+/eulerRotation false def
+% Matrix multiplication procedure
+/matmul {
+
+ /M@tMulDict 20 dict def
+ M@tMulDict begin
+ /m2 ED
+ /m1 ED
+ m1 dup length 2 sub 2 getinterval aload pop
+ /col1max ED
+ /row1max ED
+ m2 dup length 2 sub 2 getinterval aload pop
+ /col2max ED
+ /row2max ED
+ /m3 row1max col2max mul 2 add array def
+ m3 dup length 2 sub row1max col2max 2 array astore putinterval
+ 0 1 row1max 1 sub {
+ /row ED
+ 0 1 col2max 1 sub {
+ /col ED
+ /sum 0 def
+ 0 1 col1max 1 sub{
+ /rowcol ED
+ sum
+ m1 row col1max mul rowcol add get
+ m2 rowcol col2max mul col add get
+ mul add
+ /sum ED
+ } for
+ m3 row col2max mul col add sum put
+ } for
+ } for
+ m3
+ end % end of M@tMulDict
+
+} def
+%
+/SetMQuaternion {
+
+ /MnewTOold 11 array def
+
+ /Qu@ternionDict 30 dict def
+ Qu@ternionDict begin
+
+ /normRotVec xRotVec yRotVec zRotVec 3 array astore VecNorm def
+ normRotVec 0 gt
+ {/xRotVecNorm xRotVec normRotVec div def
+ /yRotVecNorm yRotVec normRotVec div def
+ /zRotVecNorm zRotVec normRotVec div def
+ RotAngle}
+ {/xRotVecNorm 1 def
+ /yRotVecNorm 0 def
+ /zRotVecNorm 0 def
+ 0} ifelse
+
+ 2 div dup
+ /q0 exch cos def
+ sin dup dup
+ /q1 exch xRotVecNorm mul def
+ /q2 exch yRotVecNorm mul def
+ /q3 exch zRotVecNorm mul def
+
+ /q0q0 q0 q0 mul def
+ /q0q1 q0 q1 mul def
+ /q0q2 q0 q2 mul def
+ /q0q3 q0 q3 mul def
+
+ /q1q1 q1 q1 mul def
+ /q1q2 q1 q2 mul def
+ /q1q3 q1 q3 mul def
+
+ /q2q2 q2 q2 mul def
+ /q2q3 q2 q3 mul def
+
+ /q3q3 q3 q3 mul def
+
+ MnewTOold 0 q0q0 q1q1 add q2q2 sub q3q3 sub put
+ MnewTOold 1 q1q2 q0q3 sub 2 mul put
+ MnewTOold 2 q1q3 q0q2 add 2 mul put
+
+ MnewTOold 3 q1q2 q0q3 add 2 mul put
+ MnewTOold 4 q0q0 q1q1 sub q2q2 add q3q3 sub put
+ MnewTOold 5 q2q3 q0q1 sub 2 mul put
+
+ MnewTOold 6 q1q3 q0q2 sub 2 mul put
+ MnewTOold 7 q2q3 q0q1 add 2 mul put
+ MnewTOold 8 q0q0 q1q1 sub q2q2 sub q3q3 add put
+
+ MnewTOold 9 3 put
+ MnewTOold 10 3 put
+
+ end % end of Qu@ternionDict
+
+} def
+%
+/SetMxyz {
+ 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 3 3 11 array astore /MnewTOold ED
+ RotSequence cvx exec % Now create a new MnewTOold using xyz, etc.
+} def
+%
+/ConcatMQuaternion {
+ MnewTOold % Push onto stack
+ SetMQuaternion % Uses [xyz]RotVec and RotAngle to make MnewToOld
+ MnewTOold matmul /MnewTOold ED
+} def
+%
+/ConcatMxyz {
+ MnewTOold % Push onto stack
+ SetMxyz % Uses RotX, etc. to set MnewTOold
+ MnewTOold matmul /MnewTOold ED
+} def
+%
+/RotatePoint{
+ MnewTOold x y z 3 1 5 array astore matmul
+ 0 3 getinterval aload pop
+ /z ED
+ /y ED
+ /x ED
+} def
+%
+/makeMoldTOnew {
+ /MoldTOnew 11 array def
+ MoldTOnew 0 MnewTOold 0 get put
+ MoldTOnew 1 MnewTOold 3 get put
+ MoldTOnew 2 MnewTOold 6 get put
+ MoldTOnew 3 MnewTOold 1 get put
+ MoldTOnew 4 MnewTOold 4 get put
+ MoldTOnew 5 MnewTOold 7 get put
+ MoldTOnew 6 MnewTOold 2 get put
+ MoldTOnew 7 MnewTOold 5 get put
+ MoldTOnew 8 MnewTOold 8 get put
+ MoldTOnew 9 3 put
+ MoldTOnew 10 3 put
+} def
+%
+/RotXaxis {
+ eulerRotation
+ {1 0 0}
+ {makeMoldTOnew MoldTOnew 1 0 0 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotX def
+ ConcatMQuaternion
+} def
+/RotYaxis {
+ eulerRotation
+ {0 1 0}
+ {makeMoldTOnew MoldTOnew 0 1 0 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotY def
+ ConcatMQuaternion
+} def
+/RotZaxis {
+ eulerRotation
+ {0 0 1}
+ {makeMoldTOnew MoldTOnew 0 0 1 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotZ def
+ ConcatMQuaternion
+} def
+/xyz { RotXaxis RotYaxis RotZaxis } def
+/yxz { RotYaxis RotXaxis RotZaxis } def
+/yzx { RotYaxis RotZaxis RotXaxis } def
+/xzy { RotXaxis RotZaxis RotYaxis } def
+/zxy { RotZaxis RotXaxis RotYaxis } def
+/zyx { RotZaxis RotYaxis RotXaxis } def
+/quaternion { } def % Null
+%
+/VecNorm { 0 exch { dup mul add } forall sqrt } def
+%
+/UnitVec { % on stack is [a]; returns a vector with [a][a]/|a|=1
+ dup VecNorm /norm ED
+ norm 0 lt {/norm 0 def} if
+ { norm div } forall 3 array astore } def
+%
+/AxB { % on the stack are the two vectors [a][b]
+ aload pop /b3 ED /b2 ED /b1 ED
+ aload pop /a3 ED /a2 ED /a1 ED
+ a2 b3 mul a3 b2 mul sub
+ a3 b1 mul a1 b3 mul sub
+ a1 b2 mul a2 b1 mul sub
+ 3 array astore } def
+%
+/AaddB { % on the stack are the two vectors [a][b]
+ aload pop /b3 ED /b2 ED /b1 ED
+ aload pop /a3 ED /a2 ED /a1 ED
+ a1 b1 add a2 b2 add a3 b3 add
+ 3 array astore } def
+%
+/AmulC { % on stack is [a] and c; returns [a] mul c
+ /factor ED { factor mul } forall 3 array astore } def
+%
+%
+/setColorLight { % expects 7 values on stack C M Y K xL yL zL
+% les rayons de lumi�re
+ xLight dup mul yLight dup mul zLight dup mul add add sqrt /NormeLight ED
+% the color values
+ /K ED
+ /Yellow ED
+ /Magenta ED
+ /Cyan ED
+} def
+%
+/facetteSphere {
+ newpath
+ /Xpoint Rsphere theta cos mul phi cos mul CX add def
+ /Ypoint Rsphere theta sin mul phi cos mul CY add def
+ /Zpoint Rsphere phi sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end moveto
+ theta 1 theta increment add {%
+ /theta1 ED
+ /Xpoint Rsphere theta1 cos mul phi cos mul CX add def
+ /Ypoint Rsphere theta1 sin mul phi cos mul CY add def
+ /Zpoint Rsphere phi sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ phi 1 phi increment add {
+ /phi1 ED
+ /Xpoint Rsphere theta increment add cos mul phi1 cos mul CX add def
+ /Ypoint Rsphere theta increment add sin mul phi1 cos mul CY add def
+ /Zpoint Rsphere phi1 sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ theta increment add -1 theta {%
+ /theta1 ED
+ /Xpoint Rsphere theta1 cos mul phi increment add cos mul CX add def
+ /Ypoint Rsphere theta1 sin mul phi increment add cos mul CY add def
+ /Zpoint Rsphere phi increment add sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ phi increment add -1 phi {
+ /phi1 ED
+ /Xpoint Rsphere theta cos mul phi1 cos mul CX add def
+ /Ypoint Rsphere theta sin mul phi1 cos mul CY add def
+ /Zpoint Rsphere phi1 sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ closepath
+} def
+%
+/MaillageSphere {
+% on stack must be x y z Radius increment C M Y K
+ setColorLight
+ /increment ED
+ /Rsphere ED
+ /CZ ED
+ /CY ED
+ /CX ED
+ /StartTheta 0 def
+ /condition { PSfacetteSphere 0 ge } def
+ -90 increment 90 increment sub {%
+ /phi ED
+ StartTheta increment 360 StartTheta add increment sub {%
+ /theta ED
+ % Centre de la facette
+ /Xpoint Rsphere theta increment 2 div add cos mul phi increment 2 div add cos mul CX add def
+ /Ypoint Rsphere theta increment 2 div add sin mul phi increment 2 div add cos mul CY add def
+ /Zpoint Rsphere phi increment 2 div add sin mul CZ add def
+ % normale � la facette
+ /nXfacette Xpoint CX sub def
+ /nYfacette Ypoint CY sub def
+ /nZfacette Zpoint CZ sub def
+ % test de visibilit�
+ /PSfacetteSphere
+ vX nXfacette mul
+ vY nYfacette mul add
+ vZ nZfacette mul add
+ def
+ condition {
+ gsave
+ facetteSphere
+ /cosV { 1 xLight nXfacette mul
+ yLight nYfacette mul
+ zLight nZfacette mul
+ add add
+ NormeLight
+ nXfacette dup mul
+ nYfacette dup mul
+ nZfacette dup mul
+ add add sqrt mul div sub } bind def
+ Cyan cosV mul Magenta cosV mul Yellow cosV mul K cosV mul setcmykcolor fill
+ grestore
+% 0 setgray
+ showgrid { facetteSphere stroke } if
+ } if
+ } for
+ % /StartTheta StartTheta increment 2 div add def
+ } for
+} def
+%
+%---------------------- Cylinder ---------------------------
+%
+/PlanCoupeCylinder { %
+ /TableauxPoints [
+ 0 1 359 {
+ /phi ED
+ [ Radius phi Height ConvCyl2d ] % on décrit le cercle
+ } for
+ ] def
+ newpath
+ TableauxPoints 0 get aload pop moveto
+ 1 1 359 { TableauxPoints exch get aload pop lineto } for
+ closepath
+} def
+%
+/facetteCylinder { %
+ newpath
+ Radius phi currentHeight ConvCyl2d moveto
+ phi 1 phi dAngle add { % loop variable on stack
+ Radius exch currentHeight ConvCyl2d lineto
+ } for
+ phi dAngle add -1 phi { % fill dHeight
+ Radius exch currentHeight dHeight add ConvCyl2d lineto
+ } for
+ closepath
+ } def % facette
+%
+/MaillageCylinder { % on stack true or false for saving values
+ { setColorLight % expects 4 values on stack C M Y K
+ /dHeight ED /dAngle ED /Height ED /Radius ED
+ /CZ ED /CY ED /CX ED } if
+%
+ 0 dHeight Height dHeight sub {
+ /currentHeight ED
+ 0 dAngle 360 dAngle sub {
+ /phi ED
+% Normal vector of the center
+ /nXfacetteCylinder Radius phi dAngle 2 div add cos mul CX add def
+ /nYfacetteCylinder Radius phi dAngle 2 div add sin mul CY add def
+ /nZfacetteCylinder currentHeight dHeight 2 div add CZ add def
+ /NormeN
+ nXfacetteCylinder dup mul
+ nYfacetteCylinder dup mul
+ nZfacetteCylinder dup mul
+ add add sqrt def
+ NormeN 0 eq { /NormeN 1e-10 def } if
+% test de visibilité
+ /PSfacetteCylinder
+ vX nXfacetteCylinder mul
+ vY nYfacetteCylinder mul add
+ vZ nZfacetteCylinder mul add def
+ condition {
+ facetteCylinder
+ /cosV
+ 1 xLight nXfacetteCylinder mul
+ yLight nYfacetteCylinder mul
+ zLight nZfacetteCylinder mul
+ add add
+ NormeLight NormeN mul div sub def
+ Cyan Magenta Yellow K
+ cosV mul 4 1 roll cosV mul 4 1 roll
+ cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll
+ setcmykcolor fill
+ showgrid {
+ 0 setgray
+ facetteCylinder % drawing the segments
+ stroke } if
+ } if
+ } for
+ } for
+} def
+%
+%------------------------ Cylinder type II -----------------------
+%
+/MoveTo { Conv3D2D moveto } def
+/LineTo { Conv3D2D lineto } def
+
+/IIIDEllipse { % x y z rA rB startAngle endAngle Wedge
+ /dAngle 1 def
+ /isWedge ED
+ /endAngle ED
+ /startAngle ED
+ /radiusB ED
+ /radiusA ED
+ startAngle cos radiusA mul startAngle sin radiusB mul 0
+ isWedge { 0 0 moveto LineTo }{ MoveTo } ifelse
+ /Angle startAngle def
+ startAngle dAngle endAngle {
+ /Angle ED
+ Angle cos radiusA mul Angle sin radiusB mul 0 LineTo
+ } for
+ isWedge { 0 0 lineto } if
+} def
+
+/IIIDCircle { % x y z r startAngle endAngle Wedge
+ 7 3 roll % startAngle endAngle Wedge x y z r
+ dup % startAngle endAngle Wedge x y z r r
+ 8 -3 roll
+ IIIDEllipse
+} def
+
+/IIIDWedge { % x y z r startAngle endAngle
+ true IIIDCircle
+} def
+
+/IIIDCylinder {% x y z r h start end wedge
+ /isWedge ED
+ /increment ED
+ /endAngle ED
+ /startAngle ED
+ /height ED
+ /radius ED
+ startAngle increment endAngle {
+ /Angle ED
+ radius Angle 0 ConvCylToCartesian MoveTo
+ radius Angle height ConvCylToCartesian LineTo
+ } for
+ stroke
+} def
+%
+%---------------------- Box ---------------------------
+%
+/PlanCoupeBox { % x y z
+ /TableauxPoints [
+ [ CX CY CZ Height add ConvBox2d ] % top or bottom
+ [ CX CY Depth add CZ Height add ConvBox2d ]
+ [ CX Width add CY Depth add CZ Height add ConvBox2d ]
+ [ CX Width add CY CZ Height add ConvBox2d ]
+ [ CX CY CZ Height add ConvBox2d ] % bottom
+ ] def
+ newpath
+ TableauxPoints 0 get aload pop moveto
+ 0 1 3 {
+ TableauxPoints exch get aload pop
+ lineto } for
+ closepath
+} def
+%
+/facetteBox { %
+ newpath
+ dup
+ 1 eq { % back
+ CX CY CZ ConvBox2d moveto
+ CX CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ ConvBox2d lineto
+ CX CY CZ ConvBox2d lineto
+ } if
+ dup
+ 2 eq { % right
+ CX CY CZ ConvBox2d moveto
+ CX CY CZ Height add ConvBox2d lineto
+ CX CY Depth add CZ Height add ConvBox2d lineto
+ CX CY Depth add CZ ConvBox2d lineto
+ CX CY CZ ConvBox2d lineto
+ } if
+ dup
+ 3 eq { % left
+ CX Width add CY CZ ConvBox2d moveto
+ CX Width add CY Depth add CZ ConvBox2d lineto
+ CX Width add CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ ConvBox2d lineto
+ } if
+ 4 eq { % front
+ CX CY Depth add CZ ConvBox2d moveto
+ CX CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY Depth add CZ ConvBox2d lineto
+ CX CY Depth add CZ ConvBox2d lineto
+ } if
+ closepath
+ } def % facette
+%
+/TestPlane { % on stack x y z of the plane center and # of plane
+ /nZfacetteBox ED /nYfacetteBox ED /nXfacetteBox ED
+ /Plane ED
+ /NormeN
+ nXfacetteBox dup mul
+ nYfacetteBox dup mul
+ nZfacetteBox dup mul
+ add add sqrt def
+ NormeN 0 eq { /NormeN 1e-10 def } if
+% test de visibilit�
+ /PSfacetteBox
+ vX nXfacetteBox mul
+ vY nYfacetteBox mul add
+ vZ nZfacetteBox mul add def
+ condition {
+ Plane facetteBox
+ /cosV
+ 1 xLight nXfacetteBox mul
+ yLight nYfacetteBox mul
+ zLight nZfacetteBox mul
+ add add
+ NormeLight NormeN mul div sub def
+ Cyan Magenta Yellow K
+ cosV mul 4 1 roll cosV mul 4 1 roll
+ cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll
+ setcmykcolor fill
+ 0 setgray
+ Plane facetteBox % drawing the segments
+ stroke
+ } if
+} def
+%
+/MaillageBox { % on stack true or false for saving values
+ { setColorLight % expects 4 values on stack C M Y K
+ /Depth ED /Height ED /Width ED
+ /CZ ED /CY ED /CX ED } if
+%
+% Normal vector of the box center
+ /PlaneSet [
+ [ Width 2 div CX add
+ CY
+ Height 2 div CZ add ] % normal back
+ [ CX
+ Depth 2 div CY add
+ Height 2 div CZ add ] % normal right
+ [ Width CX add
+ Depth 2 div CY add
+ Height 2 div CZ add ] % normal left
+ [ Width 2 div CX add
+ Depth CY add
+ Height 2 div CZ add ] % normal front
+ ] def
+ PlaneSequence length 0 eq { % user defined?
+ Alpha abs cvi 360 mod /iAlpha ED
+ iAlpha 90 lt { [ 1 2 3 4 ]
+ }{ iAlpha 180 lt { [ 2 4 1 3 ]
+ }{ iAlpha 270 lt { [ 3 4 1 2 ] }{ [ 3 1 4 2] } ifelse } ifelse } ifelse
+ }{ PlaneSequence } ifelse
+ { dup 1 sub PlaneSet exch get aload pop TestPlane } forall
+} def
+%
+%--------------------------- Paraboloid -----------------------------
+/PlanCoupeParaboloid {
+ /Z height store
+ /V {Z sqrt} bind def
+ /TableauxPoints [
+ 0 1 359 {
+ /U ED [ U U Z V calculate2DPoint ] % on d�crit le cercle
+ } for
+ ] def
+ newpath
+ TableauxPoints 0 get aload pop moveto
+ 0 1 359 {
+ /compteur ED
+ TableauxPoints compteur get aload pop
+ lineto } for
+ closepath
+} def
+%
+/facetteParaboloid{
+ newpath
+ U U Z V calculate2DPoint moveto
+ U 1 U increment add {%
+ /U1 ED
+ U1 U1 Z V calculate2DPoint lineto
+ } for
+ Z pas10 Z pas add pas10 add{
+ /Z1 ED
+ /V {Z1 sqrt} bind def
+ U1 U1 Z1 V calculate2DPoint lineto
+ } for
+ U increment add -1 U {%
+ /U2 ED
+ U2 U2 Z pas add V calculate2DPoint lineto
+ } for
+ Z pas add pas10 sub pas10 neg Z pas10 sub {
+ /Z2 ED
+ /V Z2 abs sqrt def
+ U U Z2 V calculate2DPoint lineto
+ } for
+ closepath
+} def % facette
+%
+/MaillageParaboloid {
+ % on stack true or false for saving values
+ { setColorLight % expects 7 values on stack C M Y K xL yL zL
+% /CZ ED /CY ED /CX ED
+ } if
+ 0 pas height pas sub {%
+ /Z ED
+ /V Z sqrt def
+ 0 increment 360 increment sub {%
+ /U ED
+% Centre de la facette
+ /Ucentre U increment 2 div add def
+ /Vcentre Z pas 2 div add sqrt def
+% normale à la facette
+ /nXfacetteParaboloid 2 Vcentre dup mul mul Ucentre cos mul radius mul def
+ /nYfacetteParaboloid 2 Vcentre dup mul mul Ucentre sin mul radius mul def
+ /nZfacetteParaboloid Vcentre neg radius dup mul mul def
+ /NormeN {
+ nXfacetteParaboloid dup mul
+ nYfacetteParaboloid dup mul
+ nZfacetteParaboloid dup mul
+ add add sqrt} bind def
+ NormeN 0 eq {/NormeN 1e-10 def} if
+% test de visibilit�
+ /PSfacetteParaboloid vX nXfacetteParaboloid mul
+ vY nYfacetteParaboloid mul add
+ vZ nZfacetteParaboloid mul add def
+ condition {
+ facetteParaboloid
+ /cosV 1 xLight nXfacetteParaboloid mul
+ yLight nYfacetteParaboloid mul
+ zLight nZfacetteParaboloid mul
+ add add
+ NormeLight
+ NormeN mul div sub def
+ Cyan Magenta Yellow K
+ cosV mul 4 1 roll cosV mul 4 1 roll cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll
+ setcmykcolor fill
+ showgrid {
+ 0 setgray
+ facetteParaboloid
+ stroke } if
+ } if
+ } for
+ } for
+} def
+%
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+% u -> e_u with |e_u|=1
+/vector-unit { 1 dict begin
+ dup vector-length 1 exch div
+ vector-scale
+ end
+} def
+%
+% u v -> u+v
+/vector-add { 1 dict begin
+ /v exch def
+ [ exch
+ 0 % u i
+ exch { % i u[i]
+ v % i u[i] v
+ 2 index get add % i u[i]+v[i]
+ exch 1 add % i
+ } forall
+ pop
+ ]
+ end
+} def
+%
+% u v -> u-v
+/vector-sub { 1 dict begin
+ /v exch def
+ [ exch
+ 0 % u i
+ exch { % i u[i]
+ v % i u[i] v
+ 2 index get sub % i u[i]+v[i]
+ exch 1 add % i
+ } forall
+ pop
+ ]
+end } def
+%
+% [v] c -> [c.v]
+/vector-scale { 1 dict begin
+ /c exch def
+ [ exch
+ { % s i u[i]
+ c mul % s i u[i] v
+ } forall
+ ]
+ end } def
+%
+%
+% [u] [v] -> [u x v]
+/vector-prod { %% x1 y1 z1 x2 y2 z2
+6 dict begin
+ aload pop
+ /zp exch def /yp exch def /xp exch def
+ aload pop
+ /z exch def /y exch def /x exch def
+ [ y zp mul z yp mul sub
+ z xp mul x zp mul sub
+ x yp mul y xp mul sub ]
+end
+} def
+%
+% [u] [v] -> u.v
+/vector-mul { %% x1 y1 z1 x2 y2 z2
+6 dict begin
+ aload pop
+ /zp exch def /yp exch def /xp exch def
+ aload pop
+ /z exch def /y exch def /x exch def
+ x xp mul y yp mul add z zp mul add
+end
+} def
+%
+% [x y z ... ] -> r
+% watch out for overflow
+/vector-length { 1 dict begin
+dup
+% find maximum entry
+/max 0 def
+{ % max
+ abs dup max gt {
+ % if abs gt max
+ /max exch def
+ } {
+ pop
+ } ifelse
+} forall
+max 0 ne {
+ 0 exch
+ { % 0 v[i]
+ max div dup mul add
+ } forall
+ sqrt
+ max mul
+} {
+ pop 0
+} ifelse
+end } def
+%
+end % tx@3DPlotDict
+
+
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 107.33167 0.0 107.33167 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 115.99823 0.0 115.99823 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 124.6648 0.0 124.6648 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 150.6643 0.0 150.6643 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
+@beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 167.99744 0.0 167.99744 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
+@setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 0.0 12.0 0.0 /Lineto /lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 7.99988 12.0 7.99988 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+{ } def /ArrowInside { } def [ 168.0 15.99976 12.0 15.99976 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+% $Id: pstricks.pro 801 2013-07-09 18:10:41Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 1.17, 2013/07/08
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
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+} def
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+ y2 y1 sub a div 2 add cvi /Ny ED
+ x2 x1 sub a div 2 add cvi /Nx ED
+ clipType % must be defined in pstricks.tex: clip -- eoclip
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+ /xA0 x1 dotRadius add CLW add def
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+ /xA xA0 def
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+} def
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+ Scale dup scale
+ /border_colour ED
+ /kite_colour ED
+ /dart_colour ED
+ clip
+
+ newpath
+ gsave
+ 100 100 translate
+ 6
+ Scale 1 lt { 1 Scale dup add div mul cvi } if %%%% Number of iterations
+ 10 %%%% Long side length in millimeters
+ /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
+ /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
+ /f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio
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+ /c{36 cos L mul}bind def %%%% c = L*cos(36)
+ /s{36 sin L mul}bind def %%%% s = L*sin(36)
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+ dup f exch neg exp dup scale
+ 5 {kite 72 rotate } repeat stroke
+ grestore
+} def
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+/TruchetFill { % on stack: scaling factor
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+ dup dup scale
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+ /i exch def
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+ /j exch def
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+ } for
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+ end % local user dict
+} def
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+ /@mtrx CM def
+ gsave
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+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
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+%
+/Arrow {
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+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
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+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
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+} def
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+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
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+ 0 DS z add CLW 4 div sub
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+} def
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+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
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+% { ] aload /Points ED }
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+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 801 2013-07-09 18:10:41Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
+%
+/Simpson { % on stack must be a b M --- simple version ---
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+%
+/LogGamma { 5 dict begin % z on stack
+ /z ED
+ /sum 0 def
+ /k 1 def
+ {
+ z k div dup 1 add ln sub dup
+ abs eps8 lt { pop exit } if
+ sum add /sum exch def
+ /k k 1 add def
+ } loop
+ sum z ln sub CEuler z mul sub
+ end
+} def
+%
+/ChebyshevT { 5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 2 k mul MoverN mul
+ add
+ } for
+ end
+} def
+%
+/ChebyshevU {5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 1 add 2 k mul 1 add MoverN mul
+ add
+ } for
+ end
+} def
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+%
+end
+
+%%EndProcSet
+%%BeginProcSet: pst-3dplot.pro 0 0
+%% $Id: pst-3dplot.pro 236 2009-12-31 08:59:43Z herbert $
+%%
+%% This is file `pst-3dplot.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-3dplot.tex'
+%%
+%% Herbert Voss <voss _at_ PSTricks.de>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-3dplot' is a PSTricks package to draw 3d curves and graphical objects
+%%
+%%
+%% version 0.30 / 2010-01-01 Herbert Voss <voss _at_ PSTricks.de>
+%% with contributions of Darrell Lamm <darrell.lamm _at_ gtri.gatech.edu<
+%%
+%
+/tx@3DPlotDict 200 dict def
+tx@3DPlotDict begin
+%
+/printDot { gsave 2 copy 2 0 360 arc fill stroke grestore } def
+%
+/saveCoor {
+ dzUnit mul /z ED
+ dyUnit mul /y ED
+ dxUnit mul /x ED
+} def
+%
+/ConvertTo2D {
+ RotatePoint
+ 1 { % dummy loop, will run only 1 time, allows exit
+ coorType 0 le { % the default |
+ /x2D x leftHanded not { neg } if Alpha cos mul y Alpha sin mul add def % /\ co system
+ /y2D x leftHanded { neg } if Alpha sin mul y Alpha cos mul add neg Beta sin mul z Beta cos mul add def
+ exit } if
+ coorType 1 le {
+ /x2D y x Alpha 90 sub sin mul sub def % |/_ co system, no shortened x axis
+ /y2D z x Alpha 90 sub cos mul sub def
+ exit } if
+ coorType 2 le { % coorType |/_ with a 1/sqrt(2) shortend x-axis and 135 degrees
+ /x2D y x 0.5 mul sub def
+ /y2D z x 0.5 mul sub def
+ exit } if
+ coorType 3 le { % coorType |/_ with a 1/sqrt(2) shortend x-axis and 135 degrees
+ /x2D y x -0.5 mul sub def
+ /y2D z x -0.5 mul sub def
+ exit } if
+ coorType 4 le { % Normalbild in Trimetrie Skalierung so, dass coorType2
+ /x2D x -0.5 mul y 1 mul add def
+ /y2D x -0.5 mul y -0.25 mul add z 1 mul add def
+ exit } if
+ } repeat
+} def
+%
+/Conv3D2D { /z ED /y ED /x ED ConvertTo2D x2D y2D } def
+%
+/ConvertToCartesian {
+ /latitude exch def
+ /longitude exch def
+ /Radius exch def
+ 1 { % dummy loop, will run only 1 time, allows exit
+ SphericalCoorType 0 le { % the default |
+ /z { Radius latitude sin mul } def
+ /x { Radius longitude cos mul latitude cos mul } def
+ /y { Radius longitude sin mul latitude cos mul } def
+ exit } if
+ SphericalCoorType 2 le {
+ /z { Radius longitude cos mul } def
+ /x { Radius longitude sin mul latitude cos mul} def
+ /y { Radius longitude sin mul latitude sin mul } def
+ exit } if
+ } repeat
+} def
+%
+/ConvCylToCartesian { % r phi h -> x y z
+ 3 1 roll % h r phi
+ /Phi ED
+ /Radius ED % h->z on stack
+ Radius Phi cos mul exch % x z
+ Radius Phi sin mul exch % x y z
+} def
+%
+/SphericalTo2D {
+ x y z ConvertToCartesian ConvertTo2D
+} def
+%
+/CylinderTo2D { % r phi h
+ x y z ConvCylToCartesian ConvertTo2D
+} def
+%
+/convertStackTo2D {
+ counttomark
+ /n ED /n3 n 3 div cvi def
+ n3 {
+ n -3 roll
+ SphericalCoor { ConvertToCartesian } { saveCoor } ifelse
+ ConvertTo2D
+ x2D xUnit y2D yUnit
+ /n n 1 sub def
+ } repeat
+} def
+%
+% the angle in the parameter equation for an ellipse is not proportional to the real angle!
+% phi=atan(b*tan(angle)/a)+floor(angle/180+0.5)*180
+%
+/getPhi { % on stack: vecA vecB angle
+ 3 dict begin
+ /angle exch def /vecB exch def /vecA exch def
+ angle cvi 90 mod 0 eq { angle } { vecA angle tan mul vecB atan
+ angle 180 div .5 add floor 180 mul add } ifelse
+ end
+} def
+%
+/RotSet (set ) def
+%
+/eulerRotation false def
+% Matrix multiplication procedure
+/matmul {
+
+ /M@tMulDict 20 dict def
+ M@tMulDict begin
+ /m2 ED
+ /m1 ED
+ m1 dup length 2 sub 2 getinterval aload pop
+ /col1max ED
+ /row1max ED
+ m2 dup length 2 sub 2 getinterval aload pop
+ /col2max ED
+ /row2max ED
+ /m3 row1max col2max mul 2 add array def
+ m3 dup length 2 sub row1max col2max 2 array astore putinterval
+ 0 1 row1max 1 sub {
+ /row ED
+ 0 1 col2max 1 sub {
+ /col ED
+ /sum 0 def
+ 0 1 col1max 1 sub{
+ /rowcol ED
+ sum
+ m1 row col1max mul rowcol add get
+ m2 rowcol col2max mul col add get
+ mul add
+ /sum ED
+ } for
+ m3 row col2max mul col add sum put
+ } for
+ } for
+ m3
+ end % end of M@tMulDict
+
+} def
+%
+/SetMQuaternion {
+
+ /MnewTOold 11 array def
+
+ /Qu@ternionDict 30 dict def
+ Qu@ternionDict begin
+
+ /normRotVec xRotVec yRotVec zRotVec 3 array astore VecNorm def
+ normRotVec 0 gt
+ {/xRotVecNorm xRotVec normRotVec div def
+ /yRotVecNorm yRotVec normRotVec div def
+ /zRotVecNorm zRotVec normRotVec div def
+ RotAngle}
+ {/xRotVecNorm 1 def
+ /yRotVecNorm 0 def
+ /zRotVecNorm 0 def
+ 0} ifelse
+
+ 2 div dup
+ /q0 exch cos def
+ sin dup dup
+ /q1 exch xRotVecNorm mul def
+ /q2 exch yRotVecNorm mul def
+ /q3 exch zRotVecNorm mul def
+
+ /q0q0 q0 q0 mul def
+ /q0q1 q0 q1 mul def
+ /q0q2 q0 q2 mul def
+ /q0q3 q0 q3 mul def
+
+ /q1q1 q1 q1 mul def
+ /q1q2 q1 q2 mul def
+ /q1q3 q1 q3 mul def
+
+ /q2q2 q2 q2 mul def
+ /q2q3 q2 q3 mul def
+
+ /q3q3 q3 q3 mul def
+
+ MnewTOold 0 q0q0 q1q1 add q2q2 sub q3q3 sub put
+ MnewTOold 1 q1q2 q0q3 sub 2 mul put
+ MnewTOold 2 q1q3 q0q2 add 2 mul put
+
+ MnewTOold 3 q1q2 q0q3 add 2 mul put
+ MnewTOold 4 q0q0 q1q1 sub q2q2 add q3q3 sub put
+ MnewTOold 5 q2q3 q0q1 sub 2 mul put
+
+ MnewTOold 6 q1q3 q0q2 sub 2 mul put
+ MnewTOold 7 q2q3 q0q1 add 2 mul put
+ MnewTOold 8 q0q0 q1q1 sub q2q2 sub q3q3 add put
+
+ MnewTOold 9 3 put
+ MnewTOold 10 3 put
+
+ end % end of Qu@ternionDict
+
+} def
+%
+/SetMxyz {
+ 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 3 3 11 array astore /MnewTOold ED
+ RotSequence cvx exec % Now create a new MnewTOold using xyz, etc.
+} def
+%
+/ConcatMQuaternion {
+ MnewTOold % Push onto stack
+ SetMQuaternion % Uses [xyz]RotVec and RotAngle to make MnewToOld
+ MnewTOold matmul /MnewTOold ED
+} def
+%
+/ConcatMxyz {
+ MnewTOold % Push onto stack
+ SetMxyz % Uses RotX, etc. to set MnewTOold
+ MnewTOold matmul /MnewTOold ED
+} def
+%
+/RotatePoint{
+ MnewTOold x y z 3 1 5 array astore matmul
+ 0 3 getinterval aload pop
+ /z ED
+ /y ED
+ /x ED
+} def
+%
+/makeMoldTOnew {
+ /MoldTOnew 11 array def
+ MoldTOnew 0 MnewTOold 0 get put
+ MoldTOnew 1 MnewTOold 3 get put
+ MoldTOnew 2 MnewTOold 6 get put
+ MoldTOnew 3 MnewTOold 1 get put
+ MoldTOnew 4 MnewTOold 4 get put
+ MoldTOnew 5 MnewTOold 7 get put
+ MoldTOnew 6 MnewTOold 2 get put
+ MoldTOnew 7 MnewTOold 5 get put
+ MoldTOnew 8 MnewTOold 8 get put
+ MoldTOnew 9 3 put
+ MoldTOnew 10 3 put
+} def
+%
+/RotXaxis {
+ eulerRotation
+ {1 0 0}
+ {makeMoldTOnew MoldTOnew 1 0 0 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotX def
+ ConcatMQuaternion
+} def
+/RotYaxis {
+ eulerRotation
+ {0 1 0}
+ {makeMoldTOnew MoldTOnew 0 1 0 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotY def
+ ConcatMQuaternion
+} def
+/RotZaxis {
+ eulerRotation
+ {0 0 1}
+ {makeMoldTOnew MoldTOnew 0 0 1 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotZ def
+ ConcatMQuaternion
+} def
+/xyz { RotXaxis RotYaxis RotZaxis } def
+/yxz { RotYaxis RotXaxis RotZaxis } def
+/yzx { RotYaxis RotZaxis RotXaxis } def
+/xzy { RotXaxis RotZaxis RotYaxis } def
+/zxy { RotZaxis RotXaxis RotYaxis } def
+/zyx { RotZaxis RotYaxis RotXaxis } def
+/quaternion { } def % Null
+%
+/VecNorm { 0 exch { dup mul add } forall sqrt } def
+%
+/UnitVec { % on stack is [a]; returns a vector with [a][a]/|a|=1
+ dup VecNorm /norm ED
+ norm 0 lt {/norm 0 def} if
+ { norm div } forall 3 array astore } def
+%
+/AxB { % on the stack are the two vectors [a][b]
+ aload pop /b3 ED /b2 ED /b1 ED
+ aload pop /a3 ED /a2 ED /a1 ED
+ a2 b3 mul a3 b2 mul sub
+ a3 b1 mul a1 b3 mul sub
+ a1 b2 mul a2 b1 mul sub
+ 3 array astore } def
+%
+/AaddB { % on the stack are the two vectors [a][b]
+ aload pop /b3 ED /b2 ED /b1 ED
+ aload pop /a3 ED /a2 ED /a1 ED
+ a1 b1 add a2 b2 add a3 b3 add
+ 3 array astore } def
+%
+/AmulC { % on stack is [a] and c; returns [a] mul c
+ /factor ED { factor mul } forall 3 array astore } def
+%
+%
+/setColorLight { % expects 7 values on stack C M Y K xL yL zL
+% les rayons de lumi�re
+ xLight dup mul yLight dup mul zLight dup mul add add sqrt /NormeLight ED
+% the color values
+ /K ED
+ /Yellow ED
+ /Magenta ED
+ /Cyan ED
+} def
+%
+/facetteSphere {
+ newpath
+ /Xpoint Rsphere theta cos mul phi cos mul CX add def
+ /Ypoint Rsphere theta sin mul phi cos mul CY add def
+ /Zpoint Rsphere phi sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end moveto
+ theta 1 theta increment add {%
+ /theta1 ED
+ /Xpoint Rsphere theta1 cos mul phi cos mul CX add def
+ /Ypoint Rsphere theta1 sin mul phi cos mul CY add def
+ /Zpoint Rsphere phi sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ phi 1 phi increment add {
+ /phi1 ED
+ /Xpoint Rsphere theta increment add cos mul phi1 cos mul CX add def
+ /Ypoint Rsphere theta increment add sin mul phi1 cos mul CY add def
+ /Zpoint Rsphere phi1 sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ theta increment add -1 theta {%
+ /theta1 ED
+ /Xpoint Rsphere theta1 cos mul phi increment add cos mul CX add def
+ /Ypoint Rsphere theta1 sin mul phi increment add cos mul CY add def
+ /Zpoint Rsphere phi increment add sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ phi increment add -1 phi {
+ /phi1 ED
+ /Xpoint Rsphere theta cos mul phi1 cos mul CX add def
+ /Ypoint Rsphere theta sin mul phi1 cos mul CY add def
+ /Zpoint Rsphere phi1 sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ closepath
+} def
+%
+/MaillageSphere {
+% on stack must be x y z Radius increment C M Y K
+ setColorLight
+ /increment ED
+ /Rsphere ED
+ /CZ ED
+ /CY ED
+ /CX ED
+ /StartTheta 0 def
+ /condition { PSfacetteSphere 0 ge } def
+ -90 increment 90 increment sub {%
+ /phi ED
+ StartTheta increment 360 StartTheta add increment sub {%
+ /theta ED
+ % Centre de la facette
+ /Xpoint Rsphere theta increment 2 div add cos mul phi increment 2 div add cos mul CX add def
+ /Ypoint Rsphere theta increment 2 div add sin mul phi increment 2 div add cos mul CY add def
+ /Zpoint Rsphere phi increment 2 div add sin mul CZ add def
+ % normale � la facette
+ /nXfacette Xpoint CX sub def
+ /nYfacette Ypoint CY sub def
+ /nZfacette Zpoint CZ sub def
+ % test de visibilit�
+ /PSfacetteSphere
+ vX nXfacette mul
+ vY nYfacette mul add
+ vZ nZfacette mul add
+ def
+ condition {
+ gsave
+ facetteSphere
+ /cosV { 1 xLight nXfacette mul
+ yLight nYfacette mul
+ zLight nZfacette mul
+ add add
+ NormeLight
+ nXfacette dup mul
+ nYfacette dup mul
+ nZfacette dup mul
+ add add sqrt mul div sub } bind def
+ Cyan cosV mul Magenta cosV mul Yellow cosV mul K cosV mul setcmykcolor fill
+ grestore
+% 0 setgray
+ showgrid { facetteSphere stroke } if
+ } if
+ } for
+ % /StartTheta StartTheta increment 2 div add def
+ } for
+} def
+%
+%---------------------- Cylinder ---------------------------
+%
+/PlanCoupeCylinder { %
+ /TableauxPoints [
+ 0 1 359 {
+ /phi ED
+ [ Radius phi Height ConvCyl2d ] % on décrit le cercle
+ } for
+ ] def
+ newpath
+ TableauxPoints 0 get aload pop moveto
+ 1 1 359 { TableauxPoints exch get aload pop lineto } for
+ closepath
+} def
+%
+/facetteCylinder { %
+ newpath
+ Radius phi currentHeight ConvCyl2d moveto
+ phi 1 phi dAngle add { % loop variable on stack
+ Radius exch currentHeight ConvCyl2d lineto
+ } for
+ phi dAngle add -1 phi { % fill dHeight
+ Radius exch currentHeight dHeight add ConvCyl2d lineto
+ } for
+ closepath
+ } def % facette
+%
+/MaillageCylinder { % on stack true or false for saving values
+ { setColorLight % expects 4 values on stack C M Y K
+ /dHeight ED /dAngle ED /Height ED /Radius ED
+ /CZ ED /CY ED /CX ED } if
+%
+ 0 dHeight Height dHeight sub {
+ /currentHeight ED
+ 0 dAngle 360 dAngle sub {
+ /phi ED
+% Normal vector of the center
+ /nXfacetteCylinder Radius phi dAngle 2 div add cos mul CX add def
+ /nYfacetteCylinder Radius phi dAngle 2 div add sin mul CY add def
+ /nZfacetteCylinder currentHeight dHeight 2 div add CZ add def
+ /NormeN
+ nXfacetteCylinder dup mul
+ nYfacetteCylinder dup mul
+ nZfacetteCylinder dup mul
+ add add sqrt def
+ NormeN 0 eq { /NormeN 1e-10 def } if
+% test de visibilité
+ /PSfacetteCylinder
+ vX nXfacetteCylinder mul
+ vY nYfacetteCylinder mul add
+ vZ nZfacetteCylinder mul add def
+ condition {
+ facetteCylinder
+ /cosV
+ 1 xLight nXfacetteCylinder mul
+ yLight nYfacetteCylinder mul
+ zLight nZfacetteCylinder mul
+ add add
+ NormeLight NormeN mul div sub def
+ Cyan Magenta Yellow K
+ cosV mul 4 1 roll cosV mul 4 1 roll
+ cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll
+ setcmykcolor fill
+ showgrid {
+ 0 setgray
+ facetteCylinder % drawing the segments
+ stroke } if
+ } if
+ } for
+ } for
+} def
+%
+%------------------------ Cylinder type II -----------------------
+%
+/MoveTo { Conv3D2D moveto } def
+/LineTo { Conv3D2D lineto } def
+
+/IIIDEllipse { % x y z rA rB startAngle endAngle Wedge
+ /dAngle 1 def
+ /isWedge ED
+ /endAngle ED
+ /startAngle ED
+ /radiusB ED
+ /radiusA ED
+ startAngle cos radiusA mul startAngle sin radiusB mul 0
+ isWedge { 0 0 moveto LineTo }{ MoveTo } ifelse
+ /Angle startAngle def
+ startAngle dAngle endAngle {
+ /Angle ED
+ Angle cos radiusA mul Angle sin radiusB mul 0 LineTo
+ } for
+ isWedge { 0 0 lineto } if
+} def
+
+/IIIDCircle { % x y z r startAngle endAngle Wedge
+ 7 3 roll % startAngle endAngle Wedge x y z r
+ dup % startAngle endAngle Wedge x y z r r
+ 8 -3 roll
+ IIIDEllipse
+} def
+
+/IIIDWedge { % x y z r startAngle endAngle
+ true IIIDCircle
+} def
+
+/IIIDCylinder {% x y z r h start end wedge
+ /isWedge ED
+ /increment ED
+ /endAngle ED
+ /startAngle ED
+ /height ED
+ /radius ED
+ startAngle increment endAngle {
+ /Angle ED
+ radius Angle 0 ConvCylToCartesian MoveTo
+ radius Angle height ConvCylToCartesian LineTo
+ } for
+ stroke
+} def
+%
+%---------------------- Box ---------------------------
+%
+/PlanCoupeBox { % x y z
+ /TableauxPoints [
+ [ CX CY CZ Height add ConvBox2d ] % top or bottom
+ [ CX CY Depth add CZ Height add ConvBox2d ]
+ [ CX Width add CY Depth add CZ Height add ConvBox2d ]
+ [ CX Width add CY CZ Height add ConvBox2d ]
+ [ CX CY CZ Height add ConvBox2d ] % bottom
+ ] def
+ newpath
+ TableauxPoints 0 get aload pop moveto
+ 0 1 3 {
+ TableauxPoints exch get aload pop
+ lineto } for
+ closepath
+} def
+%
+/facetteBox { %
+ newpath
+ dup
+ 1 eq { % back
+ CX CY CZ ConvBox2d moveto
+ CX CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ ConvBox2d lineto
+ CX CY CZ ConvBox2d lineto
+ } if
+ dup
+ 2 eq { % right
+ CX CY CZ ConvBox2d moveto
+ CX CY CZ Height add ConvBox2d lineto
+ CX CY Depth add CZ Height add ConvBox2d lineto
+ CX CY Depth add CZ ConvBox2d lineto
+ CX CY CZ ConvBox2d lineto
+ } if
+ dup
+ 3 eq { % left
+ CX Width add CY CZ ConvBox2d moveto
+ CX Width add CY Depth add CZ ConvBox2d lineto
+ CX Width add CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ ConvBox2d lineto
+ } if
+ 4 eq { % front
+ CX CY Depth add CZ ConvBox2d moveto
+ CX CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY Depth add CZ ConvBox2d lineto
+ CX CY Depth add CZ ConvBox2d lineto
+ } if
+ closepath
+ } def % facette
+%
+/TestPlane { % on stack x y z of the plane center and # of plane
+ /nZfacetteBox ED /nYfacetteBox ED /nXfacetteBox ED
+ /Plane ED
+ /NormeN
+ nXfacetteBox dup mul
+ nYfacetteBox dup mul
+ nZfacetteBox dup mul
+ add add sqrt def
+ NormeN 0 eq { /NormeN 1e-10 def } if
+% test de visibilit�
+ /PSfacetteBox
+ vX nXfacetteBox mul
+ vY nYfacetteBox mul add
+ vZ nZfacetteBox mul add def
+ condition {
+ Plane facetteBox
+ /cosV
+ 1 xLight nXfacetteBox mul
+ yLight nYfacetteBox mul
+ zLight nZfacetteBox mul
+ add add
+ NormeLight NormeN mul div sub def
+ Cyan Magenta Yellow K
+ cosV mul 4 1 roll cosV mul 4 1 roll
+ cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll
+ setcmykcolor fill
+ 0 setgray
+ Plane facetteBox % drawing the segments
+ stroke
+ } if
+} def
+%
+/MaillageBox { % on stack true or false for saving values
+ { setColorLight % expects 4 values on stack C M Y K
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 24.99957 0.0 24.99957 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 29.33276 0.0 29.33276 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 33.66595 0.0 33.66595 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 37.99915 0.0 37.99915 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 42.33234 0.0 42.33234 144.0 /Lineto
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+pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 46.66553 0.0 46.66553 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
+@beginspecial @setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 50.99872 0.0 50.99872 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
+@setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
+@setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 89.99762 0.0 89.99762 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 94.33081 0.0 94.33081 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 98.664 0.0 98.664 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 102.9972 0.0 102.9972 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 107.33038 0.0 107.33038 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 111.66357 0.0 111.66357 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 115.99677 0.0 115.99677 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 120.32996 0.0 120.32996 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 168.0 0.0 12.0 0.0 /Lineto /lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 168.0 47.99945 12.0 47.99945 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 168.0 51.99939 12.0 51.99939 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 168.0 59.99945 12.0 59.99945 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial @setspecial
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+{ } def /ArrowInside { } def [ 168.0 63.99939 12.0 63.99939 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 67.99933 12.0 67.99933 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 71.99927 12.0 71.99927 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 75.9992 12.0 75.9992 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+
+%%EndProcSet
+%%BeginProcSet: pstricks.pro 0 0
+% $Id: pstricks.pro 801 2013-07-09 18:10:41Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 1.17, 2013/07/08
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+% Define the follwing gs-functions if not known, eg when using distiller
+%
+systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if
+systemdict /.setblendmode known not {/.setblendmode { pop } def } if
+systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
+%
+/tx@Dict 200 dict def % the main PSTricks dictionary
+tx@Dict begin
+/ADict 25 dict def % The arrow dictionary
+/CM { matrix currentmatrix } bind def
+/SLW /setlinewidth load def
+/CLW /currentlinewidth load def
+/CP /currentpoint load def
+/ED { exch def } bind def
+/L /lineto load def
+/T /translate load def
+/TMatrix { } def
+/RAngle { 0 } def
+/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments
+/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known
+/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter)
+/Div { dup 0 eq { pop } { div } ifelse } def % control the division
+/tan { dup cos abs 1.e-10 lt
+ { pop 1.e10 } % return 1.e10 as infinit
+ { dup sin exch cos div } ifelse % default sin/cos
+} def
+/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees
+/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root
+ pop pop 0 }{ sqrt exch atan} ifelse } def
+/Acos2 { 2 dict begin
+ /x ED /y ED
+ y abs 1.0e-20 lt { 1.0e30 } if
+ x y div
+ dup dup mul neg 1 add dup 0 lt { % arc cos needs two values x,y
+ pop pop 0 }{ sqrt exch atan} ifelse
+ y 0 lt { 180 add } if
+} def
+/NET { neg exch neg exch T } def % change coordinate system to the negative one
+/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter
+/Pyth2 { % Pythagoras, xA yA xB yB
+ 3 -1 roll % xA xB yB yA
+ sub % xA xB yB-yA
+ 3 1 roll % yB-yA xA xB
+ sub % yB-yA xA-xB
+ Pyth } def
+/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian
+/Rand { rand 4294967295 div } def % a real random number
+%----------------- hv added 20050516 ---------------
+/PiDiv2 1.57079632680 def
+/Pi 3.14159265359 def
+/TwoPi 6.28318530718 def
+/Euler 2.71828182846 def
+%/e Euler bind def
+%
+/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees
+/DegtoRad { Pi mul 180 div } bind def % viceversa
+%
+/startGlobal { true setglobal globaldict begin } bind def
+/endGlobal { end false setglobal } bind def
+/pssetRGBcolor /setrgbcolor load def
+/pssetCMYKcolor /setcmykcolor load def
+/pssetGraycolor /setgray load def
+%
+%----------------- hv end---------------------------
+/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def
+%
+/PathLength {
+ flattenpath /z 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def }
+ { /y ED /x ED PathLength@ }
+ {}
+ { /y y2 def /x x2 def PathLength@ }
+ /pathforall load stopped { pop pop pop pop } if
+ z
+} def
+%
+/STP { .996264 dup scale } def % BP/PT scaling
+/STV { SDict begin normalscale end STP } def %
+%
+/DashLine {
+ dup 0 gt
+ { /a .5 def PathLength exch div }
+ { pop /a 1 def PathLength } ifelse
+ /b ED % pattern should fit evenly in b
+ dup /X ED % pattern array
+ 0 get /y ED % length of first black segment
+ /z 0 X {add} forall def % length of the full pattern
+ %% Computation of the scaling factor as described by van Zandt:
+ b a .5 sub 2 mul y mul sub z Div round
+ z mul a .5 sub 2 mul y mul add b exch Div
+ %%%% scaling factor on stack.
+ /z ED %% now, z is the scaling factor
+ false % for the length test below
+ X { z mul } forall X astore %% modification TN 04-08-07
+ %%% Checking whether at least one dash in X has positive length:
+ {0 gt or} forall
+ { X 1 a sub y mul }
+ { [ 1 0 ] 0 }
+ ifelse
+ setdash stroke
+} def
+%
+/DotLine {
+ /b PathLength def
+ /a ED /z ED /y CLW def
+ /z y z add def
+ a 0 gt {
+ /b b a div def
+ }{
+ a 0 eq {
+ /b b y sub def
+ }{ a -3 eq {
+ /b b y add def } if
+ } ifelse
+ } ifelse
+ [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
+ a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
+ setdash 1 setlinecap stroke
+} def
+%
+/SymbolLine { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt
+ { %XYLength SymStep div abs cvi
+ /nSym SymStep abs cvi def }
+ { /nSym XYLength SymStep div cvi def }
+ ifelse
+ 0.5 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ /deltaX XLength nSym div def
+ /deltaY YLength nSym div def
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ nSym {
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ currentpoint translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+ /YA YB def /XA XB def
+ } repeat
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ XA YA translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ pop % delete the mark symbol
+} def
+%
+/LineFill { % hv ------------ patch 7 -------------
+ gsave
+ abs /hatchWidthInc ED
+ abs /hatchSepInc ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clipType % must be defined in pstricks.tex: clip -- eoclip
+ newpath
+ 2 setlinecap
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ x2 x1 sub 1 add {
+ x1 a mul y1 moveto 0 y2 rlineto stroke
+ /x1 x1 1 add
+ hatchWidthInc 0 gt { CLW add } if
+ def
+ hatchSepInc 0 gt hatchWidthInc 0 gt or {
+ /a a hatchSepInc add def
+ CLW hatchWidthInc add SLW
+ } if
+ } repeat
+ grestore
+ pop pop } def
+%
+/DotFill {% on stack: dot radius
+ /dotRadius ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform
+ pathbbox % llx lly urx ury of smallest bounding box
+ /y2 ED /x2 ED /y1 ED /x1 ED
+ y2 y1 sub a div 2 add cvi /Ny ED
+ x2 x1 sub a div 2 add cvi /Nx ED
+ clipType % must be defined in pstricks.tex: clip -- eoclip
+ newpath
+ /yA y1 dotRadius add CLW add def
+ /xA0 x1 dotRadius add CLW add def
+ Ny {
+ /xA xA0 def
+ Nx {
+ newpath
+ xA yA dotRadius 0 360 arc
+ SolidDot { gsave fill grestore } if
+ stroke
+ xA a add /xA ED
+ } repeat
+ yA a add /yA ED
+ } repeat
+ grestore
+} def
+%
+/PenroseFill {% on stack: scaling factor
+ /Scale ED
+% 1 exch div round /penroseFactor ED
+% a 0 dtransform round exch round exch
+% 2 copy idtransform
+% exch Atan rotate
+% idtransform pop /a ED
+% .25 .25 itransform pathbbox
+% /y2 ED
+% a Div ceiling cvi /x2 ED /y1 ED
+% a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+gsave
+ 220 150 translate
+ Scale dup scale
+ systemdict /setstrokeadjust known { true setstrokeadjust } if
+ /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
+ { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
+ [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
+ i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
+ mul j l + S rmoveto}F i L j L stroke }F}F}F}F
+ grestore
+% pop pop
+} def
+%
+/PenroseFillA {% on stack: scaling factor, border color, kite color, dart color
+ /Scale ED
+ Scale dup scale
+ /border_colour ED
+ /kite_colour ED
+ /dart_colour ED
+ clip
+
+ newpath
+ gsave
+ 100 100 translate
+ 6
+ Scale 1 lt { 1 Scale dup add div mul cvi } if %%%% Number of iterations
+ 10 %%%% Long side length in millimeters
+ /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
+ /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
+ /f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio
+ /l{L f mul}bind def %%%% Short side length l = L*f
+ /Ll{L l add}bind def %%%% Ll = L + l
+ /c{36 cos L mul}bind def %%%% c = L*cos(36)
+ /s{36 sin L mul}bind def %%%% s = L*sin(36)
+ /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
+ 0 setlinewidth stroke grestore border_colour stroke } bind def
+ /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
+ Ll 0 translate 144 rotate kite grestore }
+ { kite_colour L draw_tile }ifelse
+ pop } bind def
+ /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
+ -144 rotate Ll neg 0 translate half_dart grestore }
+ { dart_colour l draw_tile }ifelse
+ pop } bind def
+ /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
+ border_width setlinewidth 1 setlinejoin 1 setlinecap
+% 450 0 translate
+ dup f exch neg exp dup scale
+ 5 {kite 72 rotate } repeat stroke
+ grestore
+} def
+%
+%
+/TruchetFill { % on stack: scaling factor
+ 10 dict begin
+ dup dup scale
+ 1 exch div round /penroseFactor ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ /ma a neg def
+ /ha a 2 div def
+ /mha ha neg def
+ /tile {
+ rand dup 2 idiv 2 mul eq { 90 rotate } if
+ mha mha moveto ha mha lineto
+ ha ha lineto mha ha lineto
+% closepath .1 setlinewidth stroke
+ contents
+ } def
+ /contents{
+ 0 ha moveto ha 0 lineto
+ 0 mha moveto mha 0 lineto
+% 1 setlinewidth stroke
+ } def
+ /dotiling {
+ f ma mul a f a mul {
+ /i exch def
+ f ma mul a f a mul {
+ /j exch def
+ gsave i j translate
+ tile stroke grestore
+ } for
+ } for
+ } def
+%
+ /f 3 def
+ 5 srand dotiling
+ end % local user dict
+} def
+%
+/BeginArrow {
+ ADict begin % hold it local, for end see EndArrow
+ /@mtrx CM def
+ gsave
+ 2 copy T
+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
+%
+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
+%
+/Arrow {
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
+%
+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
+ gsave fill grestore
+} def
+%
+/Tbar {
+ CLW mul add /z ED
+ z -2 div CLW 2 div moveto
+ z 0 rlineto stroke
+ 0 CLW moveto
+} def
+%
+/Bracket {
+ CLW mul add dup CLW sub 2 div
+ /x ED mul CLW add /y ED /z CLW 2 div def
+ x neg y moveto
+ x neg CLW 2 div L x CLW 2 div L x y L stroke
+ 0 CLW moveto
+} def
+%
+/RoundBracket {
+ CLW mul add dup 2 div
+ /x ED mul /y ED /mtrx CM def
+ 0 CLW 2 div T x y mul 0 ne { x y scale } if
+ 1 1 moveto
+ .85 .5 .35 0 0 0 curveto
+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
+ /b ED % the color definition
+ 0 z DS SD
+ b { 0 z DS CLW sub SD } if
+ 0 DS z add CLW 4 div sub
+ moveto
+} def
+%
+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+ load } if ] cvx newpath 3 1 roll T exec } def
+%
+/NArray { % holds the coordinates and on top of stack the showpoints boolean
+ /showpoints ED
+ counttomark 2 div dup cvi /n ED % n 2 div on stack
+ n eq not { exch pop } if % even numbers of points? delete one
+ ] aload /Points ED
+ showpoints not { Points aload pop } if
+% { ] aload /Points ED }
+% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
+} def
+%
+/Line {
+ NArray n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
+ n { Lineto } repeat
+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
+%
+/LineToYAxis {
+ /Ox ED % Save the x origin value
+ NArray % all x-y pairs on stack
+ n { 2 copy moveto % go to current point
+ Ox exch Lineto % line to y-axis
+ pop % delete old x-value
+ } repeat
+} def
+%
+/LineToXAxis{
+ /Oy ED % Save the y origin value
+ NArray % all x-y pairs on stack
+ n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if
+ ArrowA
+ /n n 2 sub def
+ CP 2 copy moveto pop Oy Lineto
+ n { 2 copy moveto pop Oy Lineto } repeat
+ CP
+ 4 2 roll
+ ArrowB
+ 2 copy moveto pop Oy
+ L
+ pop pop } if
+} def
+%
+/Arcto {
+ /a [ 6 -2 roll ] cvx def
+ a r
+ /arcto load stopped { 5 } { 4 } ifelse { pop } repeat
+ a
+} def
+%
+/CheckClosed {
+ dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
+ and { pop pop /n n 1 sub def } if
+} def
+%
+/Polygon {
+ NArray n 2 eq { 0 0 /n 3 def } if
+ n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ n 2 mul -2 roll
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ n { Lineto } repeat
+ x1 y1 x0 y0 6 4 roll Lineto
+ Lineto pop pop closepath } ifelse
+} def
+%
+/SymbolPolygon { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 add /m ED
+ 2 copy m 2 roll % copy last two
+ m 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+ /nSym XYLength SymStep Div cvi def
+ /Shift Symbol stringwidth pop 2 Div def
+ /deltaX XLength nSym Div def
+ /deltaY YLength nSym Div def
+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 801 2013-07-09 18:10:41Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
+%
+/Simpson { % on stack must be a b M --- simple version ---
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+%
+/LogGamma { 5 dict begin % z on stack
+ /z ED
+ /sum 0 def
+ /k 1 def
+ {
+ z k div dup 1 add ln sub dup
+ abs eps8 lt { pop exit } if
+ sum add /sum exch def
+ /k k 1 add def
+ } loop
+ sum z ln sub CEuler z mul sub
+ end
+} def
+%
+/ChebyshevT { 5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 2 k mul MoverN mul
+ add
+ } for
+ end
+} def
+%
+/ChebyshevU {5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 1 add 2 k mul 1 add MoverN mul
+ add
+ } for
+ end
+} def
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+%
+end
+
+%%EndProcSet
+%%BeginProcSet: pst-3dplot.pro 0 0
+%% $Id: pst-3dplot.pro 236 2009-12-31 08:59:43Z herbert $
+%%
+%% This is file `pst-3dplot.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-3dplot.tex'
+%%
+%% Herbert Voss <voss _at_ PSTricks.de>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-3dplot' is a PSTricks package to draw 3d curves and graphical objects
+%%
+%%
+%% version 0.30 / 2010-01-01 Herbert Voss <voss _at_ PSTricks.de>
+%% with contributions of Darrell Lamm <darrell.lamm _at_ gtri.gatech.edu<
+%%
+%
+/tx@3DPlotDict 200 dict def
+tx@3DPlotDict begin
+%
+/printDot { gsave 2 copy 2 0 360 arc fill stroke grestore } def
+%
+/saveCoor {
+ dzUnit mul /z ED
+ dyUnit mul /y ED
+ dxUnit mul /x ED
+} def
+%
+/ConvertTo2D {
+ RotatePoint
+ 1 { % dummy loop, will run only 1 time, allows exit
+ coorType 0 le { % the default |
+ /x2D x leftHanded not { neg } if Alpha cos mul y Alpha sin mul add def % /\ co system
+ /y2D x leftHanded { neg } if Alpha sin mul y Alpha cos mul add neg Beta sin mul z Beta cos mul add def
+ exit } if
+ coorType 1 le {
+ /x2D y x Alpha 90 sub sin mul sub def % |/_ co system, no shortened x axis
+ /y2D z x Alpha 90 sub cos mul sub def
+ exit } if
+ coorType 2 le { % coorType |/_ with a 1/sqrt(2) shortend x-axis and 135 degrees
+ /x2D y x 0.5 mul sub def
+ /y2D z x 0.5 mul sub def
+ exit } if
+ coorType 3 le { % coorType |/_ with a 1/sqrt(2) shortend x-axis and 135 degrees
+ /x2D y x -0.5 mul sub def
+ /y2D z x -0.5 mul sub def
+ exit } if
+ coorType 4 le { % Normalbild in Trimetrie Skalierung so, dass coorType2
+ /x2D x -0.5 mul y 1 mul add def
+ /y2D x -0.5 mul y -0.25 mul add z 1 mul add def
+ exit } if
+ } repeat
+} def
+%
+/Conv3D2D { /z ED /y ED /x ED ConvertTo2D x2D y2D } def
+%
+/ConvertToCartesian {
+ /latitude exch def
+ /longitude exch def
+ /Radius exch def
+ 1 { % dummy loop, will run only 1 time, allows exit
+ SphericalCoorType 0 le { % the default |
+ /z { Radius latitude sin mul } def
+ /x { Radius longitude cos mul latitude cos mul } def
+ /y { Radius longitude sin mul latitude cos mul } def
+ exit } if
+ SphericalCoorType 2 le {
+ /z { Radius longitude cos mul } def
+ /x { Radius longitude sin mul latitude cos mul} def
+ /y { Radius longitude sin mul latitude sin mul } def
+ exit } if
+ } repeat
+} def
+%
+/ConvCylToCartesian { % r phi h -> x y z
+ 3 1 roll % h r phi
+ /Phi ED
+ /Radius ED % h->z on stack
+ Radius Phi cos mul exch % x z
+ Radius Phi sin mul exch % x y z
+} def
+%
+/SphericalTo2D {
+ x y z ConvertToCartesian ConvertTo2D
+} def
+%
+/CylinderTo2D { % r phi h
+ x y z ConvCylToCartesian ConvertTo2D
+} def
+%
+/convertStackTo2D {
+ counttomark
+ /n ED /n3 n 3 div cvi def
+ n3 {
+ n -3 roll
+ SphericalCoor { ConvertToCartesian } { saveCoor } ifelse
+ ConvertTo2D
+ x2D xUnit y2D yUnit
+ /n n 1 sub def
+ } repeat
+} def
+%
+% the angle in the parameter equation for an ellipse is not proportional to the real angle!
+% phi=atan(b*tan(angle)/a)+floor(angle/180+0.5)*180
+%
+/getPhi { % on stack: vecA vecB angle
+ 3 dict begin
+ /angle exch def /vecB exch def /vecA exch def
+ angle cvi 90 mod 0 eq { angle } { vecA angle tan mul vecB atan
+ angle 180 div .5 add floor 180 mul add } ifelse
+ end
+} def
+%
+/RotSet (set ) def
+%
+/eulerRotation false def
+% Matrix multiplication procedure
+/matmul {
+
+ /M@tMulDict 20 dict def
+ M@tMulDict begin
+ /m2 ED
+ /m1 ED
+ m1 dup length 2 sub 2 getinterval aload pop
+ /col1max ED
+ /row1max ED
+ m2 dup length 2 sub 2 getinterval aload pop
+ /col2max ED
+ /row2max ED
+ /m3 row1max col2max mul 2 add array def
+ m3 dup length 2 sub row1max col2max 2 array astore putinterval
+ 0 1 row1max 1 sub {
+ /row ED
+ 0 1 col2max 1 sub {
+ /col ED
+ /sum 0 def
+ 0 1 col1max 1 sub{
+ /rowcol ED
+ sum
+ m1 row col1max mul rowcol add get
+ m2 rowcol col2max mul col add get
+ mul add
+ /sum ED
+ } for
+ m3 row col2max mul col add sum put
+ } for
+ } for
+ m3
+ end % end of M@tMulDict
+
+} def
+%
+/SetMQuaternion {
+
+ /MnewTOold 11 array def
+
+ /Qu@ternionDict 30 dict def
+ Qu@ternionDict begin
+
+ /normRotVec xRotVec yRotVec zRotVec 3 array astore VecNorm def
+ normRotVec 0 gt
+ {/xRotVecNorm xRotVec normRotVec div def
+ /yRotVecNorm yRotVec normRotVec div def
+ /zRotVecNorm zRotVec normRotVec div def
+ RotAngle}
+ {/xRotVecNorm 1 def
+ /yRotVecNorm 0 def
+ /zRotVecNorm 0 def
+ 0} ifelse
+
+ 2 div dup
+ /q0 exch cos def
+ sin dup dup
+ /q1 exch xRotVecNorm mul def
+ /q2 exch yRotVecNorm mul def
+ /q3 exch zRotVecNorm mul def
+
+ /q0q0 q0 q0 mul def
+ /q0q1 q0 q1 mul def
+ /q0q2 q0 q2 mul def
+ /q0q3 q0 q3 mul def
+
+ /q1q1 q1 q1 mul def
+ /q1q2 q1 q2 mul def
+ /q1q3 q1 q3 mul def
+
+ /q2q2 q2 q2 mul def
+ /q2q3 q2 q3 mul def
+
+ /q3q3 q3 q3 mul def
+
+ MnewTOold 0 q0q0 q1q1 add q2q2 sub q3q3 sub put
+ MnewTOold 1 q1q2 q0q3 sub 2 mul put
+ MnewTOold 2 q1q3 q0q2 add 2 mul put
+
+ MnewTOold 3 q1q2 q0q3 add 2 mul put
+ MnewTOold 4 q0q0 q1q1 sub q2q2 add q3q3 sub put
+ MnewTOold 5 q2q3 q0q1 sub 2 mul put
+
+ MnewTOold 6 q1q3 q0q2 sub 2 mul put
+ MnewTOold 7 q2q3 q0q1 add 2 mul put
+ MnewTOold 8 q0q0 q1q1 sub q2q2 sub q3q3 add put
+
+ MnewTOold 9 3 put
+ MnewTOold 10 3 put
+
+ end % end of Qu@ternionDict
+
+} def
+%
+/SetMxyz {
+ 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 3 3 11 array astore /MnewTOold ED
+ RotSequence cvx exec % Now create a new MnewTOold using xyz, etc.
+} def
+%
+/ConcatMQuaternion {
+ MnewTOold % Push onto stack
+ SetMQuaternion % Uses [xyz]RotVec and RotAngle to make MnewToOld
+ MnewTOold matmul /MnewTOold ED
+} def
+%
+/ConcatMxyz {
+ MnewTOold % Push onto stack
+ SetMxyz % Uses RotX, etc. to set MnewTOold
+ MnewTOold matmul /MnewTOold ED
+} def
+%
+/RotatePoint{
+ MnewTOold x y z 3 1 5 array astore matmul
+ 0 3 getinterval aload pop
+ /z ED
+ /y ED
+ /x ED
+} def
+%
+/makeMoldTOnew {
+ /MoldTOnew 11 array def
+ MoldTOnew 0 MnewTOold 0 get put
+ MoldTOnew 1 MnewTOold 3 get put
+ MoldTOnew 2 MnewTOold 6 get put
+ MoldTOnew 3 MnewTOold 1 get put
+ MoldTOnew 4 MnewTOold 4 get put
+ MoldTOnew 5 MnewTOold 7 get put
+ MoldTOnew 6 MnewTOold 2 get put
+ MoldTOnew 7 MnewTOold 5 get put
+ MoldTOnew 8 MnewTOold 8 get put
+ MoldTOnew 9 3 put
+ MoldTOnew 10 3 put
+} def
+%
+/RotXaxis {
+ eulerRotation
+ {1 0 0}
+ {makeMoldTOnew MoldTOnew 1 0 0 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotX def
+ ConcatMQuaternion
+} def
+/RotYaxis {
+ eulerRotation
+ {0 1 0}
+ {makeMoldTOnew MoldTOnew 0 1 0 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotY def
+ ConcatMQuaternion
+} def
+/RotZaxis {
+ eulerRotation
+ {0 0 1}
+ {makeMoldTOnew MoldTOnew 0 0 1 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotZ def
+ ConcatMQuaternion
+} def
+/xyz { RotXaxis RotYaxis RotZaxis } def
+/yxz { RotYaxis RotXaxis RotZaxis } def
+/yzx { RotYaxis RotZaxis RotXaxis } def
+/xzy { RotXaxis RotZaxis RotYaxis } def
+/zxy { RotZaxis RotXaxis RotYaxis } def
+/zyx { RotZaxis RotYaxis RotXaxis } def
+/quaternion { } def % Null
+%
+/VecNorm { 0 exch { dup mul add } forall sqrt } def
+%
+/UnitVec { % on stack is [a]; returns a vector with [a][a]/|a|=1
+ dup VecNorm /norm ED
+ norm 0 lt {/norm 0 def} if
+ { norm div } forall 3 array astore } def
+%
+/AxB { % on the stack are the two vectors [a][b]
+ aload pop /b3 ED /b2 ED /b1 ED
+ aload pop /a3 ED /a2 ED /a1 ED
+ a2 b3 mul a3 b2 mul sub
+ a3 b1 mul a1 b3 mul sub
+ a1 b2 mul a2 b1 mul sub
+ 3 array astore } def
+%
+/AaddB { % on the stack are the two vectors [a][b]
+ aload pop /b3 ED /b2 ED /b1 ED
+ aload pop /a3 ED /a2 ED /a1 ED
+ a1 b1 add a2 b2 add a3 b3 add
+ 3 array astore } def
+%
+/AmulC { % on stack is [a] and c; returns [a] mul c
+ /factor ED { factor mul } forall 3 array astore } def
+%
+%
+/setColorLight { % expects 7 values on stack C M Y K xL yL zL
+% les rayons de lumi�re
+ xLight dup mul yLight dup mul zLight dup mul add add sqrt /NormeLight ED
+% the color values
+ /K ED
+ /Yellow ED
+ /Magenta ED
+ /Cyan ED
+} def
+%
+/facetteSphere {
+ newpath
+ /Xpoint Rsphere theta cos mul phi cos mul CX add def
+ /Ypoint Rsphere theta sin mul phi cos mul CY add def
+ /Zpoint Rsphere phi sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end moveto
+ theta 1 theta increment add {%
+ /theta1 ED
+ /Xpoint Rsphere theta1 cos mul phi cos mul CX add def
+ /Ypoint Rsphere theta1 sin mul phi cos mul CY add def
+ /Zpoint Rsphere phi sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ phi 1 phi increment add {
+ /phi1 ED
+ /Xpoint Rsphere theta increment add cos mul phi1 cos mul CX add def
+ /Ypoint Rsphere theta increment add sin mul phi1 cos mul CY add def
+ /Zpoint Rsphere phi1 sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ theta increment add -1 theta {%
+ /theta1 ED
+ /Xpoint Rsphere theta1 cos mul phi increment add cos mul CX add def
+ /Ypoint Rsphere theta1 sin mul phi increment add cos mul CY add def
+ /Zpoint Rsphere phi increment add sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ phi increment add -1 phi {
+ /phi1 ED
+ /Xpoint Rsphere theta cos mul phi1 cos mul CX add def
+ /Ypoint Rsphere theta sin mul phi1 cos mul CY add def
+ /Zpoint Rsphere phi1 sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ closepath
+} def
+%
+/MaillageSphere {
+% on stack must be x y z Radius increment C M Y K
+ setColorLight
+ /increment ED
+ /Rsphere ED
+ /CZ ED
+ /CY ED
+ /CX ED
+ /StartTheta 0 def
+ /condition { PSfacetteSphere 0 ge } def
+ -90 increment 90 increment sub {%
+ /phi ED
+ StartTheta increment 360 StartTheta add increment sub {%
+ /theta ED
+ % Centre de la facette
+ /Xpoint Rsphere theta increment 2 div add cos mul phi increment 2 div add cos mul CX add def
+ /Ypoint Rsphere theta increment 2 div add sin mul phi increment 2 div add cos mul CY add def
+ /Zpoint Rsphere phi increment 2 div add sin mul CZ add def
+ % normale � la facette
+ /nXfacette Xpoint CX sub def
+ /nYfacette Ypoint CY sub def
+ /nZfacette Zpoint CZ sub def
+ % test de visibilit�
+ /PSfacetteSphere
+ vX nXfacette mul
+ vY nYfacette mul add
+ vZ nZfacette mul add
+ def
+ condition {
+ gsave
+ facetteSphere
+ /cosV { 1 xLight nXfacette mul
+ yLight nYfacette mul
+ zLight nZfacette mul
+ add add
+ NormeLight
+ nXfacette dup mul
+ nYfacette dup mul
+ nZfacette dup mul
+ add add sqrt mul div sub } bind def
+ Cyan cosV mul Magenta cosV mul Yellow cosV mul K cosV mul setcmykcolor fill
+ grestore
+% 0 setgray
+ showgrid { facetteSphere stroke } if
+ } if
+ } for
+ % /StartTheta StartTheta increment 2 div add def
+ } for
+} def
+%
+%---------------------- Cylinder ---------------------------
+%
+/PlanCoupeCylinder { %
+ /TableauxPoints [
+ 0 1 359 {
+ /phi ED
+ [ Radius phi Height ConvCyl2d ] % on décrit le cercle
+ } for
+ ] def
+ newpath
+ TableauxPoints 0 get aload pop moveto
+ 1 1 359 { TableauxPoints exch get aload pop lineto } for
+ closepath
+} def
+%
+/facetteCylinder { %
+ newpath
+ Radius phi currentHeight ConvCyl2d moveto
+ phi 1 phi dAngle add { % loop variable on stack
+ Radius exch currentHeight ConvCyl2d lineto
+ } for
+ phi dAngle add -1 phi { % fill dHeight
+ Radius exch currentHeight dHeight add ConvCyl2d lineto
+ } for
+ closepath
+ } def % facette
+%
+/MaillageCylinder { % on stack true or false for saving values
+ { setColorLight % expects 4 values on stack C M Y K
+ /dHeight ED /dAngle ED /Height ED /Radius ED
+ /CZ ED /CY ED /CX ED } if
+%
+ 0 dHeight Height dHeight sub {
+ /currentHeight ED
+ 0 dAngle 360 dAngle sub {
+ /phi ED
+% Normal vector of the center
+ /nXfacetteCylinder Radius phi dAngle 2 div add cos mul CX add def
+ /nYfacetteCylinder Radius phi dAngle 2 div add sin mul CY add def
+ /nZfacetteCylinder currentHeight dHeight 2 div add CZ add def
+ /NormeN
+ nXfacetteCylinder dup mul
+ nYfacetteCylinder dup mul
+ nZfacetteCylinder dup mul
+ add add sqrt def
+ NormeN 0 eq { /NormeN 1e-10 def } if
+% test de visibilité
+ /PSfacetteCylinder
+ vX nXfacetteCylinder mul
+ vY nYfacetteCylinder mul add
+ vZ nZfacetteCylinder mul add def
+ condition {
+ facetteCylinder
+ /cosV
+ 1 xLight nXfacetteCylinder mul
+ yLight nYfacetteCylinder mul
+ zLight nZfacetteCylinder mul
+ add add
+ NormeLight NormeN mul div sub def
+ Cyan Magenta Yellow K
+ cosV mul 4 1 roll cosV mul 4 1 roll
+ cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll
+ setcmykcolor fill
+ showgrid {
+ 0 setgray
+ facetteCylinder % drawing the segments
+ stroke } if
+ } if
+ } for
+ } for
+} def
+%
+%------------------------ Cylinder type II -----------------------
+%
+/MoveTo { Conv3D2D moveto } def
+/LineTo { Conv3D2D lineto } def
+
+/IIIDEllipse { % x y z rA rB startAngle endAngle Wedge
+ /dAngle 1 def
+ /isWedge ED
+ /endAngle ED
+ /startAngle ED
+ /radiusB ED
+ /radiusA ED
+ startAngle cos radiusA mul startAngle sin radiusB mul 0
+ isWedge { 0 0 moveto LineTo }{ MoveTo } ifelse
+ /Angle startAngle def
+ startAngle dAngle endAngle {
+ /Angle ED
+ Angle cos radiusA mul Angle sin radiusB mul 0 LineTo
+ } for
+ isWedge { 0 0 lineto } if
+} def
+
+/IIIDCircle { % x y z r startAngle endAngle Wedge
+ 7 3 roll % startAngle endAngle Wedge x y z r
+ dup % startAngle endAngle Wedge x y z r r
+ 8 -3 roll
+ IIIDEllipse
+} def
+
+/IIIDWedge { % x y z r startAngle endAngle
+ true IIIDCircle
+} def
+
+/IIIDCylinder {% x y z r h start end wedge
+ /isWedge ED
+ /increment ED
+ /endAngle ED
+ /startAngle ED
+ /height ED
+ /radius ED
+ startAngle increment endAngle {
+ /Angle ED
+ radius Angle 0 ConvCylToCartesian MoveTo
+ radius Angle height ConvCylToCartesian LineTo
+ } for
+ stroke
+} def
+%
+%---------------------- Box ---------------------------
+%
+/PlanCoupeBox { % x y z
+ /TableauxPoints [
+ [ CX CY CZ Height add ConvBox2d ] % top or bottom
+ [ CX CY Depth add CZ Height add ConvBox2d ]
+ [ CX Width add CY Depth add CZ Height add ConvBox2d ]
+ [ CX Width add CY CZ Height add ConvBox2d ]
+ [ CX CY CZ Height add ConvBox2d ] % bottom
+ ] def
+ newpath
+ TableauxPoints 0 get aload pop moveto
+ 0 1 3 {
+ TableauxPoints exch get aload pop
+ lineto } for
+ closepath
+} def
+%
+/facetteBox { %
+ newpath
+ dup
+ 1 eq { % back
+ CX CY CZ ConvBox2d moveto
+ CX CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ ConvBox2d lineto
+ CX CY CZ ConvBox2d lineto
+ } if
+ dup
+ 2 eq { % right
+ CX CY CZ ConvBox2d moveto
+ CX CY CZ Height add ConvBox2d lineto
+ CX CY Depth add CZ Height add ConvBox2d lineto
+ CX CY Depth add CZ ConvBox2d lineto
+ CX CY CZ ConvBox2d lineto
+ } if
+ dup
+ 3 eq { % left
+ CX Width add CY CZ ConvBox2d moveto
+ CX Width add CY Depth add CZ ConvBox2d lineto
+ CX Width add CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ ConvBox2d lineto
+ } if
+ 4 eq { % front
+ CX CY Depth add CZ ConvBox2d moveto
+ CX CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY Depth add CZ ConvBox2d lineto
+ CX CY Depth add CZ ConvBox2d lineto
+ } if
+ closepath
+ } def % facette
+%
+/TestPlane { % on stack x y z of the plane center and # of plane
+ /nZfacetteBox ED /nYfacetteBox ED /nXfacetteBox ED
+ /Plane ED
+ /NormeN
+ nXfacetteBox dup mul
+ nYfacetteBox dup mul
+ nZfacetteBox dup mul
+ add add sqrt def
+ NormeN 0 eq { /NormeN 1e-10 def } if
+% test de visibilit�
+ /PSfacetteBox
+ vX nXfacetteBox mul
+ vY nYfacetteBox mul add
+ vZ nZfacetteBox mul add def
+ condition {
+ Plane facetteBox
+ /cosV
+ 1 xLight nXfacetteBox mul
+ yLight nYfacetteBox mul
+ zLight nZfacetteBox mul
+ add add
+ NormeLight NormeN mul div sub def
+ Cyan Magenta Yellow K
+ cosV mul 4 1 roll cosV mul 4 1 roll
+ cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll
+ setcmykcolor fill
+ 0 setgray
+ Plane facetteBox % drawing the segments
+ stroke
+ } if
+} def
+%
+/MaillageBox { % on stack true or false for saving values
+ { setColorLight % expects 4 values on stack C M Y K
+ /Depth ED /Height ED /Width ED
+ /CZ ED /CY ED /CX ED } if
+%
+% Normal vector of the box center
+ /PlaneSet [
+ [ Width 2 div CX add
+ CY
+ Height 2 div CZ add ] % normal back
+ [ CX
+ Depth 2 div CY add
+ Height 2 div CZ add ] % normal right
+ [ Width CX add
+ Depth 2 div CY add
+ Height 2 div CZ add ] % normal left
+ [ Width 2 div CX add
+ Depth CY add
+ Height 2 div CZ add ] % normal front
+ ] def
+ PlaneSequence length 0 eq { % user defined?
+ Alpha abs cvi 360 mod /iAlpha ED
+ iAlpha 90 lt { [ 1 2 3 4 ]
+ }{ iAlpha 180 lt { [ 2 4 1 3 ]
+ }{ iAlpha 270 lt { [ 3 4 1 2 ] }{ [ 3 1 4 2] } ifelse } ifelse } ifelse
+ }{ PlaneSequence } ifelse
+ { dup 1 sub PlaneSet exch get aload pop TestPlane } forall
+} def
+%
+%--------------------------- Paraboloid -----------------------------
+/PlanCoupeParaboloid {
+ /Z height store
+ /V {Z sqrt} bind def
+ /TableauxPoints [
+ 0 1 359 {
+ /U ED [ U U Z V calculate2DPoint ] % on d�crit le cercle
+ } for
+ ] def
+ newpath
+ TableauxPoints 0 get aload pop moveto
+ 0 1 359 {
+ /compteur ED
+ TableauxPoints compteur get aload pop
+ lineto } for
+ closepath
+} def
+%
+/facetteParaboloid{
+ newpath
+ U U Z V calculate2DPoint moveto
+ U 1 U increment add {%
+ /U1 ED
+ U1 U1 Z V calculate2DPoint lineto
+ } for
+ Z pas10 Z pas add pas10 add{
+ /Z1 ED
+ /V {Z1 sqrt} bind def
+ U1 U1 Z1 V calculate2DPoint lineto
+ } for
+ U increment add -1 U {%
+ /U2 ED
+ U2 U2 Z pas add V calculate2DPoint lineto
+ } for
+ Z pas add pas10 sub pas10 neg Z pas10 sub {
+ /Z2 ED
+ /V Z2 abs sqrt def
+ U U Z2 V calculate2DPoint lineto
+ } for
+ closepath
+} def % facette
+%
+/MaillageParaboloid {
+ % on stack true or false for saving values
+ { setColorLight % expects 7 values on stack C M Y K xL yL zL
+% /CZ ED /CY ED /CX ED
+ } if
+ 0 pas height pas sub {%
+ /Z ED
+ /V Z sqrt def
+ 0 increment 360 increment sub {%
+ /U ED
+% Centre de la facette
+ /Ucentre U increment 2 div add def
+ /Vcentre Z pas 2 div add sqrt def
+% normale à la facette
+ /nXfacetteParaboloid 2 Vcentre dup mul mul Ucentre cos mul radius mul def
+ /nYfacetteParaboloid 2 Vcentre dup mul mul Ucentre sin mul radius mul def
+ /nZfacetteParaboloid Vcentre neg radius dup mul mul def
+ /NormeN {
+ nXfacetteParaboloid dup mul
+ nYfacetteParaboloid dup mul
+ nZfacetteParaboloid dup mul
+ add add sqrt} bind def
+ NormeN 0 eq {/NormeN 1e-10 def} if
+% test de visibilit�
+ /PSfacetteParaboloid vX nXfacetteParaboloid mul
+ vY nYfacetteParaboloid mul add
+ vZ nZfacetteParaboloid mul add def
+ condition {
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 34.28467 0.0 34.28467 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 41.71289 0.0 41.71289 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 68.94983 0.0 68.94983 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 76.37805 0.0 76.37805 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 78.85419 0.0 78.85419 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 83.80627 0.0 83.80627 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 108.56708 0.0 108.56708 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 111.04321 0.0 111.04321 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 115.9953 0.0 115.9953 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 118.47144 0.0 118.47144 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 120.94757 0.0 120.94757 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 123.42352 0.0 123.42352 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+{ } def /ArrowInside { } def [ 168.0 11.42871 12.0 11.42871 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 13.7146 12.0 13.7146 /Lineto
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+pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 16.0003 12.0 16.0003 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 18.28601 12.0 18.28601 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 20.5719 12.0 20.5719 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 22.8576 12.0 22.8576 /Lineto
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+pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
+@beginspecial @setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 25.14331 12.0 25.14331 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
+@setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 27.4292 12.0 27.4292 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 29.7149 12.0 29.7149 /Lineto
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+pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 32.00061 12.0 32.00061 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 34.28632 12.0 34.28632 /Lineto
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+pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 36.5722 12.0 36.5722 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
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+{ } def /ArrowInside { } def [ 168.0 38.85791 12.0 38.85791 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 41.14362 12.0 41.14362 /Lineto
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+pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 43.4295 12.0 43.4295 /Lineto
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+pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 45.71521 12.0 45.71521 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+%% Version 1.17, 2013/07/08
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+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
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+ /kite_colour ED
+ /dart_colour ED
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+
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+ gsave
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+ 6
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+ /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
+ /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
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+ 5 {kite 72 rotate } repeat stroke
+ grestore
+} def
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+} def
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+ { 0 h T 1 -1 scale } if
+ w neg h moveto
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+ gsave fill grestore
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+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
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+ -.35 0 -.85 .5 -1 1 curveto
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+} def
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+ 0 DS z add CLW 4 div sub
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+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 801 2013-07-09 18:10:41Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
+%
+/Simpson { % on stack must be a b M --- simple version ---
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+%
+/LogGamma { 5 dict begin % z on stack
+ /z ED
+ /sum 0 def
+ /k 1 def
+ {
+ z k div dup 1 add ln sub dup
+ abs eps8 lt { pop exit } if
+ sum add /sum exch def
+ /k k 1 add def
+ } loop
+ sum z ln sub CEuler z mul sub
+ end
+} def
+%
+/ChebyshevT { 5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 2 k mul MoverN mul
+ add
+ } for
+ end
+} def
+%
+/ChebyshevU {5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 1 add 2 k mul 1 add MoverN mul
+ add
+ } for
+ end
+} def
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+%
+end
+
+%%EndProcSet
+%%BeginProcSet: pst-3dplot.pro 0 0
+%% $Id: pst-3dplot.pro 236 2009-12-31 08:59:43Z herbert $
+%%
+%% This is file `pst-3dplot.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-3dplot.tex'
+%%
+%% Herbert Voss <voss _at_ PSTricks.de>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-3dplot' is a PSTricks package to draw 3d curves and graphical objects
+%%
+%%
+%% version 0.30 / 2010-01-01 Herbert Voss <voss _at_ PSTricks.de>
+%% with contributions of Darrell Lamm <darrell.lamm _at_ gtri.gatech.edu<
+%%
+%
+/tx@3DPlotDict 200 dict def
+tx@3DPlotDict begin
+%
+/printDot { gsave 2 copy 2 0 360 arc fill stroke grestore } def
+%
+/saveCoor {
+ dzUnit mul /z ED
+ dyUnit mul /y ED
+ dxUnit mul /x ED
+} def
+%
+/ConvertTo2D {
+ RotatePoint
+ 1 { % dummy loop, will run only 1 time, allows exit
+ coorType 0 le { % the default |
+ /x2D x leftHanded not { neg } if Alpha cos mul y Alpha sin mul add def % /\ co system
+ /y2D x leftHanded { neg } if Alpha sin mul y Alpha cos mul add neg Beta sin mul z Beta cos mul add def
+ exit } if
+ coorType 1 le {
+ /x2D y x Alpha 90 sub sin mul sub def % |/_ co system, no shortened x axis
+ /y2D z x Alpha 90 sub cos mul sub def
+ exit } if
+ coorType 2 le { % coorType |/_ with a 1/sqrt(2) shortend x-axis and 135 degrees
+ /x2D y x 0.5 mul sub def
+ /y2D z x 0.5 mul sub def
+ exit } if
+ coorType 3 le { % coorType |/_ with a 1/sqrt(2) shortend x-axis and 135 degrees
+ /x2D y x -0.5 mul sub def
+ /y2D z x -0.5 mul sub def
+ exit } if
+ coorType 4 le { % Normalbild in Trimetrie Skalierung so, dass coorType2
+ /x2D x -0.5 mul y 1 mul add def
+ /y2D x -0.5 mul y -0.25 mul add z 1 mul add def
+ exit } if
+ } repeat
+} def
+%
+/Conv3D2D { /z ED /y ED /x ED ConvertTo2D x2D y2D } def
+%
+/ConvertToCartesian {
+ /latitude exch def
+ /longitude exch def
+ /Radius exch def
+ 1 { % dummy loop, will run only 1 time, allows exit
+ SphericalCoorType 0 le { % the default |
+ /z { Radius latitude sin mul } def
+ /x { Radius longitude cos mul latitude cos mul } def
+ /y { Radius longitude sin mul latitude cos mul } def
+ exit } if
+ SphericalCoorType 2 le {
+ /z { Radius longitude cos mul } def
+ /x { Radius longitude sin mul latitude cos mul} def
+ /y { Radius longitude sin mul latitude sin mul } def
+ exit } if
+ } repeat
+} def
+%
+/ConvCylToCartesian { % r phi h -> x y z
+ 3 1 roll % h r phi
+ /Phi ED
+ /Radius ED % h->z on stack
+ Radius Phi cos mul exch % x z
+ Radius Phi sin mul exch % x y z
+} def
+%
+/SphericalTo2D {
+ x y z ConvertToCartesian ConvertTo2D
+} def
+%
+/CylinderTo2D { % r phi h
+ x y z ConvCylToCartesian ConvertTo2D
+} def
+%
+/convertStackTo2D {
+ counttomark
+ /n ED /n3 n 3 div cvi def
+ n3 {
+ n -3 roll
+ SphericalCoor { ConvertToCartesian } { saveCoor } ifelse
+ ConvertTo2D
+ x2D xUnit y2D yUnit
+ /n n 1 sub def
+ } repeat
+} def
+%
+% the angle in the parameter equation for an ellipse is not proportional to the real angle!
+% phi=atan(b*tan(angle)/a)+floor(angle/180+0.5)*180
+%
+/getPhi { % on stack: vecA vecB angle
+ 3 dict begin
+ /angle exch def /vecB exch def /vecA exch def
+ angle cvi 90 mod 0 eq { angle } { vecA angle tan mul vecB atan
+ angle 180 div .5 add floor 180 mul add } ifelse
+ end
+} def
+%
+/RotSet (set ) def
+%
+/eulerRotation false def
+% Matrix multiplication procedure
+/matmul {
+
+ /M@tMulDict 20 dict def
+ M@tMulDict begin
+ /m2 ED
+ /m1 ED
+ m1 dup length 2 sub 2 getinterval aload pop
+ /col1max ED
+ /row1max ED
+ m2 dup length 2 sub 2 getinterval aload pop
+ /col2max ED
+ /row2max ED
+ /m3 row1max col2max mul 2 add array def
+ m3 dup length 2 sub row1max col2max 2 array astore putinterval
+ 0 1 row1max 1 sub {
+ /row ED
+ 0 1 col2max 1 sub {
+ /col ED
+ /sum 0 def
+ 0 1 col1max 1 sub{
+ /rowcol ED
+ sum
+ m1 row col1max mul rowcol add get
+ m2 rowcol col2max mul col add get
+ mul add
+ /sum ED
+ } for
+ m3 row col2max mul col add sum put
+ } for
+ } for
+ m3
+ end % end of M@tMulDict
+
+} def
+%
+/SetMQuaternion {
+
+ /MnewTOold 11 array def
+
+ /Qu@ternionDict 30 dict def
+ Qu@ternionDict begin
+
+ /normRotVec xRotVec yRotVec zRotVec 3 array astore VecNorm def
+ normRotVec 0 gt
+ {/xRotVecNorm xRotVec normRotVec div def
+ /yRotVecNorm yRotVec normRotVec div def
+ /zRotVecNorm zRotVec normRotVec div def
+ RotAngle}
+ {/xRotVecNorm 1 def
+ /yRotVecNorm 0 def
+ /zRotVecNorm 0 def
+ 0} ifelse
+
+ 2 div dup
+ /q0 exch cos def
+ sin dup dup
+ /q1 exch xRotVecNorm mul def
+ /q2 exch yRotVecNorm mul def
+ /q3 exch zRotVecNorm mul def
+
+ /q0q0 q0 q0 mul def
+ /q0q1 q0 q1 mul def
+ /q0q2 q0 q2 mul def
+ /q0q3 q0 q3 mul def
+
+ /q1q1 q1 q1 mul def
+ /q1q2 q1 q2 mul def
+ /q1q3 q1 q3 mul def
+
+ /q2q2 q2 q2 mul def
+ /q2q3 q2 q3 mul def
+
+ /q3q3 q3 q3 mul def
+
+ MnewTOold 0 q0q0 q1q1 add q2q2 sub q3q3 sub put
+ MnewTOold 1 q1q2 q0q3 sub 2 mul put
+ MnewTOold 2 q1q3 q0q2 add 2 mul put
+
+ MnewTOold 3 q1q2 q0q3 add 2 mul put
+ MnewTOold 4 q0q0 q1q1 sub q2q2 add q3q3 sub put
+ MnewTOold 5 q2q3 q0q1 sub 2 mul put
+
+ MnewTOold 6 q1q3 q0q2 sub 2 mul put
+ MnewTOold 7 q2q3 q0q1 add 2 mul put
+ MnewTOold 8 q0q0 q1q1 sub q2q2 sub q3q3 add put
+
+ MnewTOold 9 3 put
+ MnewTOold 10 3 put
+
+ end % end of Qu@ternionDict
+
+} def
+%
+/SetMxyz {
+ 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 3 3 11 array astore /MnewTOold ED
+ RotSequence cvx exec % Now create a new MnewTOold using xyz, etc.
+} def
+%
+/ConcatMQuaternion {
+ MnewTOold % Push onto stack
+ SetMQuaternion % Uses [xyz]RotVec and RotAngle to make MnewToOld
+ MnewTOold matmul /MnewTOold ED
+} def
+%
+/ConcatMxyz {
+ MnewTOold % Push onto stack
+ SetMxyz % Uses RotX, etc. to set MnewTOold
+ MnewTOold matmul /MnewTOold ED
+} def
+%
+/RotatePoint{
+ MnewTOold x y z 3 1 5 array astore matmul
+ 0 3 getinterval aload pop
+ /z ED
+ /y ED
+ /x ED
+} def
+%
+/makeMoldTOnew {
+ /MoldTOnew 11 array def
+ MoldTOnew 0 MnewTOold 0 get put
+ MoldTOnew 1 MnewTOold 3 get put
+ MoldTOnew 2 MnewTOold 6 get put
+ MoldTOnew 3 MnewTOold 1 get put
+ MoldTOnew 4 MnewTOold 4 get put
+ MoldTOnew 5 MnewTOold 7 get put
+ MoldTOnew 6 MnewTOold 2 get put
+ MoldTOnew 7 MnewTOold 5 get put
+ MoldTOnew 8 MnewTOold 8 get put
+ MoldTOnew 9 3 put
+ MoldTOnew 10 3 put
+} def
+%
+/RotXaxis {
+ eulerRotation
+ {1 0 0}
+ {makeMoldTOnew MoldTOnew 1 0 0 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotX def
+ ConcatMQuaternion
+} def
+/RotYaxis {
+ eulerRotation
+ {0 1 0}
+ {makeMoldTOnew MoldTOnew 0 1 0 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotY def
+ ConcatMQuaternion
+} def
+/RotZaxis {
+ eulerRotation
+ {0 0 1}
+ {makeMoldTOnew MoldTOnew 0 0 1 3 1 5 array astore matmul
+ 0 3 getinterval aload pop} ifelse
+ /zRotVec ED
+ /yRotVec ED
+ /xRotVec ED
+ /RotAngle RotZ def
+ ConcatMQuaternion
+} def
+/xyz { RotXaxis RotYaxis RotZaxis } def
+/yxz { RotYaxis RotXaxis RotZaxis } def
+/yzx { RotYaxis RotZaxis RotXaxis } def
+/xzy { RotXaxis RotZaxis RotYaxis } def
+/zxy { RotZaxis RotXaxis RotYaxis } def
+/zyx { RotZaxis RotYaxis RotXaxis } def
+/quaternion { } def % Null
+%
+/VecNorm { 0 exch { dup mul add } forall sqrt } def
+%
+/UnitVec { % on stack is [a]; returns a vector with [a][a]/|a|=1
+ dup VecNorm /norm ED
+ norm 0 lt {/norm 0 def} if
+ { norm div } forall 3 array astore } def
+%
+/AxB { % on the stack are the two vectors [a][b]
+ aload pop /b3 ED /b2 ED /b1 ED
+ aload pop /a3 ED /a2 ED /a1 ED
+ a2 b3 mul a3 b2 mul sub
+ a3 b1 mul a1 b3 mul sub
+ a1 b2 mul a2 b1 mul sub
+ 3 array astore } def
+%
+/AaddB { % on the stack are the two vectors [a][b]
+ aload pop /b3 ED /b2 ED /b1 ED
+ aload pop /a3 ED /a2 ED /a1 ED
+ a1 b1 add a2 b2 add a3 b3 add
+ 3 array astore } def
+%
+/AmulC { % on stack is [a] and c; returns [a] mul c
+ /factor ED { factor mul } forall 3 array astore } def
+%
+%
+/setColorLight { % expects 7 values on stack C M Y K xL yL zL
+% les rayons de lumi�re
+ xLight dup mul yLight dup mul zLight dup mul add add sqrt /NormeLight ED
+% the color values
+ /K ED
+ /Yellow ED
+ /Magenta ED
+ /Cyan ED
+} def
+%
+/facetteSphere {
+ newpath
+ /Xpoint Rsphere theta cos mul phi cos mul CX add def
+ /Ypoint Rsphere theta sin mul phi cos mul CY add def
+ /Zpoint Rsphere phi sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end moveto
+ theta 1 theta increment add {%
+ /theta1 ED
+ /Xpoint Rsphere theta1 cos mul phi cos mul CX add def
+ /Ypoint Rsphere theta1 sin mul phi cos mul CY add def
+ /Zpoint Rsphere phi sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ phi 1 phi increment add {
+ /phi1 ED
+ /Xpoint Rsphere theta increment add cos mul phi1 cos mul CX add def
+ /Ypoint Rsphere theta increment add sin mul phi1 cos mul CY add def
+ /Zpoint Rsphere phi1 sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ theta increment add -1 theta {%
+ /theta1 ED
+ /Xpoint Rsphere theta1 cos mul phi increment add cos mul CX add def
+ /Ypoint Rsphere theta1 sin mul phi increment add cos mul CY add def
+ /Zpoint Rsphere phi increment add sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ phi increment add -1 phi {
+ /phi1 ED
+ /Xpoint Rsphere theta cos mul phi1 cos mul CX add def
+ /Ypoint Rsphere theta sin mul phi1 cos mul CY add def
+ /Zpoint Rsphere phi1 sin mul CZ add def
+ Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto
+ } for
+ closepath
+} def
+%
+/MaillageSphere {
+% on stack must be x y z Radius increment C M Y K
+ setColorLight
+ /increment ED
+ /Rsphere ED
+ /CZ ED
+ /CY ED
+ /CX ED
+ /StartTheta 0 def
+ /condition { PSfacetteSphere 0 ge } def
+ -90 increment 90 increment sub {%
+ /phi ED
+ StartTheta increment 360 StartTheta add increment sub {%
+ /theta ED
+ % Centre de la facette
+ /Xpoint Rsphere theta increment 2 div add cos mul phi increment 2 div add cos mul CX add def
+ /Ypoint Rsphere theta increment 2 div add sin mul phi increment 2 div add cos mul CY add def
+ /Zpoint Rsphere phi increment 2 div add sin mul CZ add def
+ % normale � la facette
+ /nXfacette Xpoint CX sub def
+ /nYfacette Ypoint CY sub def
+ /nZfacette Zpoint CZ sub def
+ % test de visibilit�
+ /PSfacetteSphere
+ vX nXfacette mul
+ vY nYfacette mul add
+ vZ nZfacette mul add
+ def
+ condition {
+ gsave
+ facetteSphere
+ /cosV { 1 xLight nXfacette mul
+ yLight nYfacette mul
+ zLight nZfacette mul
+ add add
+ NormeLight
+ nXfacette dup mul
+ nYfacette dup mul
+ nZfacette dup mul
+ add add sqrt mul div sub } bind def
+ Cyan cosV mul Magenta cosV mul Yellow cosV mul K cosV mul setcmykcolor fill
+ grestore
+% 0 setgray
+ showgrid { facetteSphere stroke } if
+ } if
+ } for
+ % /StartTheta StartTheta increment 2 div add def
+ } for
+} def
+%
+%---------------------- Cylinder ---------------------------
+%
+/PlanCoupeCylinder { %
+ /TableauxPoints [
+ 0 1 359 {
+ /phi ED
+ [ Radius phi Height ConvCyl2d ] % on décrit le cercle
+ } for
+ ] def
+ newpath
+ TableauxPoints 0 get aload pop moveto
+ 1 1 359 { TableauxPoints exch get aload pop lineto } for
+ closepath
+} def
+%
+/facetteCylinder { %
+ newpath
+ Radius phi currentHeight ConvCyl2d moveto
+ phi 1 phi dAngle add { % loop variable on stack
+ Radius exch currentHeight ConvCyl2d lineto
+ } for
+ phi dAngle add -1 phi { % fill dHeight
+ Radius exch currentHeight dHeight add ConvCyl2d lineto
+ } for
+ closepath
+ } def % facette
+%
+/MaillageCylinder { % on stack true or false for saving values
+ { setColorLight % expects 4 values on stack C M Y K
+ /dHeight ED /dAngle ED /Height ED /Radius ED
+ /CZ ED /CY ED /CX ED } if
+%
+ 0 dHeight Height dHeight sub {
+ /currentHeight ED
+ 0 dAngle 360 dAngle sub {
+ /phi ED
+% Normal vector of the center
+ /nXfacetteCylinder Radius phi dAngle 2 div add cos mul CX add def
+ /nYfacetteCylinder Radius phi dAngle 2 div add sin mul CY add def
+ /nZfacetteCylinder currentHeight dHeight 2 div add CZ add def
+ /NormeN
+ nXfacetteCylinder dup mul
+ nYfacetteCylinder dup mul
+ nZfacetteCylinder dup mul
+ add add sqrt def
+ NormeN 0 eq { /NormeN 1e-10 def } if
+% test de visibilité
+ /PSfacetteCylinder
+ vX nXfacetteCylinder mul
+ vY nYfacetteCylinder mul add
+ vZ nZfacetteCylinder mul add def
+ condition {
+ facetteCylinder
+ /cosV
+ 1 xLight nXfacetteCylinder mul
+ yLight nYfacetteCylinder mul
+ zLight nZfacetteCylinder mul
+ add add
+ NormeLight NormeN mul div sub def
+ Cyan Magenta Yellow K
+ cosV mul 4 1 roll cosV mul 4 1 roll
+ cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll
+ setcmykcolor fill
+ showgrid {
+ 0 setgray
+ facetteCylinder % drawing the segments
+ stroke } if
+ } if
+ } for
+ } for
+} def
+%
+%------------------------ Cylinder type II -----------------------
+%
+/MoveTo { Conv3D2D moveto } def
+/LineTo { Conv3D2D lineto } def
+
+/IIIDEllipse { % x y z rA rB startAngle endAngle Wedge
+ /dAngle 1 def
+ /isWedge ED
+ /endAngle ED
+ /startAngle ED
+ /radiusB ED
+ /radiusA ED
+ startAngle cos radiusA mul startAngle sin radiusB mul 0
+ isWedge { 0 0 moveto LineTo }{ MoveTo } ifelse
+ /Angle startAngle def
+ startAngle dAngle endAngle {
+ /Angle ED
+ Angle cos radiusA mul Angle sin radiusB mul 0 LineTo
+ } for
+ isWedge { 0 0 lineto } if
+} def
+
+/IIIDCircle { % x y z r startAngle endAngle Wedge
+ 7 3 roll % startAngle endAngle Wedge x y z r
+ dup % startAngle endAngle Wedge x y z r r
+ 8 -3 roll
+ IIIDEllipse
+} def
+
+/IIIDWedge { % x y z r startAngle endAngle
+ true IIIDCircle
+} def
+
+/IIIDCylinder {% x y z r h start end wedge
+ /isWedge ED
+ /increment ED
+ /endAngle ED
+ /startAngle ED
+ /height ED
+ /radius ED
+ startAngle increment endAngle {
+ /Angle ED
+ radius Angle 0 ConvCylToCartesian MoveTo
+ radius Angle height ConvCylToCartesian LineTo
+ } for
+ stroke
+} def
+%
+%---------------------- Box ---------------------------
+%
+/PlanCoupeBox { % x y z
+ /TableauxPoints [
+ [ CX CY CZ Height add ConvBox2d ] % top or bottom
+ [ CX CY Depth add CZ Height add ConvBox2d ]
+ [ CX Width add CY Depth add CZ Height add ConvBox2d ]
+ [ CX Width add CY CZ Height add ConvBox2d ]
+ [ CX CY CZ Height add ConvBox2d ] % bottom
+ ] def
+ newpath
+ TableauxPoints 0 get aload pop moveto
+ 0 1 3 {
+ TableauxPoints exch get aload pop
+ lineto } for
+ closepath
+} def
+%
+/facetteBox { %
+ newpath
+ dup
+ 1 eq { % back
+ CX CY CZ ConvBox2d moveto
+ CX CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ ConvBox2d lineto
+ CX CY CZ ConvBox2d lineto
+ } if
+ dup
+ 2 eq { % right
+ CX CY CZ ConvBox2d moveto
+ CX CY CZ Height add ConvBox2d lineto
+ CX CY Depth add CZ Height add ConvBox2d lineto
+ CX CY Depth add CZ ConvBox2d lineto
+ CX CY CZ ConvBox2d lineto
+ } if
+ dup
+ 3 eq { % left
+ CX Width add CY CZ ConvBox2d moveto
+ CX Width add CY Depth add CZ ConvBox2d lineto
+ CX Width add CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY CZ Height add ConvBox2d lineto
+ CX Width add CY CZ ConvBox2d lineto
+ } if
+ 4 eq { % front
+ CX CY Depth add CZ ConvBox2d moveto
+ CX CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY Depth add CZ Height add ConvBox2d lineto
+ CX Width add CY Depth add CZ ConvBox2d lineto
+ CX CY Depth add CZ ConvBox2d lineto
+ } if
+ closepath
+ } def % facette
+%
+/TestPlane { % on stack x y z of the plane center and # of plane
+ /nZfacetteBox ED /nYfacetteBox ED /nXfacetteBox ED
+ /Plane ED
+ /NormeN
+ nXfacetteBox dup mul
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 59.04547 0.0 59.04547 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 66.4737 0.0 66.4737 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 96.18677 0.0 96.18677 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 98.66272 0.0 98.66272 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 101.13885 0.0 101.13885 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 103.61499 0.0 103.61499 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 106.09113 0.0 106.09113 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 108.56708 0.0 108.56708 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
+@beginspecial @setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 111.04321 0.0 111.04321 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 113.51935 0.0 113.51935 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
+@setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+{ } def /ArrowInside { } def [ 133.32788 0.0 133.32788 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 135.80402 0.0 135.80402 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 138.28015 0.0 138.28015 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 140.7561 0.0 140.7561 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 143.23224 0.0 143.23224 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 145.70837 0.0 145.70837 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 148.18433 0.0 148.18433 144.0 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
+
+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+pop pop Lineto } repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat
+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def
+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 0.0 12.0 0.0 /Lineto /lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 168.0 2.2857 12.0 2.2857 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 168.0 6.8573 12.0 6.8573 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 168.0 9.143 12.0 9.143 /Lineto /lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
+{ } def /ArrowInside { } def [ 168.0 11.42871 12.0 11.42871 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
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+{ } def /ArrowInside { } def [ 168.0 13.7146 12.0 13.7146 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial @beginspecial @setspecial
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+/ArrowInside { } def 0.2 SLW 0 setgray /ArrowA { moveto } def /ArrowB
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
+ 1. .setopacityalpha 1 setlinejoin 0 setlinecap stroke grestore
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 168.0 75.43011 12.0 75.43011 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+{ } def /ArrowInside { } def [ 168.0 82.28741 12.0 82.28741 /Lineto
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial @setspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+@endspecial @beginspecial
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+end
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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+} ifelse CP 4 2 roll ArrowB L pop pop } if gsave 0.2 SLW 0 setgray
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diff --git a/info/pstricks_calcnotes/For_Ps_Output/vecb1.eps b/info/pstricks_calcnotes/For_Ps_Output/vecb1.eps
new file mode 100644
index 0000000000..8954f47408
--- /dev/null
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@@ -0,0 +1,14943 @@
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+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
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+ /pstZeros exch def
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+ /k exch def
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+} def
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+} def
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+} def
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+/cxmake2 { 2 array astore } def % dito, both given
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+} def
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+%%EndFont
+%%BeginFont: CMR8
+%!PS-AdobeFont-1.0: CMR8 003.002
+%%Title: CMR8
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR8.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMR8 known{/CMR8 findfont dup/UniqueID known{dup
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+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMR8 def
+/FontBBox {-36 -250 1070 750 }readonly def
+/UniqueID 5000791 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR8.) readonly def
+/FullName (CMR8) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
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+dup 51 /three put
+readonly def
+currentdict end
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.9 0.9 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.9 0.9 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (0.6+((0.35)*t)*(1/sqrt(1+(sin(0.6)*cos(-1.0))^2))|-1.0+((0.35)*t)*(1/sqrt(1+(sin(0.6)*cos(-1.0))^2))*(sin(0.6)*cos(-1.0))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.5 0.5 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
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+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.5 0.5 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (1.0+((0.35)*t)*(1/sqrt(1+(sin(1.0)*cos(-1.0))^2))|-1.0+((0.35)*t)*(1/sqrt(1+(sin(1.0)*cos(-1.0))^2))*(sin(1.0)*cos(-1.0))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.3 0.3 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.3 0.3 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.2 0.2 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
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+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.2 0.2 setrgbcolor
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+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (1.8+((0.35)*t)*(1/sqrt(1+(sin(1.8)*cos(-1.0))^2))|-1.0+((0.35)*t)*(1/sqrt(1+(sin(1.8)*cos(-1.0))^2))*(sin(1.8)*cos(-1.0))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.2 0.2 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.2 0.2 setrgbcolor
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+end
+
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+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
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+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.3 0.3 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.3 0.3 setrgbcolor
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+end
+
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+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
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+def NewNode end end
+ 998 901 a @beginspecial
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.8 0.8 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.8 0.8 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.3 0.3 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.3 0.3 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
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+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
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+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0 0 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
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+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0 0 setrgbcolor 1.
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+
+@endspecial 998 901 a
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+ 998 901 a 998 901
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
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+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
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+def NewNode end end
+ 998 901 a @beginspecial
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
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+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0 0 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
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+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0 0 setrgbcolor 1.
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+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
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+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0 0 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
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+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
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+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
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+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+
+@endspecial 998 901 a
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
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+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
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+def NewNode end end
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
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+ %% Computation of the scaling factor as described by van Zandt:
+ b a .5 sub 2 mul y mul sub z Div round
+ z mul a .5 sub 2 mul y mul add b exch Div
+ %%%% scaling factor on stack.
+ /z ED %% now, z is the scaling factor
+ false % for the length test below
+ X { z mul } forall X astore %% modification TN 04-08-07
+ %%% Checking whether at least one dash in X has positive length:
+ {0 gt or} forall
+ { X 1 a sub y mul }
+ { [ 1 0 ] 0 }
+ ifelse
+ setdash stroke
+} def
+%
+/DotLine {
+ /b PathLength def
+ /a ED /z ED /y CLW def
+ /z y z add def
+ a 0 gt {
+ /b b a div def
+ }{
+ a 0 eq {
+ /b b y sub def
+ }{ a -3 eq {
+ /b b y add def } if
+ } ifelse
+ } ifelse
+ [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
+ a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
+ setdash 1 setlinecap stroke
+} def
+%
+/SymbolLine { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt
+ { %XYLength SymStep div abs cvi
+ /nSym SymStep abs cvi def }
+ { /nSym XYLength SymStep div cvi def }
+ ifelse
+ 0.5 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ /deltaX XLength nSym div def
+ /deltaY YLength nSym div def
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ nSym {
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ currentpoint translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+ /YA YB def /XA XB def
+ } repeat
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ XA YA translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ pop % delete the mark symbol
+} def
+%
+/LineFill { % hv ------------ patch 7 -------------
+ gsave
+ abs /hatchWidthInc ED
+ abs /hatchSepInc ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clipType % must be defined in pstricks.tex: clip -- eoclip
+ newpath
+ 2 setlinecap
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ x2 x1 sub 1 add {
+ x1 a mul y1 moveto 0 y2 rlineto stroke
+ /x1 x1 1 add
+ hatchWidthInc 0 gt { CLW add } if
+ def
+ hatchSepInc 0 gt hatchWidthInc 0 gt or {
+ /a a hatchSepInc add def
+ CLW hatchWidthInc add SLW
+ } if
+ } repeat
+ grestore
+ pop pop } def
+%
+/DotFill {% on stack: dot radius
+ /dotRadius ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform
+ pathbbox % llx lly urx ury of smallest bounding box
+ /y2 ED /x2 ED /y1 ED /x1 ED
+ y2 y1 sub a div 2 add cvi /Ny ED
+ x2 x1 sub a div 2 add cvi /Nx ED
+ clipType % must be defined in pstricks.tex: clip -- eoclip
+ newpath
+ /yA y1 dotRadius add CLW add def
+ /xA0 x1 dotRadius add CLW add def
+ Ny {
+ /xA xA0 def
+ Nx {
+ newpath
+ xA yA dotRadius 0 360 arc
+ SolidDot { gsave fill grestore } if
+ stroke
+ xA a add /xA ED
+ } repeat
+ yA a add /yA ED
+ } repeat
+ grestore
+} def
+%
+/PenroseFill {% on stack: scaling factor
+ /Scale ED
+% 1 exch div round /penroseFactor ED
+% a 0 dtransform round exch round exch
+% 2 copy idtransform
+% exch Atan rotate
+% idtransform pop /a ED
+% .25 .25 itransform pathbbox
+% /y2 ED
+% a Div ceiling cvi /x2 ED /y1 ED
+% a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+gsave
+ 220 150 translate
+ Scale dup scale
+ systemdict /setstrokeadjust known { true setstrokeadjust } if
+ /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
+ { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
+ [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
+ i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
+ mul j l + S rmoveto}F i L j L stroke }F}F}F}F
+ grestore
+% pop pop
+} def
+%
+/PenroseFillA {% on stack: scaling factor, border color, kite color, dart color
+ /Scale ED
+ Scale dup scale
+ /border_colour ED
+ /kite_colour ED
+ /dart_colour ED
+ clip
+
+ newpath
+ gsave
+ 100 100 translate
+ 6
+ Scale 1 lt { 1 Scale dup add div mul cvi } if %%%% Number of iterations
+ 10 %%%% Long side length in millimeters
+ /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
+ /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
+ /f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio
+ /l{L f mul}bind def %%%% Short side length l = L*f
+ /Ll{L l add}bind def %%%% Ll = L + l
+ /c{36 cos L mul}bind def %%%% c = L*cos(36)
+ /s{36 sin L mul}bind def %%%% s = L*sin(36)
+ /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
+ 0 setlinewidth stroke grestore border_colour stroke } bind def
+ /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
+ Ll 0 translate 144 rotate kite grestore }
+ { kite_colour L draw_tile }ifelse
+ pop } bind def
+ /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
+ -144 rotate Ll neg 0 translate half_dart grestore }
+ { dart_colour l draw_tile }ifelse
+ pop } bind def
+ /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
+ border_width setlinewidth 1 setlinejoin 1 setlinecap
+% 450 0 translate
+ dup f exch neg exp dup scale
+ 5 {kite 72 rotate } repeat stroke
+ grestore
+} def
+%
+%
+/TruchetFill { % on stack: scaling factor
+ 10 dict begin
+ dup dup scale
+ 1 exch div round /penroseFactor ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ /ma a neg def
+ /ha a 2 div def
+ /mha ha neg def
+ /tile {
+ rand dup 2 idiv 2 mul eq { 90 rotate } if
+ mha mha moveto ha mha lineto
+ ha ha lineto mha ha lineto
+% closepath .1 setlinewidth stroke
+ contents
+ } def
+ /contents{
+ 0 ha moveto ha 0 lineto
+ 0 mha moveto mha 0 lineto
+% 1 setlinewidth stroke
+ } def
+ /dotiling {
+ f ma mul a f a mul {
+ /i exch def
+ f ma mul a f a mul {
+ /j exch def
+ gsave i j translate
+ tile stroke grestore
+ } for
+ } for
+ } def
+%
+ /f 3 def
+ 5 srand dotiling
+ end % local user dict
+} def
+%
+/BeginArrow {
+ ADict begin % hold it local, for end see EndArrow
+ /@mtrx CM def
+ gsave
+ 2 copy T
+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
+%
+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
+%
+/Arrow {
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
+%
+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
+ gsave fill grestore
+} def
+%
+/Tbar {
+ CLW mul add /z ED
+ z -2 div CLW 2 div moveto
+ z 0 rlineto stroke
+ 0 CLW moveto
+} def
+%
+/Bracket {
+ CLW mul add dup CLW sub 2 div
+ /x ED mul CLW add /y ED /z CLW 2 div def
+ x neg y moveto
+ x neg CLW 2 div L x CLW 2 div L x y L stroke
+ 0 CLW moveto
+} def
+%
+/RoundBracket {
+ CLW mul add dup 2 div
+ /x ED mul /y ED /mtrx CM def
+ 0 CLW 2 div T x y mul 0 ne { x y scale } if
+ 1 1 moveto
+ .85 .5 .35 0 0 0 curveto
+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
+ /b ED % the color definition
+ 0 z DS SD
+ b { 0 z DS CLW sub SD } if
+ 0 DS z add CLW 4 div sub
+ moveto
+} def
+%
+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+ load } if ] cvx newpath 3 1 roll T exec } def
+%
+/NArray { % holds the coordinates and on top of stack the showpoints boolean
+ /showpoints ED
+ counttomark 2 div dup cvi /n ED % n 2 div on stack
+ n eq not { exch pop } if % even numbers of points? delete one
+ ] aload /Points ED
+ showpoints not { Points aload pop } if
+% { ] aload /Points ED }
+% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
+} def
+%
+/Line {
+ NArray n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
+ n { Lineto } repeat
+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
+%
+/LineToYAxis {
+ /Ox ED % Save the x origin value
+ NArray % all x-y pairs on stack
+ n { 2 copy moveto % go to current point
+ Ox exch Lineto % line to y-axis
+ pop % delete old x-value
+ } repeat
+} def
+%
+/LineToXAxis{
+ /Oy ED % Save the y origin value
+ NArray % all x-y pairs on stack
+ n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if
+ ArrowA
+ /n n 2 sub def
+ CP 2 copy moveto pop Oy Lineto
+ n { 2 copy moveto pop Oy Lineto } repeat
+ CP
+ 4 2 roll
+ ArrowB
+ 2 copy moveto pop Oy
+ L
+ pop pop } if
+} def
+%
+/Arcto {
+ /a [ 6 -2 roll ] cvx def
+ a r
+ /arcto load stopped { 5 } { 4 } ifelse { pop } repeat
+ a
+} def
+%
+/CheckClosed {
+ dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
+ and { pop pop /n n 1 sub def } if
+} def
+%
+/Polygon {
+ NArray n 2 eq { 0 0 /n 3 def } if
+ n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ n 2 mul -2 roll
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ n { Lineto } repeat
+ x1 y1 x0 y0 6 4 roll Lineto
+ Lineto pop pop closepath } ifelse
+} def
+%
+/SymbolPolygon { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 add /m ED
+ 2 copy m 2 roll % copy last two
+ m 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+ /nSym XYLength SymStep Div cvi def
+ /Shift Symbol stringwidth pop 2 Div def
+ /deltaX XLength nSym Div def
+ /deltaY YLength nSym Div def
+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
+%
+/Simpson { % on stack must be a b M --- simple version ---
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+%
+/LogGamma { 5 dict begin % z on stack
+ /z ED
+ /sum 0 def
+ /k 1 def
+ {
+ z k div dup 1 add ln sub dup
+ abs eps8 lt { pop exit } if
+ sum add /sum exch def
+ /k k 1 add def
+ } loop
+ sum z ln sub CEuler z mul sub
+ end
+} def
+%
+/ChebyshevT { 5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 2 k mul MoverN mul
+ add
+ } for
+ end
+} def
+%
+/ChebyshevU {5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 1 add 2 k mul 1 add MoverN mul
+ add
+ } for
+ end
+} def
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+%
+end
+
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+%%EndFont
+%%BeginFont: CMR8
+%!PS-AdobeFont-1.0: CMR8 003.002
+%%Title: CMR8
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR8.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+/FontName /CMR8 def
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+/version (003.002) readonly def
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+/FullName (CMR8) readonly def
+/FamilyName (Computer Modern) readonly def
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+end readonly def
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+) AlgParser cvx def end
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+) AlgParser cvx def end
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+) AlgParser cvx def end
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+) AlgParser cvx def end
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
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+) AlgParser cvx def end
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+ {}
+ { /y y2 def /x x2 def PathLength@ }
+ /pathforall load stopped { pop pop pop pop } if
+ z
+} def
+%
+/STP { .996264 dup scale } def % BP/PT scaling
+/STV { SDict begin normalscale end STP } def %
+%
+/DashLine {
+ dup 0 gt
+ { /a .5 def PathLength exch div }
+ { pop /a 1 def PathLength } ifelse
+ /b ED % pattern should fit evenly in b
+ dup /X ED % pattern array
+ 0 get /y ED % length of first black segment
+ /z 0 X {add} forall def % length of the full pattern
+ %% Computation of the scaling factor as described by van Zandt:
+ b a .5 sub 2 mul y mul sub z Div round
+ z mul a .5 sub 2 mul y mul add b exch Div
+ %%%% scaling factor on stack.
+ /z ED %% now, z is the scaling factor
+ false % for the length test below
+ X { z mul } forall X astore %% modification TN 04-08-07
+ %%% Checking whether at least one dash in X has positive length:
+ {0 gt or} forall
+ { X 1 a sub y mul }
+ { [ 1 0 ] 0 }
+ ifelse
+ setdash stroke
+} def
+%
+/DotLine {
+ /b PathLength def
+ /a ED /z ED /y CLW def
+ /z y z add def
+ a 0 gt {
+ /b b a div def
+ }{
+ a 0 eq {
+ /b b y sub def
+ }{ a -3 eq {
+ /b b y add def } if
+ } ifelse
+ } ifelse
+ [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
+ a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
+ setdash 1 setlinecap stroke
+} def
+%
+/SymbolLine { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt
+ { %XYLength SymStep div abs cvi
+ /nSym SymStep abs cvi def }
+ { /nSym XYLength SymStep div cvi def }
+ ifelse
+ 0.5 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ /deltaX XLength nSym div def
+ /deltaY YLength nSym div def
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ nSym {
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ currentpoint translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+ /YA YB def /XA XB def
+ } repeat
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ XA YA translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ pop % delete the mark symbol
+} def
+%
+/LineFill { % hv ------------ patch 7 -------------
+ gsave
+ abs /hatchWidthInc ED
+ abs /hatchSepInc ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clipType % must be defined in pstricks.tex: clip -- eoclip
+ newpath
+ 2 setlinecap
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ x2 x1 sub 1 add {
+ x1 a mul y1 moveto 0 y2 rlineto stroke
+ /x1 x1 1 add
+ hatchWidthInc 0 gt { CLW add } if
+ def
+ hatchSepInc 0 gt hatchWidthInc 0 gt or {
+ /a a hatchSepInc add def
+ CLW hatchWidthInc add SLW
+ } if
+ } repeat
+ grestore
+ pop pop } def
+%
+/DotFill {% on stack: dot radius
+ /dotRadius ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform
+ pathbbox % llx lly urx ury of smallest bounding box
+ /y2 ED /x2 ED /y1 ED /x1 ED
+ y2 y1 sub a div 2 add cvi /Ny ED
+ x2 x1 sub a div 2 add cvi /Nx ED
+ clipType % must be defined in pstricks.tex: clip -- eoclip
+ newpath
+ /yA y1 dotRadius add CLW add def
+ /xA0 x1 dotRadius add CLW add def
+ Ny {
+ /xA xA0 def
+ Nx {
+ newpath
+ xA yA dotRadius 0 360 arc
+ SolidDot { gsave fill grestore } if
+ stroke
+ xA a add /xA ED
+ } repeat
+ yA a add /yA ED
+ } repeat
+ grestore
+} def
+%
+/PenroseFill {% on stack: scaling factor
+ /Scale ED
+% 1 exch div round /penroseFactor ED
+% a 0 dtransform round exch round exch
+% 2 copy idtransform
+% exch Atan rotate
+% idtransform pop /a ED
+% .25 .25 itransform pathbbox
+% /y2 ED
+% a Div ceiling cvi /x2 ED /y1 ED
+% a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+gsave
+ 220 150 translate
+ Scale dup scale
+ systemdict /setstrokeadjust known { true setstrokeadjust } if
+ /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
+ { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
+ [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
+ i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
+ mul j l + S rmoveto}F i L j L stroke }F}F}F}F
+ grestore
+% pop pop
+} def
+%
+/PenroseFillA {% on stack: scaling factor, border color, kite color, dart color
+ /Scale ED
+ Scale dup scale
+ /border_colour ED
+ /kite_colour ED
+ /dart_colour ED
+ clip
+
+ newpath
+ gsave
+ 100 100 translate
+ 6
+ Scale 1 lt { 1 Scale dup add div mul cvi } if %%%% Number of iterations
+ 10 %%%% Long side length in millimeters
+ /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
+ /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
+ /f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio
+ /l{L f mul}bind def %%%% Short side length l = L*f
+ /Ll{L l add}bind def %%%% Ll = L + l
+ /c{36 cos L mul}bind def %%%% c = L*cos(36)
+ /s{36 sin L mul}bind def %%%% s = L*sin(36)
+ /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
+ 0 setlinewidth stroke grestore border_colour stroke } bind def
+ /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
+ Ll 0 translate 144 rotate kite grestore }
+ { kite_colour L draw_tile }ifelse
+ pop } bind def
+ /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
+ -144 rotate Ll neg 0 translate half_dart grestore }
+ { dart_colour l draw_tile }ifelse
+ pop } bind def
+ /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
+ border_width setlinewidth 1 setlinejoin 1 setlinecap
+% 450 0 translate
+ dup f exch neg exp dup scale
+ 5 {kite 72 rotate } repeat stroke
+ grestore
+} def
+%
+%
+/TruchetFill { % on stack: scaling factor
+ 10 dict begin
+ dup dup scale
+ 1 exch div round /penroseFactor ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ /ma a neg def
+ /ha a 2 div def
+ /mha ha neg def
+ /tile {
+ rand dup 2 idiv 2 mul eq { 90 rotate } if
+ mha mha moveto ha mha lineto
+ ha ha lineto mha ha lineto
+% closepath .1 setlinewidth stroke
+ contents
+ } def
+ /contents{
+ 0 ha moveto ha 0 lineto
+ 0 mha moveto mha 0 lineto
+% 1 setlinewidth stroke
+ } def
+ /dotiling {
+ f ma mul a f a mul {
+ /i exch def
+ f ma mul a f a mul {
+ /j exch def
+ gsave i j translate
+ tile stroke grestore
+ } for
+ } for
+ } def
+%
+ /f 3 def
+ 5 srand dotiling
+ end % local user dict
+} def
+%
+/BeginArrow {
+ ADict begin % hold it local, for end see EndArrow
+ /@mtrx CM def
+ gsave
+ 2 copy T
+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
+%
+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
+%
+/Arrow {
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
+%
+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
+ gsave fill grestore
+} def
+%
+/Tbar {
+ CLW mul add /z ED
+ z -2 div CLW 2 div moveto
+ z 0 rlineto stroke
+ 0 CLW moveto
+} def
+%
+/Bracket {
+ CLW mul add dup CLW sub 2 div
+ /x ED mul CLW add /y ED /z CLW 2 div def
+ x neg y moveto
+ x neg CLW 2 div L x CLW 2 div L x y L stroke
+ 0 CLW moveto
+} def
+%
+/RoundBracket {
+ CLW mul add dup 2 div
+ /x ED mul /y ED /mtrx CM def
+ 0 CLW 2 div T x y mul 0 ne { x y scale } if
+ 1 1 moveto
+ .85 .5 .35 0 0 0 curveto
+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
+ /b ED % the color definition
+ 0 z DS SD
+ b { 0 z DS CLW sub SD } if
+ 0 DS z add CLW 4 div sub
+ moveto
+} def
+%
+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+ load } if ] cvx newpath 3 1 roll T exec } def
+%
+/NArray { % holds the coordinates and on top of stack the showpoints boolean
+ /showpoints ED
+ counttomark 2 div dup cvi /n ED % n 2 div on stack
+ n eq not { exch pop } if % even numbers of points? delete one
+ ] aload /Points ED
+ showpoints not { Points aload pop } if
+% { ] aload /Points ED }
+% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
+} def
+%
+/Line {
+ NArray n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
+ n { Lineto } repeat
+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
+%
+/LineToYAxis {
+ /Ox ED % Save the x origin value
+ NArray % all x-y pairs on stack
+ n { 2 copy moveto % go to current point
+ Ox exch Lineto % line to y-axis
+ pop % delete old x-value
+ } repeat
+} def
+%
+/LineToXAxis{
+ /Oy ED % Save the y origin value
+ NArray % all x-y pairs on stack
+ n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if
+ ArrowA
+ /n n 2 sub def
+ CP 2 copy moveto pop Oy Lineto
+ n { 2 copy moveto pop Oy Lineto } repeat
+ CP
+ 4 2 roll
+ ArrowB
+ 2 copy moveto pop Oy
+ L
+ pop pop } if
+} def
+%
+/Arcto {
+ /a [ 6 -2 roll ] cvx def
+ a r
+ /arcto load stopped { 5 } { 4 } ifelse { pop } repeat
+ a
+} def
+%
+/CheckClosed {
+ dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
+ and { pop pop /n n 1 sub def } if
+} def
+%
+/Polygon {
+ NArray n 2 eq { 0 0 /n 3 def } if
+ n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ n 2 mul -2 roll
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ n { Lineto } repeat
+ x1 y1 x0 y0 6 4 roll Lineto
+ Lineto pop pop closepath } ifelse
+} def
+%
+/SymbolPolygon { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 add /m ED
+ 2 copy m 2 roll % copy last two
+ m 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+ /nSym XYLength SymStep Div cvi def
+ /Shift Symbol stringwidth pop 2 Div def
+ /deltaX XLength nSym Div def
+ /deltaY YLength nSym Div def
+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
+%
+/Simpson { % on stack must be a b M --- simple version ---
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+%
+/LogGamma { 5 dict begin % z on stack
+ /z ED
+ /sum 0 def
+ /k 1 def
+ {
+ z k div dup 1 add ln sub dup
+ abs eps8 lt { pop exit } if
+ sum add /sum exch def
+ /k k 1 add def
+ } loop
+ sum z ln sub CEuler z mul sub
+ end
+} def
+%
+/ChebyshevT { 5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 2 k mul MoverN mul
+ add
+ } for
+ end
+} def
+%
+/ChebyshevU {5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 1 add 2 k mul 1 add MoverN mul
+ add
+ } for
+ end
+} def
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+%
+end
+
+%%EndProcSet
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+%%BeginFont: CMR8
+%!PS-AdobeFont-1.0: CMR8 003.002
+%%Title: CMR8
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR8.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
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+/FontName /CMR8 def
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+/version (003.002) readonly def
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+/FullName (CMR8) readonly def
+/FamilyName (Computer Modern) readonly def
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+end readonly def
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.7 0.7 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
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+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.7 0.7 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (-1.0+((0.35)*t)*(1/sqrt(1+((-2.6)-(-1.0))^2))|-2.6+((0.35)*t)*(1/sqrt(1+((-2.6)-(-1.0))^2))*((-2.6)-(-1.0))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.6 0.6 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
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+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
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+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
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+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.6 0.6 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.5 0.5 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
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+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
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+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.5 0.5 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
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+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.4 0.4 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.4 0.4 setrgbcolor
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+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
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+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.3 0.3 setrgbcolor
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+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.2 0.2 setrgbcolor
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+) AlgParser cvx def end
+ 998 901 a 998 901 a
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+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
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+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
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+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.8 0.8 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.8 0.8 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (-1.0+((0.35)*t)*(1/sqrt(1+((-2.2)-(-1.0))^2))|-2.2+((0.35)*t)*(1/sqrt(1+((-2.2)-(-1.0))^2))*((-2.2)-(-1.0))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.8 0.8 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.8 0.8 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (-0.6+((0.35)*t)*(1/sqrt(1+((-2.2)-(-0.6))^2))|-2.2+((0.35)*t)*(1/sqrt(1+((-2.2)-(-0.6))^2))*((-2.2)-(-0.6))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.7 0.7 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.7 0.7 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (-0.2+((0.35)*t)*(1/sqrt(1+((-2.2)-(-0.2))^2))|-2.2+((0.35)*t)*(1/sqrt(1+((-2.2)-(-0.2))^2))*((-2.2)-(-0.2))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.5 0.5 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.5 0.5 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (0.2+((0.35)*t)*(1/sqrt(1+((-2.2)-(0.2))^2))|-2.2+((0.35)*t)*(1/sqrt(1+((-2.2)-(0.2))^2))*((-2.2)-(0.2))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.5 0.5 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.5 0.5 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (0.6+((0.35)*t)*(1/sqrt(1+((-2.2)-(0.6))^2))|-2.2+((0.35)*t)*(1/sqrt(1+((-2.2)-(0.6))^2))*((-2.2)-(0.6))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.3 0.3 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.3 0.3 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (1.0+((0.35)*t)*(1/sqrt(1+((-2.2)-(1.0))^2))|-2.2+((0.35)*t)*(1/sqrt(1+((-2.2)-(1.0))^2))*((-2.2)-(1.0))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.3 0.3 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.3 0.3 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 998 901 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 998 901 a 998 901
+a
+tx@Dict begin /Func (1.4+((0.35)*t)*(1/sqrt(1+((-2.2)-(1.4))^2))|-2.2+((0.35)*t)*(1/sqrt(1+((-2.2)-(1.4))^2))*((-2.2)-(1.4))
+) AlgParser cvx def end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a 998 901 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 998 901 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.2 0.2 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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diff --git a/info/pstricks_calcnotes/For_Ps_Output/vecb4.eps b/info/pstricks_calcnotes/For_Ps_Output/vecb4.eps
new file mode 100644
index 0000000000..8dc5ea2157
--- /dev/null
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+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
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+} def
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+/cxmake2 { 2 array astore } def % dito, both given
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+%%EndFont
+%%BeginFont: CMR8
+%!PS-AdobeFont-1.0: CMR8 003.002
+%%Title: CMR8
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR8.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMR8 known{/CMR8 findfont dup/UniqueID known{dup
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+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMR8 def
+/FontBBox {-36 -250 1070 750 }readonly def
+/UniqueID 5000791 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
+/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR8.) readonly def
+/FullName (CMR8) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/isFixedPitch false def
+/UnderlinePosition -100 def
+/UnderlineThickness 50 def
+end readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
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+readonly def
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+) AlgParser cvx def end
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+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+tx@NodeDict /N@P0 known { /N@P0 load GetCenter } { 0 0 } ifelse end
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+) AlgParser cvx def end
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+) AlgParser cvx def end
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+) AlgParser cvx def end
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+ } def /ArrowInside { } def [ tx@NodeDict begin tx@NodeDict /N@P1
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+/a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg
+a neg rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow
+ } def /ArrowInside { } def [ tx@NodeDict begin tx@NodeDict /N@P1
+known { /N@P1 load GetCenter } { 0 0 } ifelse end tx@NodeDict begin
+tx@NodeDict /N@P0 known { /N@P0 load GetCenter } { 0 0 } ifelse end
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+{ n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
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+/a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg
+a neg rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow
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+known { /N@P1 load GetCenter } { 0 0 } ifelse end tx@NodeDict begin
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
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+/a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg
+a neg rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow
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+known { /N@P1 load GetCenter } { 0 0 } ifelse end tx@NodeDict begin
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
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+) AlgParser cvx def end
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+ 998 901 a @beginspecial
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+a neg rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
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+) AlgParser cvx def end
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+def NewNode end end
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
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+) AlgParser cvx def end
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+) AlgParser cvx def end
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+ { /a .5 def PathLength exch div }
+ { pop /a 1 def PathLength } ifelse
+ /b ED % pattern should fit evenly in b
+ dup /X ED % pattern array
+ 0 get /y ED % length of first black segment
+ /z 0 X {add} forall def % length of the full pattern
+ %% Computation of the scaling factor as described by van Zandt:
+ b a .5 sub 2 mul y mul sub z Div round
+ z mul a .5 sub 2 mul y mul add b exch Div
+ %%%% scaling factor on stack.
+ /z ED %% now, z is the scaling factor
+ false % for the length test below
+ X { z mul } forall X astore %% modification TN 04-08-07
+ %%% Checking whether at least one dash in X has positive length:
+ {0 gt or} forall
+ { X 1 a sub y mul }
+ { [ 1 0 ] 0 }
+ ifelse
+ setdash stroke
+} def
+%
+/DotLine {
+ /b PathLength def
+ /a ED /z ED /y CLW def
+ /z y z add def
+ a 0 gt {
+ /b b a div def
+ }{
+ a 0 eq {
+ /b b y sub def
+ }{ a -3 eq {
+ /b b y add def } if
+ } ifelse
+ } ifelse
+ [ 0 b b z Div round Div dup 0 le { pop 1 } if ]
+ a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
+ setdash 1 setlinecap stroke
+} def
+%
+/SymbolLine { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt
+ { %XYLength SymStep div abs cvi
+ /nSym SymStep abs cvi def }
+ { /nSym XYLength SymStep div cvi def }
+ ifelse
+ 0.5 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ /deltaX XLength nSym div def
+ /deltaY YLength nSym div def
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ nSym {
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ currentpoint translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+ /YA YB def /XA XB def
+ } repeat
+ curveticks
+ { XA YA moveto }
+ { XA Shift sub YA Shift sub moveto }
+ ifelse
+ gsave
+ curveticks
+ { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
+ XA YA translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ pop % delete the mark symbol
+} def
+%
+/LineFill { % hv ------------ patch 7 -------------
+ gsave
+ abs /hatchWidthInc ED
+ abs /hatchSepInc ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clipType % must be defined in pstricks.tex: clip -- eoclip
+ newpath
+ 2 setlinecap
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ x2 x1 sub 1 add {
+ x1 a mul y1 moveto 0 y2 rlineto stroke
+ /x1 x1 1 add
+ hatchWidthInc 0 gt { CLW add } if
+ def
+ hatchSepInc 0 gt hatchWidthInc 0 gt or {
+ /a a hatchSepInc add def
+ CLW hatchWidthInc add SLW
+ } if
+ } repeat
+ grestore
+ pop pop } def
+%
+/DotFill {% on stack: dot radius
+ /dotRadius ED
+ abs CLW add /a ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform
+ pathbbox % llx lly urx ury of smallest bounding box
+ /y2 ED /x2 ED /y1 ED /x1 ED
+ y2 y1 sub a div 2 add cvi /Ny ED
+ x2 x1 sub a div 2 add cvi /Nx ED
+ clipType % must be defined in pstricks.tex: clip -- eoclip
+ newpath
+ /yA y1 dotRadius add CLW add def
+ /xA0 x1 dotRadius add CLW add def
+ Ny {
+ /xA xA0 def
+ Nx {
+ newpath
+ xA yA dotRadius 0 360 arc
+ SolidDot { gsave fill grestore } if
+ stroke
+ xA a add /xA ED
+ } repeat
+ yA a add /yA ED
+ } repeat
+ grestore
+} def
+%
+/PenroseFill {% on stack: scaling factor
+ /Scale ED
+% 1 exch div round /penroseFactor ED
+% a 0 dtransform round exch round exch
+% 2 copy idtransform
+% exch Atan rotate
+% idtransform pop /a ED
+% .25 .25 itransform pathbbox
+% /y2 ED
+% a Div ceiling cvi /x2 ED /y1 ED
+% a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+gsave
+ 220 150 translate
+ Scale dup scale
+ systemdict /setstrokeadjust known { true setstrokeadjust } if
+ /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
+ { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
+ [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
+ i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
+ mul j l + S rmoveto}F i L j L stroke }F}F}F}F
+ grestore
+% pop pop
+} def
+%
+/PenroseFillA {% on stack: scaling factor, border color, kite color, dart color
+ /Scale ED
+ Scale dup scale
+ /border_colour ED
+ /kite_colour ED
+ /dart_colour ED
+ clip
+
+ newpath
+ gsave
+ 100 100 translate
+ 6
+ Scale 1 lt { 1 Scale dup add div mul cvi } if %%%% Number of iterations
+ 10 %%%% Long side length in millimeters
+ /border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
+ /L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
+ /f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio
+ /l{L f mul}bind def %%%% Short side length l = L*f
+ /Ll{L l add}bind def %%%% Ll = L + l
+ /c{36 cos L mul}bind def %%%% c = L*cos(36)
+ /s{36 sin L mul}bind def %%%% s = L*sin(36)
+ /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
+ 0 setlinewidth stroke grestore border_colour stroke } bind def
+ /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
+ Ll 0 translate 144 rotate kite grestore }
+ { kite_colour L draw_tile }ifelse
+ pop } bind def
+ /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
+ -144 rotate Ll neg 0 translate half_dart grestore }
+ { dart_colour l draw_tile }ifelse
+ pop } bind def
+ /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
+ border_width setlinewidth 1 setlinejoin 1 setlinecap
+% 450 0 translate
+ dup f exch neg exp dup scale
+ 5 {kite 72 rotate } repeat stroke
+ grestore
+} def
+%
+%
+/TruchetFill { % on stack: scaling factor
+ 10 dict begin
+ dup dup scale
+ 1 exch div round /penroseFactor ED
+ a 0 dtransform round exch round exch
+ 2 copy idtransform
+ exch Atan rotate
+ idtransform pop /a ED
+ .25 .25 itransform pathbbox
+ /y2 ED
+ a Div ceiling cvi /x2 ED /y1 ED
+ a Div cvi /x1 ED /y2 y2 y1 sub def
+ clip
+ newpath
+ systemdict
+ /setstrokeadjust known { true setstrokeadjust } if
+ /ma a neg def
+ /ha a 2 div def
+ /mha ha neg def
+ /tile {
+ rand dup 2 idiv 2 mul eq { 90 rotate } if
+ mha mha moveto ha mha lineto
+ ha ha lineto mha ha lineto
+% closepath .1 setlinewidth stroke
+ contents
+ } def
+ /contents{
+ 0 ha moveto ha 0 lineto
+ 0 mha moveto mha 0 lineto
+% 1 setlinewidth stroke
+ } def
+ /dotiling {
+ f ma mul a f a mul {
+ /i exch def
+ f ma mul a f a mul {
+ /j exch def
+ gsave i j translate
+ tile stroke grestore
+ } for
+ } for
+ } def
+%
+ /f 3 def
+ 5 srand dotiling
+ end % local user dict
+} def
+%
+/BeginArrow {
+ ADict begin % hold it local, for end see EndArrow
+ /@mtrx CM def
+ gsave
+ 2 copy T
+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
+%
+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
+%
+/Arrow {
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
+%
+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
+ gsave fill grestore
+} def
+%
+/Tbar {
+ CLW mul add /z ED
+ z -2 div CLW 2 div moveto
+ z 0 rlineto stroke
+ 0 CLW moveto
+} def
+%
+/Bracket {
+ CLW mul add dup CLW sub 2 div
+ /x ED mul CLW add /y ED /z CLW 2 div def
+ x neg y moveto
+ x neg CLW 2 div L x CLW 2 div L x y L stroke
+ 0 CLW moveto
+} def
+%
+/RoundBracket {
+ CLW mul add dup 2 div
+ /x ED mul /y ED /mtrx CM def
+ 0 CLW 2 div T x y mul 0 ne { x y scale } if
+ 1 1 moveto
+ .85 .5 .35 0 0 0 curveto
+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
+ /b ED % the color definition
+ 0 z DS SD
+ b { 0 z DS CLW sub SD } if
+ 0 DS z add CLW 4 div sub
+ moveto
+} def
+%
+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+ load } if ] cvx newpath 3 1 roll T exec } def
+%
+/NArray { % holds the coordinates and on top of stack the showpoints boolean
+ /showpoints ED
+ counttomark 2 div dup cvi /n ED % n 2 div on stack
+ n eq not { exch pop } if % even numbers of points? delete one
+ ] aload /Points ED
+ showpoints not { Points aload pop } if
+% { ] aload /Points ED }
+% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
+} def
+%
+/Line {
+ NArray n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
+ n { Lineto } repeat
+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
+%
+/LineToYAxis {
+ /Ox ED % Save the x origin value
+ NArray % all x-y pairs on stack
+ n { 2 copy moveto % go to current point
+ Ox exch Lineto % line to y-axis
+ pop % delete old x-value
+ } repeat
+} def
+%
+/LineToXAxis{
+ /Oy ED % Save the y origin value
+ NArray % all x-y pairs on stack
+ n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if
+ ArrowA
+ /n n 2 sub def
+ CP 2 copy moveto pop Oy Lineto
+ n { 2 copy moveto pop Oy Lineto } repeat
+ CP
+ 4 2 roll
+ ArrowB
+ 2 copy moveto pop Oy
+ L
+ pop pop } if
+} def
+%
+/Arcto {
+ /a [ 6 -2 roll ] cvx def
+ a r
+ /arcto load stopped { 5 } { 4 } ifelse { pop } repeat
+ a
+} def
+%
+/CheckClosed {
+ dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
+ and { pop pop /n n 1 sub def } if
+} def
+%
+/Polygon {
+ NArray n 2 eq { 0 0 /n 3 def } if
+ n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ n 2 mul -2 roll
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ n { Lineto } repeat
+ x1 y1 x0 y0 6 4 roll Lineto
+ Lineto pop pop closepath } ifelse
+} def
+%
+/SymbolPolygon { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 add /m ED
+ 2 copy m 2 roll % copy last two
+ m 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+ /nSym XYLength SymStep Div cvi def
+ /Shift Symbol stringwidth pop 2 Div def
+ /deltaX XLength nSym Div def
+ /deltaY YLength nSym Div def
+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
+ /BezierType ED
+ 1 exch div /epsilon ED
+ ] /Points ED % yi xi ... y3 x3 y2 x2 y1 x1 y0 x0
+ epsilon GetBezierCoor % next Bezier point
+ Points 0 get Points 1 get % starting point
+ ArrowA moveto
+ epsilon epsilon 1 {
+ /t ED
+ t GetBezierCoor
+ t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB pop pop pop pop } ifelse
+ } for
+% end
+} def
+%
+/Bernstein { % on stack tStart tEnd plotpoints i n
+ 12 dict begin % hold all local
+ /envelope ED % plot envelope?
+ /n ED
+ /i ED
+ /ni n i sub def
+ /epsilon ED % step=1/plotpoints
+ /tEnd ED
+ /tStart ED
+%
+% B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i} (Bernstein)
+% f_n(x)=\frac{1}{\sqrt{\pi n\cdot x(1-x)}} (envelope)
+%
+ n i MoverN /noveri ED % \binom{n}{i}
+ [ % for the array of points
+ tStart epsilon tEnd {
+ dup dup /t ED % leave one on stack
+ neg 1 add /t1 ED % t1=1-t
+ envelope
+ { t t1 mul 4 mul Pi2 mul n mul sqrt 1 exch Div } % envelope
+ { noveri t i exp mul t1 ni exp mul } ifelse % t f(t)
+ ScreenCoor % convert to screen coor
+ } for
+ end
+ false /Lineto /lineto load def Line
+} def
+%
+/Si { % integral sin from 0 to x (arg on stack)
+ /arg exch def
+ /Sum arg def
+ /sign -1 def
+ /index 3 def
+ {
+ arg index exp index div index factorial div sign mul
+ dup abs eps8 lt { pop exit } if
+ Sum add /Sum exch def
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+} def
+/si { % integral sin from x to infty -> si(x)=Si(x)-pi/2
+ Si Pi2 sub
+} def
+/Ci { % integral cosin from x to infty (arg on stack)
+ abs /arg exch def
+ arg 0 eq { 0 } {
+ /argExp 1 def
+ /fact 1 def
+ /Sum CEuler arg ln add def
+ /sign -1 def
+ /index 2 def
+ {
+ /argExp argExp arg arg mul mul def
+ /fact fact index 1 sub index mul mul def
+ argExp index div fact div sign mul
+ dup abs exch Sum add /Sum exch def
+ eps8 lt { exit } if
+ /sign sign neg def
+ /index index 2 add def
+ } loop
+ Sum
+ } ifelse
+} def
+/ci { % integral cosin from x to infty -> ci(x)=-Ci(x)+ln(x)+CEuler
+ dup Ci neg exch abs ln add CEuler add
+} def
+%
+/MaxIter 255 def
+/func { coeff Derivation FuncValue } def
+/func' { coeff Derivation 1 add FuncValue } def
+/func'' { coeff Derivation 2 add FuncValue } def
+%
+/NewtonMehrfach {% the start value must be on top of the stack
+ /Nx exch def
+ /Iter 0 def
+ {
+ /Iter Iter 1 add def
+ Nx func /F exch def % f(Nx)
+ F abs eps2 lt { exit } if
+ Nx func' /FS exch def % f'(Nx)
+ FS 0 eq { /FS 1.0e-06 def } if
+ Nx func'' /F2S exch def % f''(Nx)
+ 1.0 1.0 F F2S mul FS dup mul div sub div /J exch def
+ J F mul FS div /Diff exch def
+ /Nx Nx Diff sub def
+ Diff abs eps1 lt Iter MaxIter gt or { exit } if
+ } loop
+ Nx % the returned value ist the zero point
+} def
+
+/Steffensen {% the start value must be on top of the stack
+ /y0 exch def % the start value
+ /Iter 0 def
+ {
+ y0 func /F exch def
+ F abs eps2 lt { exit } if
+ y0 F sub /Phi exch def
+ Phi func /F2 exch def
+ F2 abs eps2 le { exit }{
+ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def
+ y0 Diff sub /y0 exch def
+ Diff abs eps1 le { exit } if
+ } ifelse
+ /Iter Iter 1 add def
+ Iter MaxIter gt { exit } if
+ } loop
+ y0 % the returned value ist the zero point
+} def
+%
+/Horner {% x [coeff] must be on top of the stack
+ aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop % the y value is on top of the stack
+} def
+%
+/FuncValue {% x [coeff] Derivation must be on top of the stack
+ {
+ aload % a0 a1 a2 ... a(n-1) [array]
+ length % a0 a1 a2 ... a(n-1) n
+ 1 sub /grad exch def % a0 a1 a2 ... a(n-1)
+ grad -1 1 { % for n=grad step -1 until 1
+ /n exch def % Laufvariable speichern
+ n % a0 a1 a2 ... a(n-1) n
+ mul % a0 a1 a2 ... a(n-1)*n
+ grad 1 add % a0 a1 a2 ... a(n-1)*n grad+1
+ 1 roll % an*na0 a1 a2 ... a(n-2)
+ } for
+ pop % loesche a0
+ grad array astore % [ a1 a2 ... a(n-2)]
+ } repeat
+ Horner
+} def
+%
+/FindZeros { % dxN dxZ must be on top of the stack (x0..x1 the intervall) => []
+ 12 dict begin
+ /dxZ exch def /dxN exch def
+ /pstZeros [] def
+ x0 dxZ x1 { % suche Nullstellen
+ /xWert exch def
+ xWert NewtonMehrfach
+ %xWert Steffensen
+ /xNull exch def
+ pstZeros aload length /Laenge exch def % now test if value is a new one
+ Laenge 0 eq
+ { xNull 1 }
+ { /newZero true def
+ Laenge {
+ xNull sub abs dxN lt { /newZero false def } if
+ } repeat
+ pstZeros aload pop
+ newZero { xNull Laenge 1 add } { Laenge } ifelse } ifelse
+ array astore
+ /pstZeros exch def
+ } for
+ pstZeros % the end array is now on the stack
+ end
+} def
+%
+/Simpson { % on stack must be a b M --- simple version ---
+% /SFunc must be defined
+ /M ED /b ED /a ED
+ /h b a sub M 2 mul div def
+ /s1 0 def
+ /s2 0 def
+ 1 1 M {
+ /k exch def
+ /x k 2 mul 1 sub h mul a add def
+ /s1 s1 x SFunc add def
+ } for
+ 1 1 M 1 sub {
+ /k exch def
+ /x k 2 mul h mul a add def
+ /s2 s2 x SFunc add def
+ } for
+ /I a SFunc b SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
+} def
+%
+/LogGamma { 5 dict begin % z on stack
+ /z ED
+ /sum 0 def
+ /k 1 def
+ {
+ z k div dup 1 add ln sub dup
+ abs eps8 lt { pop exit } if
+ sum add /sum exch def
+ /k k 1 add def
+ } loop
+ sum z ln sub CEuler z mul sub
+ end
+} def
+%
+/ChebyshevT { 5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 2 k mul MoverN mul
+ add
+ } for
+ end
+} def
+%
+/ChebyshevU {5 dict begin % z on stack
+ /xtmp exch def
+ /n exch def
+ 0 0 1 n .5 mul floor {
+ /k exch def
+ xtmp xtmp mul 1 sub k exp
+ xtmp n 2 k mul sub exp mul
+ n 1 add 2 k mul 1 add MoverN mul
+ add
+ } for
+ end
+} def
+%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+%
+end
+
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+%%EndFont
+%%BeginFont: CMR8
+%!PS-AdobeFont-1.0: CMR8 003.002
+%%Title: CMR8
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR8.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMR8 known{/CMR8 findfont dup/UniqueID known{dup
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+{save true}{false}ifelse}{false}ifelse
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+/FontName /CMR8 def
+/FontBBox {-36 -250 1070 750 }readonly def
+/UniqueID 5000791 def
+/PaintType 0 def
+/FontInfo 9 dict dup begin
+/version (003.002) readonly def
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+/FullName (CMR8) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
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+/UnderlineThickness 50 def
+end readonly def
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.8 0.8 setrgbcolor
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+) AlgParser cvx def end
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+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.7 0.7 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.7 0.7 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+ 762 664 a @beginspecial
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+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+ 762 664 a @beginspecial
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+ 762 664 a @beginspecial
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.7 0.7 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.7 0.7 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 762 664 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
+a
+tx@Dict begin /Func (0.4+((0.3)*t)*(1/sqrt(1+((0.4)-2*(1.3))^2))|1.3+((0.3)*t)*(1/sqrt(1+((0.4)-2*(1.3))^2))*((0.4)-2*(1.3))
+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.7 0.7 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.7 0.7 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 762 664 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
+a
+tx@Dict begin /Func (0.7+((0.3)*t)*(1/sqrt(1+((0.7)-2*(1.3))^2))|1.3+((0.3)*t)*(1/sqrt(1+((0.7)-2*(1.3))^2))*((0.7)-2*(1.3))
+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.8 0.8 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.8 0.8 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 762 664 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
+a
+tx@Dict begin /Func (1.0+((0.3)*t)*(1/sqrt(1+((1.0)-2*(1.3))^2))|1.3+((0.3)*t)*(1/sqrt(1+((1.0)-2*(1.3))^2))*((1.0)-2*(1.3))
+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.8 0.8 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.8 0.8 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 762 664 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
+a
+tx@Dict begin /Func (1.3+((0.3)*t)*(1/sqrt(1+((1.3)-2*(1.3))^2))|1.3+((0.3)*t)*(1/sqrt(1+((1.3)-2*(1.3))^2))*((1.3)-2*(1.3))
+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.9 0.9 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.9 0.9 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 762 664 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
+a
+tx@Dict begin /Func (1.6+((0.3)*t)*(1/sqrt(1+((1.6)-2*(1.3))^2))|1.3+((0.3)*t)*(1/sqrt(1+((1.6)-2*(1.3))^2))*((1.6)-2*(1.3))
+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.9 0.9 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.9 0.9 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 762 664 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
+a
+tx@Dict begin /Func (1.9+((0.3)*t)*(1/sqrt(1+((1.9)-2*(1.3))^2))|1.3+((0.3)*t)*(1/sqrt(1+((1.9)-2*(1.3))^2))*((1.9)-2*(1.3))
+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.9 0.9 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
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+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.9 0.9 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
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+a
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+) AlgParser cvx def end
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+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.3 0.3 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
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+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
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+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.6 0.6 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
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+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
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+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.6 0.6 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
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+@endspecial 762 664 a
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+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
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+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
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+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.7 0.7 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.7 0.7 setrgbcolor
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+) AlgParser cvx def end
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+def NewNode end end
+ 762 664 a @beginspecial
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+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.7 0.7 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.7 0.7 setrgbcolor
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+) AlgParser cvx def end
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+ 762 664 a @beginspecial
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+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.7 0.7 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.7 0.7 setrgbcolor
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+) AlgParser cvx def end
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+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
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+ 762 664 a @beginspecial
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+} ifelse } def /logLines { false } def /LSstroke { 0 setlinejoin
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+} if showOrigin { gsave false { cntTick minTickline moveto cntTick
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+} if showOrigin { gsave cntTick tickstart moveto cntTick tickend
+lineto Twidth SLW TColor LSstroke grestore }{ /showOrigin true def
+} ifelse } for } if end
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+@endspecial @beginspecial @setspecial
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+} ifelse def /epsilon 0.01 def /minTickline -57.0 def /maxTickline
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diff --git a/info/pstricks_calcnotes/For_Ps_Output/vecb6.eps b/info/pstricks_calcnotes/For_Ps_Output/vecb6.eps
new file mode 100644
index 0000000000..7d96857165
--- /dev/null
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+ 0 ha moveto ha 0 lineto
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+% 1 setlinewidth stroke
+ } def
+ /dotiling {
+ f ma mul a f a mul {
+ /i exch def
+ f ma mul a f a mul {
+ /j exch def
+ gsave i j translate
+ tile stroke grestore
+ } for
+ } for
+ } def
+%
+ /f 3 def
+ 5 srand dotiling
+ end % local user dict
+} def
+%
+/BeginArrow {
+ ADict begin % hold it local, for end see EndArrow
+ /@mtrx CM def
+ gsave
+ 2 copy T
+ 2 index sub neg exch
+ 3 index sub exch Atan
+ rotate newpath
+} def
+%
+/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
+%
+/Arrow {
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /a ED
+ { 0 h T 1 -1 scale } if
+ w neg h moveto
+ 0 0 L w h L w neg a neg rlineto
+ gsave fill grestore
+} def
+%
+/ArrowD { % the sides are drawn as curves (hv 20071211)
+ CLW mul add dup
+ 2 div /w ED
+ mul dup /h ED
+ mul /Inset ED
+ { 0 h T 1 -1 scale } if % changes the direction
+% we use y=w/h^2 * x^2 as equation for the control points
+% for the coordinates the arrow is seen from top to bottom
+% the bottom (tip) is (0;0)
+ w neg h moveto % lower left of >
+ w 9 div 4 mul neg h 3 div 2 mul
+ w 9 div neg h 3 div
+ 0 0 curveto % tip of >
+ w 9 div h 3 div
+ w 9 div 4 mul h 3 div 2 mul
+ w h curveto % upper left of >
+ w neg Inset neg rlineto % move to x=0 and inset
+ gsave fill grestore
+} def
+%
+/Tbar {
+ CLW mul add /z ED
+ z -2 div CLW 2 div moveto
+ z 0 rlineto stroke
+ 0 CLW moveto
+} def
+%
+/Bracket {
+ CLW mul add dup CLW sub 2 div
+ /x ED mul CLW add /y ED /z CLW 2 div def
+ x neg y moveto
+ x neg CLW 2 div L x CLW 2 div L x y L stroke
+ 0 CLW moveto
+} def
+%
+/RoundBracket {
+ CLW mul add dup 2 div
+ /x ED mul /y ED /mtrx CM def
+ 0 CLW 2 div T x y mul 0 ne { x y scale } if
+ 1 1 moveto
+ .85 .5 .35 0 0 0 curveto
+ -.35 0 -.85 .5 -1 1 curveto
+ mtrx setmatrix stroke 0 CLW moveto
+} def
+%
+/SD { 0 360 arc fill } def
+%
+/EndDot { % DS is the dot size
+ { /z DS def } { /z 0 def } ifelse % outer or inner dimen
+ /b ED % the color definition
+ 0 z DS SD
+ b { 0 z DS CLW sub SD } if
+ 0 DS z add CLW 4 div sub
+ moveto
+} def
+%
+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
+ /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+ load } if ] cvx newpath 3 1 roll T exec } def
+%
+/NArray { % holds the coordinates and on top of stack the showpoints boolean
+ /showpoints ED
+ counttomark 2 div dup cvi /n ED % n 2 div on stack
+ n eq not { exch pop } if % even numbers of points? delete one
+ ] aload /Points ED
+ showpoints not { Points aload pop } if
+% { ] aload /Points ED }
+% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
+} def
+%
+/Line {
+ NArray n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
+ n { Lineto } repeat
+ CP 4 2 roll ArrowB L pop pop
+ } if
+} def
+%
+/LineToYAxis {
+ /Ox ED % Save the x origin value
+ NArray % all x-y pairs on stack
+ n { 2 copy moveto % go to current point
+ Ox exch Lineto % line to y-axis
+ pop % delete old x-value
+ } repeat
+} def
+%
+/LineToXAxis{
+ /Oy ED % Save the y origin value
+ NArray % all x-y pairs on stack
+ n 0 eq not
+ { n 1 eq { 0 0 /n 2 def } if
+ ArrowA
+ /n n 2 sub def
+ CP 2 copy moveto pop Oy Lineto
+ n { 2 copy moveto pop Oy Lineto } repeat
+ CP
+ 4 2 roll
+ ArrowB
+ 2 copy moveto pop Oy
+ L
+ pop pop } if
+} def
+%
+/Arcto {
+ /a [ 6 -2 roll ] cvx def
+ a r
+ /arcto load stopped { 5 } { 4 } ifelse { pop } repeat
+ a
+} def
+%
+/CheckClosed {
+ dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
+ and { pop pop /n n 1 sub def } if
+} def
+%
+/Polygon {
+ NArray n 2 eq { 0 0 /n 3 def } if
+ n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ n 2 mul -2 roll
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ x1 y1
+ /x1 x0 x1 add 2 div def
+ /y1 y0 y1 add 2 div def
+ x1 y1 moveto
+ /n n 2 sub def
+ n { Lineto } repeat
+ x1 y1 x0 y0 6 4 roll Lineto
+ Lineto pop pop closepath } ifelse
+} def
+%
+/SymbolPolygon { % on stack [ x y x y ...
+ counttomark % number of elements
+ 2 add /m ED
+ 2 copy m 2 roll % copy last two
+ m 2 div cvi /n ED % n pairs
+ /YA ED /XA ED % the start point
+ n 1 sub {
+ /YB ED /XB ED
+ /XLength XB XA sub def
+ /YLength YB YA sub def
+ /PAngle YLength XLength Atan def
+ /XYLength XLength YLength Pyth def
+ /nSym XYLength SymStep Div cvi def
+ /Shift Symbol stringwidth pop 2 Div def
+ /deltaX XLength nSym Div def
+ /deltaY YLength nSym Div def
+ XA Shift sub YA Shift sub moveto
+ nSym {
+ gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
+ Symbol show
+ grestore
+ deltaX deltaY rmoveto
+ } repeat
+% XB Shift sub YB Shift sub moveto Symbol show
+ /YA YB def /XA XB def
+ } repeat
+ pop % delete the mark symbol
+} def
+%
+/Diamond {
+ /mtrx CM def
+ T rotate
+ /h ED
+ /w ED
+ dup 0 eq { pop } { CLW mul neg
+ /d ED
+ /a w h Atan def
+ /h d a sin Div h add def
+ /w d a cos Div w add def } ifelse
+ mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false Line
+ closepath mtrx setmatrix } def
+%
+/Triangle {
+ /mtrx CM def
+ translate
+ rotate /h ED 2 div /w ED
+ dup CLW mul /d ED
+ /h h d w h Atan sin Div sub def
+ /w w d h w Atan 2 div dup cos exch sin Div mul sub def
+ mark
+ 0 d w neg d 0 h w d 0 d
+ /ArrowA { moveto } def
+ /ArrowB { } def
+ false
+ Line
+ closepath
+ mtrx
+% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+ setmatrix pop
+} def
+% DG/SR modification end
+%
+/CCA {
+ /y ED /x ED
+ 2 copy y sub /dy1 ED
+ x sub /dx1 ED
+ /l1 dx1 dy1 Pyth def
+} def
+%
+/CC {
+ /l0 l1 def
+ /x1 x dx sub def
+ /y1 y dy sub def
+ /dx0 dx1 def
+ /dy0 dy1 def
+ CCA
+ /dx dx0 l1 c exp mul dx1 l0 c exp mul add def
+ /dy dy0 l1 c exp mul dy1 l0 c exp mul add def
+ /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
+ /x2 x l0 dx mul m mul sub def
+ /y2 y l0 dy mul m mul sub def
+ /dx l1 dx mul m mul neg def
+ /dy l1 dy mul m mul neg def
+} def
+%
+/IC {
+ /c c 1 add def
+ c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
+ /a a 2 mul 3 div 45 cos b exp div def
+ CCA
+ /dx 0 def
+ /dy 0 def
+} def
+%
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+%
+/OpenCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { BOC /n n 3 sub def n { NC } repeat EOC } ifelse
+} def
+%
+/CurvePath {
+ %% for negative SymStep we calculate the distance
+ SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
+ 0.5 setflat
+ flattenpath /z 0 def /z0 0 def
+ { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+ x1 Shift sub y1 Shift sub moveto
+ gsave
+ curveticks
+ { x1 y1 translate startAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ { startAngle rotate Symbol show }
+ ifelse
+ grestore /z0 z def }
+ { /y ED /x ED PathLength@ z z0 sub SymStep ge {
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore /z0 z def } if
+ /yOld y def /xOld x def }
+ {} %% the lineto part
+ { /y y2 def /x x2 def PathLength@
+ x Shift sub y Shift sub moveto
+ gsave
+ curveticks
+ { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
+ x y translate rotAngle rotate
+ 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+ SymbolLinewidth setlinewidth stroke
+ }
+ {
+ x Shift sub y Shift sub moveto
+ rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
+ Symbol show
+ }
+ ifelse
+ grestore
+ }
+ pathforall
+% curveticks
+% { gsave
+% x y translate rotAngle rotate
+% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
+% SymbolLinewidth setlinewidth stroke grestore
+% } if
+ z
+} def
+%
+/OpenSymbolCurve {
+ OpenCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/AltCurve {
+ { false NArray n 2 mul 2 roll
+ [ n 2 mul 3 sub 1 roll ] aload
+ /Points ED
+ n 2 mul -2 roll }
+ { false NArray } ifelse
+ n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
+} def
+%
+/AltOpenSymbolCurve {
+ AltCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedCurve {
+ NArray n 3 lt
+ { n { pop pop } repeat }
+ { n 3 gt { CheckClosed } if
+ 6 copy n 2 mul 6 add 6 roll
+ IC CC x y moveto n { NC } repeat
+ closepath pop pop
+ } ifelse
+} def
+%
+/ClosedSymbolCurve {
+ ClosedCurve
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
+%
+/FontDot {
+ DS 2 mul dup
+ matrix scale matrix concatmatrix exch matrix
+ rotate matrix concatmatrix exch
+ findfont exch makefont setfont
+} def
+%
+/Rect {
+ x1 y1 y2 add 2 div moveto
+ x1 y2 lineto
+ x2 y2 lineto
+ x2 y1 lineto
+ x1 y1 lineto
+ closepath
+} def
+%
+/OvalFrame {
+ x1 x2 eq y1 y2 eq or
+ { pop pop x1 y1 moveto x2 y2 L }
+ { y1 y2 sub abs x1 x2 sub abs 2 copy gt
+ { exch pop } { pop } ifelse
+ 2 div exch { dup 3 1 roll mul exch } if
+ 2 copy lt { pop } { exch pop } ifelse
+ /b ED
+ x1 y1 y2 add 2 div moveto
+ x1 y2 x2 y2 b arcto
+ x2 y2 x2 y1 b arcto
+ x2 y1 x1 y1 b arcto
+ x1 y1 x1 y2 b arcto
+ 16 { pop } repeat
+ closepath
+ } ifelse
+} def
+%
+/Frame {
+ CLW mul /a ED
+ 3 -1 roll
+ 2 copy gt { exch } if
+ a sub /y2 ED
+ a add /y1 ED
+ 2 copy gt { exch } if
+ a sub /x2 ED
+ a add /x1 ED
+ 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
+} def
+%
+/BezierNArray {
+ /f ED
+ counttomark 2 div dup cvi /n ED
+ n eq not { exch pop } if
+ n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
+ f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
+} def
+%
+/OpenBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { ArrowA n 4 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ 6 2 roll 4 2 roll ArrowB curveto } ifelse
+} def
+%
+/OpenSymbolBezier {
+ OpenBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+} def
+%
+/ClosedBezier {
+ BezierNArray
+ n 1 eq
+ { pop pop }
+ { moveto n 1 sub 3 idiv
+ { 6 2 roll 4 2 roll curveto } repeat
+ closepath } ifelse
+} def
+%
+/ClosedSymbolBezier {
+ /f ED % save showpoints value
+ 2 copy /yEnd ED /xEnd ED
+ counttomark -2 roll 2 copy /yStart ED /xStart ED
+ counttomark 2 roll
+ f
+ ClosedBezier
+ 0.1 setflat
+ /Shift Symbol stringwidth pop 2 div def
+ CurvePath
+ [ xEnd yEnd xStart yStart SymbolLine
+} def
+%
+/BezierShowPoints {
+ gsave
+ Points aload length 2 div cvi /n ED
+ moveto
+ n 1 sub { lineto } repeat
+ CLW 2 div SLW [ 4 4 ] 0 setdash stroke
+ grestore
+} def
+%
+/Parab {
+ /y0 ED /x0 ED /y1 ED /x1 ED
+ /dx x0 x1 sub 3 div def
+ /dy y0 y1 sub 3 div def
+ x0 dx sub y0 dy add x1 y1 ArrowA
+ x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
+} def
+%
+/Parab1 { % 1 end | 0 SP
+ /ySP ED /xSP ED /y1 ED /x1 ED
+ /dx xSP x1 sub 3 div def
+ /dy ySP y1 sub 3 div def
+ newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
+ x1 ySP lineto closepath clip
+ currentpoint
+ newpath moveto
+ xSP dx sub ySP dy add x1 y1 ArrowA
+ xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
+ curveto
+ /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
+} def
+%
+/Grid {
+ newpath
+ /a 4 string def
+ /b ED % psk@gridlabels in pt
+ /c ED % { \pst@usecolor\psgridlabelcolor }
+ /n ED % psk@griddots
+ cvi dup 1 lt { pop 1 } if
+ /s ED % \psk@subgriddiv
+ s div dup 0 eq { pop 1 } if
+ /dy ED s div dup 0 eq { pop 1 } if % \pst@number\psyunit abs
+ /dx ED dy div round dy mul % \pst@number\psxunit abs
+ /y0 ED dx div round dx mul
+ /x0 ED dy div round cvi
+ /y2 ED dx div round cvi
+ /x2 ED dy div round cvi
+ /y1 ED dx div round cvi
+ /x1 ED
+ /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
+ /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
+ b 0 gt {
+ /z1 b 4 div CLW 2 div add def
+% /Helvetica findfont b scalefont setfont
+ /b b .95 mul CLW 2 div add def } if
+ systemdict /setstrokeadjust known
+ { true setstrokeadjust /t { } def }
+ { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+ exch itransform } bind def } ifelse
+ gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
+ /i x1 def
+ /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
+ /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
+ x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
+ { i dx mul dup y0 moveto
+ b 0 gt
+ { gsave c i a cvs dup stringwidth pop
+ /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse
+ h 0 gt {b neg}{z1} ifelse
+ rmoveto show grestore } if
+ dup t f moveto
+ g t L stroke
+ /i i w add def
+ } repeat
+ grestore
+ gsave
+ n 0 gt
+ % DG/SR modification begin - Nov. 7, 1997 - Patch 1
+ %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+ { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+ % DG/SR modification end
+ { 2 setlinecap } ifelse
+ /i y1 def
+ /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
+ /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
+ y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
+ { newpath i dy mul dup x0 exch moveto
+ b 0 gt { gsave c i a cvs dup stringwidth pop
+ /z2 ED
+ w 0 gt {z1 z2 add neg} {z1} ifelse
+ h 0 gt {z1} {b neg} ifelse
+ rmoveto show grestore } if
+ dup f exch t moveto
+ g exch t L stroke
+ /i i h add def
+ } repeat
+ grestore
+} def
+%
+/ArcArrow {
+ /d ED /b ED /a ED
+ gsave
+ newpath 0 -1000 moveto clip
+ newpath
+ 0 1 0 0 b
+ grestore
+ c mul
+ /e ED
+ pop pop pop r a e d PtoC y add exch x add
+ exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+ mul neg d
+} def
+%
+/Ellipse {
+ /rotAngle ED
+ /mtrx CM def
+ T
+ rotAngle rotate
+ scale 0 0 1 5 3 roll arc
+ mtrx setmatrix
+} def
+%
+/ArcAdjust { %%%% Vincent Guirardel
+% given a target length (targetLength) and an initial angle (angle0) [in the stack],
+% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
+% This computes an angle t such that (x0,y0) is at distance
+% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
+% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
+% contrary to TvZ's code.
+% To achieve, this, one iterates the following process: start with some angle t,
+% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
+% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
+%
+% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
+% the value of d = add/sub is used to know on which side we have to move.
+% It is only used in the initialisation of the angle before the iteration.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Input stack: 1: target length 2: initial angle
+% variables used : rx, ry, d (=add/sub)
+%
+ /targetLength ED /angle0 ED
+ /x0 rx angle0 cos mul def
+ /y0 ry angle0 sin mul def
+% we are looking for an angle t such that (x0,y0) is at distance targetLength
+% from the point M(t)=(rx*cos(t),ry*sin(t)))
+%initialisation of angle (using 1st order approx = TvZ's code)
+ targetLength 57.2958 mul
+ angle0 sin rx mul dup mul
+ angle0 cos ry mul dup mul
+ add sqrt div
+% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
+% (if the ellipse is very curved at the point where we draw the arrow, %
+% the value can be much more than 360 degrees !)
+% this should avoid going on the wrong side (more than 180 degrees) or go near
+% a bad attractive point (at 180 degrees)
+ dup 90 ge { pop 90 } if
+ angle0 exch d % add or sub
+% maximum number of times to iterate the iterative procedure:
+% iterative procedure: takes an angle t on top of stack, computes a
+% better angle (and put it on top of stack)
+ 30 { dup
+% compute distance D between (x0,y0) and M(t)
+ dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
+% if D almost equals targetLength, we stop
+ dup targetLength sub abs 1e-5 le { pop exit } if
+% stack now contains D t
+% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
+% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
+ exch dup cos rx mul x0 sub exch sin ry mul y0 sub
+% stack contains: y(t)-y0, x(t)-x0, d
+ 2 index Div targetLength mul y0 add ry Div exch
+ 2 index Div targetLength mul x0 add rx Div
+% stack contains x(t')/rx , y(t')/ry , d
+% now compute t', and remove D from stack
+ atan exch pop
+ } repeat
+% we don't look at what happened... in particular, if targetLength is greater
+% than the diameter of the ellipse...
+% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
+% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
+% to give back the result as a an angle relative to angle0 we could add the following line:
+% angle0 sub 0 exch d
+%
+% begin bug fix 2006-01-11
+% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
+%(we don't want to make the ellipse turn more or less than it should)...
+dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
+% end bug fix
+} def
+%
+/EllipticArcArrow {
+ /d ED % is add or sub
+ /b ED % arrow procedure
+ /a1 ED % angle
+ gsave
+ newpath
+ 0 -1000 moveto
+ clip % Set clippath far from arrow.
+ newpath
+ 0 1 0 0 b % Draw arrow to determine length.
+ grestore
+% Length of arrow is on top of stack. Next 3 numbers are junk.
+%
+ a1 exch ArcAdjust % Angular position of base of arrow.
+ /a2 ED
+ pop pop pop
+ a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
+ a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
+ a1 cos rx mul xOrig add %
+ a1 sin ry mul yOrig add %
+% Now arrow tip coor and base coor are on stack.
+ b pop pop pop pop % Draw arrow, and discard coordinates.
+ a2 CLW 8 div
+% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
+ ArcAdjust
+% resets original value of d
+ 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
+} def
+%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
+%
+/Rot { CP CP translate 3 -1 roll neg rotate NET } def
+%
+/RotBegin {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+ /a ED
+ a Rot /RAngle [ RAngle dup a add ] cvx def
+} def
+%
+/RotEnd {
+ /TMatrix [ TMatrix setmatrix ] cvx def
+ /RAngle [ RAngle pop ] cvx def
+} def
+%
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/Uput {
+ /a ED
+ add 2 div /h ED 2
+ div /w ED
+ /s a sin def
+ /c a cos def
+ /b s abs c abs 2 copy gt dup
+ /q ED
+ { pop } { exch pop } ifelse def
+ /w1 c b div w mul def
+ /h1 s b div h mul def
+ q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
+} def
+%
+/UUput {
+ /z ED
+ abs /y ED
+ /x ED
+ q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
+ { x x mul y y mul sub z z mul add sqrt z add }
+ { q { x s div } { x c div } ifelse abs
+ } ifelse
+ a PtoC
+ h1 add exch
+ w1 add exch
+} def
+%
+/BeginOL {
+ dup (all) eq exch TheOL eq or
+ { IfVisible not { Visible /IfVisible true def } if }
+ { IfVisible { Invisible /IfVisible false def } if } ifelse
+} def
+%
+/InitOL {
+ /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+ /Visible { CP OLUnit idtransform T moveto } def
+ /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def
+ /BOL { BeginOL } def
+ /IfVisible true def
+} def
+%
+end
+%-----------------------------------------------------------------------------%
+%
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-algparser.pro 0 0
+% $Id: pst-algparser.pro 594 2011-10-31 18:13:18Z herbert $
+%%
+%% PostScript prologue for PSTricks algorithm parser
+%% Version 0.04, 2011/10/21
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%%-----------------------------------------------------------------------------%
+%
+/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez
+%
+/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
+%
+% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
+%
+% 09/2011 DR factorial with ! added
+%
+% E->T|E+T
+% T->FS|T*FS
+% FS -> F | +FS | -FS
+% F->P|F^SF|P!
+% P->(E)|literal
+% literal->number|var|var[E]|func(params)
+% params->E|E,param
+% number->TOBEFINISHED
+%
+%% E expression, T term, SF signed factor, F factor, P power
+%
+%% parser
+%
+%% str
+%
+%% C->E<condition_operators>E
+%% STR index -> STR index+lenExpr
+/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def
+%
+%% analyze Expression List (separator , or | )
+%% STR index -> STR index+lenExpr
+%% /AnalyzeListOfE {
+%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
+%% NextNonBlankChar dup 0 eq { pop exit } if
+%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
+%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
+%% AnalyzeListOfEPostHook
+%% } def
+/AnalyzeListOfE {
+ /NotFirst false def
+ { NextNonBlankChar pop AnalyzeExpr
+ NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
+ dup Strlen eq { exit } if NextNonBlankChar
+ dup 44 ne 1 index 124 ne and
+ { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
+ if pop 1 add } loop
+ AnalyzeListOfEPostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% E->T|E+T
+%% STR index -> STR index+lenExpr
+/AnalyzeExpr {
+ AnalyzePreHook AnalyzeTerm IsEndingExpr
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% T->FS|T*FS
+%% STR index
+/AnalyzeTerm {
+ AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
+ ifelse
+ AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% FS -> F | +FS | -FS
+%% STR index
+/AnalyzeSignedFactor {
+ AnalyzePreHook 2 copy get dup IsUnaryOp
+ { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
+ { pop AnalyzeFactor }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% F->P|F^P|P!
+%% STR index
+/AnalyzeFactor {
+ AnalyzePreHook AnalyzePower IsEndingFactor
+ { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
+ { { dup 33 eq%% is there a ! DR 09/2011
+ { pop 1 add NextNonBlankChar pop EvalFactorial }
+ { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
+ ifelse
+ IsEndingFactor { pop exit } if } loop }
+ ifelse AnalyzePostHook
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% P->(E)|literal
+%% STR index
+/AnalyzePower {
+ %% depending of first char either a number, or a literal
+ 2 copy get dup 40 eq%%an open par
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
+ { AnalyzeLiteral }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index STR[index] -> STR index
+%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
+/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% recognize + or -
+%% chr -> T/F
+/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadNumber {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read mantissa
+ { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
+ dup 101 eq exch 69 eq or
+ %%% there is a "e" or "E" -> read exponant
+ { 1 add 2 copy get dup IsUnaryOp
+ { pop 1 add 2 copy get } if
+ { IsNumber not { exit } if 1 add 2 copy get } loop }
+ if
+ dup 4 1 roll
+ 3 -1 roll exch 1 index sub getinterval
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a number can contain only : 0123456789.
+%% chr -> T/F
+/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index number
+%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
+%% STR index -> STR index' number
+/ReadCondOp {
+ NextNonBlankChar 1 index 4 1 roll
+ { IsCondOp not { exit } if 1 add 2 copy get } loop
+ 2 copy 5 -1 roll
+ exch 1 index sub getinterval 3 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can contain only : 0123456789.
+%% chr -> T/F
+/IsLiteral {%
+ dup 48 ge exch dup 57 le 3 -1 roll and exch
+ dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch
+ dup 97 ge exch 122 le and or } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
+%% STR index -> literal STR index' nextchr
+/ReadLiteral {
+ exch dup 3 -1 roll dup 3 1 roll
+ %%read literal core
+ { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
+ 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a clpar
+%% STR index -> STR index STR[index] T/F
+/IsEndingExpr {%
+ 2 copy dup Strlen eq
+ %% if end of str is reached -> end !
+ { pop pop 0 true }
+ %% ending chr -> clpar, comma, |, <, >, =, !,
+ {get dup dup 41 eq
+ exch dup 124 eq
+ exch dup 93 eq
+ exch dup 44 eq
+ exch dup 30 eq
+ exch dup 60 ge exch 62 le and or or or or or}
+ ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or a +-
+%% STR index -> STR index STR[index] T/F
+/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or */
+%% STR index -> STR index STR[index] T/F
+/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% expr is ended by end of str or ^
+%% STR index -> STR index STR[index] T/F
+/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% STR index -> STR index STR[index]
+/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
+/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%
+%% DEBUG
+/BRK {false} def
+/BRKtrue {/BRK true def} def
+/BRKStop {BRK {BRKtoto} if } def
+/BRKEvalStop {BRK exch if } def
+/BRKBRK2true {BRK {BRK2true} if } def
+/BRK2 {false} def
+/BRK2true {/BRK2 true def} def
+/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
+end
+%
+%-------------------------------------------------------------------------------%
+%
+/tx@AlgToPs 12 dict def tx@AlgToPs begin
+%
+%% algExpr -> PSVector
+/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
+/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
+/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
+/Strlen 0 def
+/EvalListOfExpr {} def%
+/EvalNumber {%
+ ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
+ exch 1 add array astore def NextNonBlankChar pop } def
+/EvalAddSub {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
+} def
+/EvalMulDiv {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
+} def
+/EvalPower {%
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
+ pop /exp cvx exch 1 add array astore def
+} def
+/EvalFactorial {% DR 09/2011
+ /ExpressionVector ExpressionVector aload length
+ /fact cvx exch 1 add array astore def
+} def
+/EvalLiteral {%
+ ReadLiteral
+ dup 40 eq%%% there is an open par -> function call
+ { pop 2 index
+ dup (Sum) eq { EvalSum }
+ { dup (IfTE) eq { EvalCond }
+ { dup (Derive) eq { pop EvalDerive }
+ { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
+ /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
+ exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
+ { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
+ dup 91 eq%%% there is an open bracket -> vector element
+ { pop 1 add NextNonBlankChar pop AnalyzeExpr
+ /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
+ { pop NextNonBlankChar pop }
+ ifelse}
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% the derive function : Derive(n,f(x))
+%% firstparindex lastparindex ->
+/EvalDerive {
+ %% manage the function descripiton
+ 1 add ReadNumber 3 1 roll NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ 1 add NextNonBlankChar pop
+ 3 -1 roll cvi
+ dup 0 eq
+ { pop AnalyzeExpr 3 -1 roll pop 1 add }
+ { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll
+ { (x) tx@Derive begin Derive end } repeat
+ ExpressionVector exch /ExpressionVector [] def
+ AlgToPs aload length
+ /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def
+ l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
+ 1 index length /Strlen exch def } ifelse
+} def
+/EvalSum {%
+ pop 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
+ 5 -1 roll 4 add array astore def
+ %% keep ExpressionVector for later and create a new one for internal Sum computation
+ ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
+ 1 add NextNonBlankChar pop AnalyzeExpr
+ %% add each term
+ /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
+ /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
+ array astore def 3 -1 roll pop 1 add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+/EvalCond {%
+ pop 1 add AnalyzeCond NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ ExpressionVector 3 1 roll /ExpressionVector [] def
+ 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
+ NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add AnalyzeExpr
+ NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
+ ExpressionVector
+ /ExpressionVector 6 -1 roll aload length dup
+ 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
+ 1 add 3 -1 roll pop
+} def
+%% CondOp STR index
+/EvalCondOp {%
+ 3 -1 roll
+ dup (=) eq { /eq } {%
+ dup (<) eq { /lt } {%
+ dup (>) eq { /gt } {%
+ dup (>=) eq { /ge } {%
+ dup (<=) eq { /ge } {%
+ dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
+ ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
+ cvx exch pop
+ /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
+/EvalUnaryOp {
+ 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook {} bind def
+/PreEvalHook {} bind def
+/AnalyzeListOfEPostHook {} bind def
+/AnalyzePostHook {} def
+/RollOp { 3 1 roll } bind def
+end %tx@CoreAnalyzerDict
+%
+%--------------------------------------------------------------------%
+%
+/tx@Derive 41 dict def tx@Derive begin
+%%increase ^^ for each function added
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable -> PSVector
+/Derive {%
+ 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
+} def
+/Strlen 0 def
+/InitParser { dup length /Strlen exch def 0 } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% algExpr variable index -> PSVector
+/DeriveIndexed {%
+ 3 1 roll 10240 string 3 1 roll 0 3 1 roll
+ /Variable exch def
+ tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u,v)'=-(u',v')
+/EvalListOfExpr {%
+ 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
+ 2 copy 7 -1 roll dup length 4 1 roll putinterval add
+ 6 -2 roll pop pop
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (-u)'=-(u')
+/EvalUnaryOp {
+ 4 -2 roll 4 index (0) eq
+ { (0) StrConcat 7 -1 roll pop }
+ { 7 -1 roll 45 eq
+ { AddSub AddOpPar true } { false } ifelse
+ 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (number)'=0
+/EvalNumber { ReadNumber (0) 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u+v)'=u'+v'
+/EvalAddSub {%
+ 7 index dup (0) eq
+ { pop true }%% du=0 nothing added
+ { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
+ ifelse
+ 5 index dup (0) eq
+ { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0
+ { exch
+ { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
+ { 5 -2 roll 7 index 43 eq%%something yet added
+ { AddAdd false } { AddSub AddOpPar true } ifelse }
+ ifelse 11 1 roll
+ 3 -1 roll StrConcat 10 -1 roll { AddClPar } if
+ 2 copy pop 0 6 2 roll GetIntervalNewStr }
+ ifelse
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)' or (u/v)'
+/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u*v)'=u'*v+u*v'
+/EvalMul {%
+ 4 -2 roll 7 index dup (0) eq
+ { pop false }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
+ true }%%du!=0
+ ifelse
+ 5 1 roll 5 index (0) eq
+ { 5 -1 roll not { (0) StrConcat } if }%%dv=0
+ { 5 -1 roll { AddAdd } if
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ }%%dv!=0
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u/v)'=(u'*v-u*v')/v^2
+/EvalDiv {%
+ 4 -2 roll
+ 4 index (0) eq%%dv=0 -> u'/v
+ { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
+ { 7 index dup (0) eq
+ { pop }%%du=0
+ { (1) eq%%du=1
+ { false }
+ { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
+ 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
+ ifelse
+ AddSub
+ 4 index (1) eq
+ { 8 index StrConcat }
+ { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
+ ifelse
+ %}%%dv!=0
+ 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
+ AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
+ ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str1 index str2 -> str1 index
+/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
+/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+/EvalPower {%
+ 4 -2 roll 7 index (0) eq
+ {%%if du=0 then (u^v)'=v'ln(u)u^v
+ 4 index (0) eq
+ { (0) StrConcat }%%if dv=0 then (u^v)'=0
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
+ AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
+ }
+ {%%du!=0
+ 4 index (0) eq
+ {%%if dv=0 then (u^v)'=vu'u^(v-1)
+ 5 index dup IsStrNumber
+ { dup (0) eq
+ { StrConcat }
+ { dup dup (1) eq exch (1.0) eq or
+ { StrConcat }
+ { StrConcat
+ 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
+ { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
+ (*\() StrConcat 8 index StrConcat (\)) StrConcat
+ 5 index dup dup (2) eq exch (2.0) eq or
+ { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
+ { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)) StrConcat } ifelse
+ }
+ {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
+ 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
+ AddOpPar 5 index StrConcat (\)*\() StrConcat
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (-1\)+\() StrConcat
+ 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
+ 8 index StrConcat (\)^\() StrConcat
+ 5 index StrConcat (\)*ln\() StrConcat
+ 8 index StrConcat AddClPar
+ } ifelse
+ } ifelse
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for factorial ! only cst => null derivative
+/EvalFactorial {% DR 09/2011
+ 4 index (0) eq
+ { (0) mark 8 -2 roll cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
+ { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% str -> true/false
+/IsStrNumber {%
+ true exch
+ { dup 48 lt exch dup 57 gt 3 -1 roll or
+ exch dup 46 ne%%.
+ exch dup 43 ne%%+
+ exch 45 ne%%-
+ and and and { pop false } if } forall
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalLiteral {%
+ ReadLiteral dup 40 eq%%% there is an open par -> function call
+ { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
+ { dup 91 eq%%% there is an open bracket -> vector element
+ { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
+ { pop EvalVariable }
+ ifelse }
+ ifelse
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% first last parpos Expr[first:parpos-1] ->
+/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% (f(u))'=u'f'(u)
+/EvalFunc {
+ 4 2 roll 4 index (1) ne
+ { AddOpPar 4 index StrConcat (\)*) StrConcat } if
+ (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Func derivative -> Eval<func>
+/EvalFunc_sin {%
+ PreCommonFunc
+ { (cos\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_cos {%
+ PreCommonFunc
+ { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_tan {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_asin {%
+ PreCommonFunc
+ { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_acos {%
+ PreCommonFunc
+ { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_atg {%
+ PreCommonFunc
+ { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_ln {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_exp {%
+ PreCommonFunc
+ { (exp\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_EXP {%
+ PreCommonFunc
+ { (EXP\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_sqrt {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Fact {%
+ PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
+ PostCommonFunc } def
+/EvalFunc_sh {%
+ PreCommonFunc
+ { (ch\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_ch {%
+ PreCommonFunc
+ { (sh\() StrConcat 5 index StrConcat AddClPar } if
+ PostCommonFunc } def
+/EvalFunc_th {%
+ PreCommonFunc
+ { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argsh {%
+ PreCommonFunc
+ { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argch {%
+ PreCommonFunc
+ { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
+ PostCommonFunc } def
+/EvalFunc_Argth {%
+ PreCommonFunc
+ { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
+ PostCommonFunc } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/PreCommonFunc {
+ 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 2 roll 4 index (0) eq
+ { (0) StrConcat false }
+ { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
+} def
+/PostCommonFunc {
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+/EvalFunc_Derive {%
+ 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
+ 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
+ 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
+ exch 6 2 roll } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_Sum {%
+ 1 add NextNonBlankChar pop
+ %% read the variable name
+ ReadLiteral pop 3 -1 roll pop NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
+ %% read the initial value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
+ %% read the increment value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
+ %% read the limit value
+ 1 add NextNonBlankChar pop ReadNumber pop
+ 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
+ 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
+ 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% literal switch -> func call, vector, variables
+/EvalFunc_IfTE {%
+ 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
+ NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop dup 5 1 roll
+ AnalyzeExpr NextNonBlankChar
+ 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
+ 1 add NextNonBlankChar pop
+ AnalyzeExpr 1 add NextNonBlankChar pop
+ 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
+ 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
+ 2 copy pop 0 6 2 roll GetIntervalNewStr
+ mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% advance in str until a comma is found (no error detection!)
+%% str index -> str index'
+/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Convert to radians if trigo function call
+%% (name) ->
+/TrigoFunc {
+ dup (cos) eq 1 index (sin) eq or exch (tan) eq or
+ { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
+ array astore def
+ } if
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% No derivative for condition....
+/EvalCondOp { 3 -1 roll pop } bind def
+/PutIntervalOneAdd {putinterval 1 add} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add close parenthesis in string at the given index
+%% str index -> str index+1
+/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add 0 in string at the given index
+%% str index -> str index+1
+/AddZero {2 copy (0) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddMul {2 copy (*) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add open parenthesis in string at the given index
+%% str index -> str index+1
+/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a plus sign in string at the given index
+%% str index -> str index+1
+/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a minus sign in string at the given index
+%% str index -> str index+1
+/AddSub {2 copy (-) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Add a pipe sign in string at the given index
+%% str index -> str index+1
+/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% H O O K S
+/AnalyzePreHook { dup 5 1 roll } bind def
+/PreEvalHook {} def
+/AnalyzePostHook { 7 -1 roll pop } bind def
+/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
+/RollOp { 5 1 roll } bind def
+end%%%tx@CoreAnalyzerDict
+/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% NEW FUNC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
+%% x -> theta
+/asin {%
+ dup abs 1 gt { EQDFasinrangeerror } if
+ dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
+} def
+%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
+%% x -> theta
+/acos {%
+ dup abs 1 gt { EQDFacosrangeerror } if
+ dup dup mul 1 exch sub sqrt exch atan DegtoRad
+} def
+%% function arctangent in radians
+%% x -> theta
+/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
+%% HYPERBOLIC FUNCTIONS
+/sh { dup Ex exch neg Ex sub 2 div } def
+/ch { dup Ex exch neg Ex add 2 div } def
+/th { dup sh exch ch div } def
+/Argsh { dup dup mul 1 add sqrt add ln } def
+/Argch { dup dup mul 1 sub sqrt add ln } def
+/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
+%% modified exponential funtion for 0
+%% x n -> x^n
+/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
+%% modified exponential funtion for 0
+%% x -> e^x
+/Ex { Euler exch exp } bind def
+%%
+%% factorial function
+%% n -> n!
+/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
+/fact { Fact } bind def
+/! { Fact } bind def
+end
+%
+% END pst-algparser.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-tools.pro 0 0
+% $Id: pst-tools.pro 713 2012-10-16 14:25:00Z herbert $
+%
+%% PostScript tools prologue for pstricks.tex.
+%% Version 0.03, 2012/10/16
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+%
+/Pi2 1.57079632679489661925640 def
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% subroutines for complex numbers, given as an array [a b]
+% which is a+bi = Real+i Imag
+%
+/cxadd { % [a1 b1] [a2 b2] = [a1+a2 b1+b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ 3 -1 roll % [a2 b2] a2 [a1 b1]
+ dup 0 get % [a2 b2] a2 [a1 b1] a1
+ 3 -1 roll % [a2 b2] [a1 b1] a1 a2
+ add % [a2 b2] [a1 b1] a1+a2
+ 3 1 roll % a1+a2 [a2 b2] [a1 b1]
+ 1 get % a1+a2 [a2 b2] b1
+ exch 1 get % a1+a2 b1 b2
+ add 2 array astore
+} def
+%
+/cxneg { % [a b]
+ dup 1 get % [a b] b
+ exch 0 get % b a
+ neg exch neg % -a -b
+ 2 array astore
+} def
+%
+/cxsub { cxneg cxadd } def % same as negative addition
+%
+% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
+/cxmul { % [a1 b1] [a2 b2]
+ dup 0 get % [a1 b1] [a2 b2] a2
+ exch 1 get % [a1 b1] a2 b2
+ 3 -1 roll % a2 b2 [a1 b1]
+ dup 0 get % a2 b2 [a1 b1] a1
+ exch 1 get % a2 b2 a1 b1
+ dup % a2 b2 a1 b1 b1
+ 5 -1 roll dup % b2 a1 b1 b1 a2 a2
+ 3 1 roll mul % b2 a1 b1 a2 b1a2
+ 5 -2 roll dup % b1 a2 b1a2 b2 a1 a1
+ 3 -1 roll dup % b1 a2 b1a2 a1 a1 b2 b2
+ 3 1 roll mul % b1 a2 b1a2 a1 b2 a1b2
+ 4 -1 roll add % b1 a2 a1 b2 b3
+ 4 2 roll mul % b1 b2 b3 a1a2
+ 4 2 roll mul sub % b3 a3
+ exch 2 array astore
+} def
+%
+% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
+/cxsqr { % [a b] square root
+ dup 0 get exch 1 get % a b
+ dup dup mul % a b b^2
+ 3 -1 roll % b b^2 a
+ dup dup mul % b b^2 a a^2
+ 3 -1 roll sub % b a a2
+ 3 1 roll mul 2 mul % a2 b2
+ 2 array astore
+} def
+%
+/cxsqrt { % [a b]
+% dup cxnorm sqrt /r exch def
+% cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
+ cxlog % log[a b]
+ 2 cxrdiv % log[a b]/2
+ aload pop exch % b a
+ 2.781 exch exp % b exp(a)
+ exch cxconv exch % [Re +iIm] exp(a)
+ cxrmul %
+} def
+%
+/cxarg { % [a b]
+ aload pop % a b
+ exch atan % arctan b/a
+ DegtoRad % arg(z)=atan(b/a)
+} def
+%
+% log[a b] = [a^2-b^2 2ab] = [a2 b2]
+/cxlog { % [a b]
+ dup % [a b][a b]
+ cxnorm % [a b] |z|
+ log % [a b] log|z|
+ exch % log|z|[a b]
+ cxarg % log|z| Theta
+ cxmake2 % [log|z| Theta]
+} def
+%
+% square of magnitude of complex number
+/cxnorm2 { % [a b]
+ dup 0 get exch 1 get % a b
+ dup mul % a b^2
+ exch dup mul add % a^2+b^2
+} def
+%
+/cxnorm { % [a b]
+ cxnorm2 sqrt
+} def
+%
+/cxconj { % conjugent complex
+ dup 0 get exch 1 get % a b
+ neg 2 array astore % [a -b]
+} def
+%
+/cxre { 0 get } def % real value
+/cxim { 1 get } def % imag value
+%
+% 1/[a b] = ([a -b]/(a^2+b^2)
+/cxrecip { % [a b]
+ dup cxnorm2 exch % n2 [a b]
+ dup 0 get exch 1 get % n2 a b
+ 3 -1 roll % a b n2
+ dup % a b n2 n2
+ 4 -1 roll exch div % b n2 a/n2
+ 3 1 roll div % a/n2 b/n2
+ neg 2 array astore
+} def
+%
+/cxmake1 { 0 2 array astore } def % make a complex number, real given
+/cxmake2 { 2 array astore } def % dito, both given
+%
+/cxdiv { cxrecip cxmul } def
+%
+% multiplikation by a real number
+/cxrmul { % [a b] r
+ exch aload pop % r a b
+ 3 -1 roll dup % a b r r
+ 3 1 roll mul % a r b*r
+ 3 1 roll mul % b*r a*r
+ exch 2 array astore % [a*r b*r]
+} def
+%
+% division by a real number
+/cxrdiv { % [a b] r
+ 1 exch div % [a b] 1/r
+ cxrmul
+} def
+%
+% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
+/cxconv { % theta
+ RadtoDeg dup sin exch cos cxmake2
+} def
+
+%%%%% ### bubblesort ###
+%% syntax : array bubblesort --> array2 trie par ordre croissant
+%% code de Bill Casselman
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/bubblesort { % on stack must be an array [ ... ]
+4 dict begin
+ /a exch def
+ /n a length 1 sub def
+ n 0 gt {
+ % at this point only the n+1 items in the bottom of a remain to
+ % the sorted largest item in that blocks is to be moved up into
+ % position n
+ n {
+ 0 1 n 1 sub {
+ /i exch def
+ a i get a i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ a i 1 add
+ a i get
+ a i a i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+ } if
+ } for
+ /n n 1 sub def
+ } repeat
+ } if
+ a % return the sorted array
+end
+} def
+%
+/concatstringarray{ % [(a) (b) ... (z)] --> (ab...z) 20100422
+ 0 1 index { length add } forall
+ string
+ 0 3 2 roll
+ { 3 copy putinterval length add }forall
+ pop
+} bind def
+%
+/dot2comma {% on stack a string (...)
+ 2 dict begin
+ /Output exch def
+ 0 1 Output length 1 sub {
+ /Index exch def
+ Output Index get 46 eq { Output Index 44 put } if
+ } for
+ Output
+ end
+} def
+%
+/rightTrim {
+ dup
+ length 1 sub -1 0 {
+ /i exch def dup i get 32 ne { exit } if
+ } for
+ 0 i 1 add getinterval
+ dup length string copy
+} bind def
+
+/psStringwidth /stringwidth load def
+/psShow /show load def
+
+%/stringwidth{ rightTrim psStringwidth } bind def
+
+%/show { rightTrim psShow } bind def
+%-----------------------------------------------------------------------------%
+% END pst-tools.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro 0 0
+% $Id: pst-dots.pro 130 2009-08-27 08:55:03Z herbert $
+%
+%% PostScript prologue for pstricks.tex.
+%% Version 2.02, 2009/06/16
+%%
+%% For distribution, see pstricks.tex.
+%%
+%% Timothy Van Zandt <tvz@Princeton.EDU>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% Modified by Etienne Riga - Dec. 16, 1999
+%% Modified by Etienne Riga - 2005/01/01 (er)
+%% to add /Diamond, /SolidDiamond and /BoldDiamond
+%% Modified by Herbert Voss (hv) - 2008/04/17
+%
+10 dict dup begin % hold local
+ /FontType 3 def
+ /FontMatrix [.001 0 0 .001 0 0] def
+% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
+ /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
+ /Encoding 256 array def
+ 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
+ Encoding % replace with given dot names
+ dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
+% % and save /Bullet at this place in Encoding
+ dup (c) 0 get /Circle put
+ dup (C) 0 get /BoldCircle put % 67
+ dup (u) 0 get /SolidTriangle put
+ dup (t) 0 get /Triangle put
+ dup (T) 0 get /BoldTriangle put
+ dup (r) 0 get /SolidSquare put
+ dup (s) 0 get /Square put
+ dup (S) 0 get /BoldSquare put
+ dup (q) 0 get /SolidPentagon put
+ dup (p) 0 get /Pentagon put
+ dup (P) 0 get /BoldPentagon put
+%%%
+ dup (k) 0 get /Asterisk put
+ dup (K) 0 get /BoldAsterisk put
+ dup (J) 0 get /SolidAsterisk put
+ dup (h) 0 get /Hexagon put
+ dup (H) 0 get /BoldHexagon put
+ dup (G) 0 get /SolidHexagon put
+ dup (f) 0 get /Octogon put % 2008-04-18 hv
+ dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
+ dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
+ dup (a) 0 get /Add put
+ dup (A) 0 get /BoldAdd put % 65
+ dup (x) 0 get /Mul put
+ dup (X) 0 get /BoldMul put
+ dup (m) 0 get /Oplus put
+ dup (M) 0 get /BOplus put
+ dup (e) 0 get /SolidOplus put
+ dup (n) 0 get /Otimes put
+ dup (N) 0 get /BOtimes put
+ dup (E) 0 get /SolidOtimes put
+ dup (i) 0 get /Bar put
+ dup (I) 0 get /BoldBar put
+ dup (l) 0 get /SolidDiamond put
+ dup (d) 0 get /Diamond put
+ (D) 0 get /BoldDiamond put
+%%%
+/CharProcs 47 dict def
+CharProcs begin
+ /CirclePath {0 0 500 0 360 arc closepath} def
+ /Bullet {CirclePath fill} def
+ /Circle {CirclePath .9 .9 scale CirclePath eofill} def
+ /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
+ /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
+ /SolidTriangle {TrianglePath fill} def
+ /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
+ /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
+ /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
+ /SolidSquare {SquarePath fill} def
+ /Square {SquarePath .89 .89 scale SquarePath eofill} def
+ /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
+ /PentagonPath {
+ -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
+ 0 574.7 lineto -546.6 177.6 lineto closepath
+ } def
+ /SolidPentagon {PentagonPath fill} def
+ /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
+ /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
+%-------------- hv begin 2004/07/25 from: er 2003/03/24
+ /HexagonPath {
+ 0 550 moveto -476 275 lineto -476 -275 lineto
+ 0 -550 lineto 476 -275 lineto 476 275 lineto closepath
+ } def
+ /SolidHexagon {HexagonPath fill} def
+ /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
+ /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
+% 2008-04-18 hv
+ /OctogonPath {
+ 550 dup 22.5 tan mul dup neg dup add /xMove exch def
+ exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
+ /SolidOctogon { OctogonPath fill } def
+ /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
+ /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
+%
+ /AsteriskPath {
+ 20 0 moveto 10 250 180 500 0 500 curveto
+ -180 500 -10 250 -20 0 curveto closepath
+ } def
+ /Asterisk {
+ AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
+ 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
+ } def
+%
+ /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
+ /BoldAsteriskPath {
+ 50 30 cos 100 mul moveto Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp 60 rotate Basterp
+ 60 rotate Basterp closepath
+ } def
+ /BoldAsterisk {BoldAsteriskPath fill} def
+ /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
+ /CrossPath {
+ 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
+ -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
+ 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
+ } def
+ /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
+ -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
+ 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
+ } def
+ /Add {CrossPath fill} def
+ /Mul {45 rotate CrossPath fill} def
+ /BoldAdd {BoldCrossPath fill} def
+ /BoldMul {45 rotate BoldCrossPath fill} def
+ /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
+ /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
+ /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
+ /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
+ /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
+ /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
+ /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
+ /Bar {BarPath fill} def
+ /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
+ /BoldBar {BoldBarPath fill} def
+ /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
+ /SolidDiamond {DiamondPath fill} def
+ /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
+ /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
+%%%
+ /.notdef { } def
+end
+%
+/BuildGlyph {
+ exch
+ begin
+% Metrics 1 index get exec 0
+ 0 0
+% BBoxes 3 index get exec
+ -1000 -1000 1000 1000
+% -571.5 -742.5 571.5 742.5
+ setcachedevice
+ CharProcs begin load exec end
+ end
+} def
+%
+/BuildChar {
+ 1 index /Encoding get exch get
+ 1 index /BuildGlyph get exec
+} bind def
+%
+end
+/PSTricksDotFont exch definefont pop
+%
+%% end
+
+%%EndProcSet
+%%BeginProcSet: pst-coil.pro 0 0
+%!ps
+% PostScript prologue for pst-coil.tex.
+% Version 1.03, 2010/02/01
+% For distribution, see pstricks.tex.
+%
+/tx@CoilDict 40 dict def tx@CoilDict begin
+/CoilLoop {
+ /t ED
+ t sin AspectSin mul t 180 div AspectCos mul add t cos lineto } def
+/Coil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED
+ /ArmB ED
+ /ArmA ED
+ /h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate
+ /BeginAngle ArmA AspectCos Div w h mul Div 360 mul def
+ /EndAngle TotalLength ArmB sub AspectCos Div
+ w h mul Div 360 mul def
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle Inc
+ EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+% DG/SR modification begin - Jun. 2, 1998 - Patch 1 (from Michael Vulis)
+% TotalLength 0 ArrowB lineto } def
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop } def
+% DG/SR modification end
+%
+/Sin {
+ /Func ED
+ /PointsPerPeriod ED
+ /ArmB ED
+ /ArmA ED
+ /Amplitude ED
+ /roundValue ED
+ /relativePeriod ED
+ /Periods ED
+ /y1 ED /x1 ED /y0 ED /x0 ED
+ x0 y0 translate y1 y0 sub x1 x0 sub 2 copy Pyth
+ dup /TotalLength ED
+ ArmA sub ArmB sub /SinLength ED
+ Atan rotate
+ 1 0 0 0 ArrowA ArmA 0 lineto
+ /mtrx CM def
+ relativePeriod
+ {}
+ { SinLength Periods div roundValue { cvi } if
+ /Periods ED } ifelse
+ /dxStep SinLength 360 div def % the default step for x pos
+ /xStep 360 PointsPerPeriod div def % the step for the for loop
+ 1 xStep 360 { % PointsPerPeriod times
+ dup dxStep mul ArmA add exch % x pos and value for the func
+ Periods mul Func Amplitude mul lineto
+ } for
+ mtrx setmatrix TotalLength ArmB sub 0 lineto CP
+ TotalLength 0 ArrowB lineto
+ pop pop pop pop
+} def
+%
+/AltCoil {
+ /Inc ED
+ dup sin /AspectSin ED
+ cos /AspectCos ED /h ED /w ED /EndAngle ED /BeginAngle ED
+ /mtrx CM def
+ w h mul 2 Div w 2 Div scale BeginAngle sin AspectSin mul
+ BeginAngle 180 div AspectCos mul add BeginAngle cos
+ /lineto load stopped { moveto } if
+ BeginAngle Inc EndAngle { CoilLoop } for
+ EndAngle CoilLoop mtrx setmatrix } def
+/ZigZag {
+ /ArmB ED /ArmA ED
+ 2 div /w ED
+ w mul /h ED /y1 ED /x1 ED /y0 ED /x0 ED
+ x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth
+ /TotalLength ED
+ Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul
+ sub 2 div dup ArmA add
+ /ArmA ED ArmB add
+ /ArmB ED
+ /x ArmB h 2 div add def
+ mark 0 0 ArmB 0
+ n { x w /w w neg def /x x h add def } repeat
+ TotalLength ArmA sub 0 TotalLength 0 } def
+%
+end
+% END pst-coil.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro 0 0
+% $Id: pst-node.pro 805 2013-07-11 13:18:11Z herbert $
+%%
+%% PostScript prologue for pst-node.tex.
+%% Version 1.14, 2012/09/18.
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%
+tx@Dict begin % from main pstricks dict
+ /T /translate load def
+ /CP /currentpoint load def
+% /startGlobal { true setglobal globaldict begin } bind def
+% /endGlobal { end false setglobal } bind def
+end
+/tx@NodeDict 400 dict def tx@NodeDict begin
+/NewNode { % on stack: { x y } boolean N@name type InitXnode
+ gsave
+ NodeScale % a bugfix for xelatex, it's empty for dvips
+ /next exch def % { x y } boolean N@name type
+ dict dup % { x y } boolean N@name dict dict
+ 3 1 roll def % { x y } boolean dict N@name dict def
+ exch { dup 3 1 roll def } if % { x y } dict boolean
+ begin % { x y } dict begin
+ tx@Dict begin
+ STV CP T exec % set scaling
+ end
+ /NodeMtrx CM def % save CM
+ next % InitXNode
+ end
+ grestore
+} def
+%
+/InitPnode {
+ /Y ED /X ED
+ /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+%
+/InitCnode {
+ /r ED /Y ED /X ED
+ /NodePos { NodeSep r add dup Cos mul exch Sin mul } def
+} def
+%
+/GetRnodePos {
+ Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse
+ Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse
+ dx Sin mul abs dy
+ Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse
+} def
+%
+/InitRnode {
+ /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED
+ /NodePos { GetRnodePos } def
+} def
+%
+/DiaNodePos {
+ w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+ Cos mul exch Sin mul
+} def
+%
+/TriNodePos {
+ Sin s lt
+ { d NodeSep sub dup Cos mul Sin Div exch }
+ { w h mul w Sin mul h Cos abs mul add Div
+ NodeSep add dup Cos mul exch Sin mul
+ } ifelse
+} def
+%
+/InitTriNode {
+ sub 2 div exch
+ 2 div exch
+ 2 copy T
+ 2 copy 4 index index /d ED
+ pop pop pop pop
+ -90 mul rotate
+ /NodeMtrx CM def
+ /X 0 def /Y 0 def
+ d sub abs neg /d ED
+ d add /h ED
+ 2 div h mul h d sub Div /w ED
+ /s d w Atan sin def
+ /NodePos { TriNodePos } def
+} def
+%
+/OvalNodePos {
+ /ww w NodeSep add def
+ /hh h NodeSep add def
+ Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul
+} def
+%
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+%
+/XYPos {
+ dup sin exch cos Do
+ /Cos ED /Sin ED /Dist ED
+ Cos 0 gt
+ { Dist Dist Sin mul Cos div }
+ { Cos 0 lt
+ { Dist neg Dist Sin mul Cos div neg }
+ { 0 Dist Sin mul } ifelse
+ } ifelse
+ Do
+} def
+%
+/GetEdge {
+ dup 0 eq
+ { pop begin 1 0 NodeMtrx dtransform
+ CM idtransform
+ exch atan sub
+ dup
+ sin /Sin ED
+ cos /Cos ED
+ /NodeSep ED
+ NodePos NodeMtrx dtransform CM idtransform end }
+ { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse
+} def
+%
+/AddOffset {
+ 1 index 0 eq
+ { pop pop }
+ { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse
+} def
+%
+/GetEdgeA {
+ NodeSepA AngleA NodeA NodeSepTypeA GetEdge
+ OffsetA AngleA AddOffset
+ yA add /yA1 ED
+ xA add /xA1 ED
+} def
+%
+/GetEdgeB {
+ NodeSepB AngleB NodeB NodeSepTypeB GetEdge
+ OffsetB AngleB AddOffset
+ yB add /yB1 ED
+ xB add /xB1 ED
+} def
+%
+/GetArmA {
+ ArmTypeA 0 eq
+ { /xA2 ArmA AngleA cos mul xA1 add def
+ /yA2 ArmA AngleA sin mul yA1 add def }
+ { ArmTypeA 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmA AngleA XYPos OffsetA AngleA AddOffset
+ yA add /yA2 ED
+ xA add /xA2 ED } ifelse
+} def
+%
+/GetArmB {
+ ArmTypeB 0 eq
+ { /xB2 ArmB AngleB cos mul xB1 add def
+ /yB2 ArmB AngleB sin mul yB1 add def }
+ { ArmTypeB 1 eq {{exch}} {{}} ifelse
+ /Do ED
+ ArmB AngleB XYPos OffsetB AngleB AddOffset
+ yB add /yB2 ED
+ xB add /xB2 ED } ifelse
+} def
+%
+/InitNC {
+ /b ED /a ED % second and first node
+ /NodeSepTypeB ED /NodeSepTypeA ED
+ /NodeSepB ED /NodeSepA ED
+ /OffsetB ED /OffsetA ED
+ tx@NodeDict a known tx@NodeDict b known and dup {
+ /NodeA a load def
+ /NodeB b load def
+ NodeA GetCenter /yA ED /xA ED
+ NodeB GetCenter /yB ED /xB ED } if
+} def
+%
+/LPutLine {
+ 4 copy
+ 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED
+ 1 t sub mul
+ 3 1 roll 1 t sub mul
+ 4 1 roll t mul add /Y ED
+ t mul add /X ED
+} def
+%
+/LPutLines {
+ mark LPutVar counttomark 2 div 1 sub /n ED
+% t floor dup n gt
+ t floor dup n ge % to allow npos<= hv 2008-08-14
+ { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse
+ cvi 2 mul { pop } repeat
+ LPutLine
+ cleartomark
+} def
+%
+/BezierMidpoint {
+ /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED
+ /cx x1 x0 sub 3 mul def
+ /cy y1 y0 sub 3 mul def
+ /bx x2 x1 sub 3 mul cx sub def
+ /by y2 y1 sub 3 mul cy sub def
+ /ax x3 x0 sub cx sub bx sub def
+ /ay y3 y0 sub cy sub by sub def
+ ax t 3 exp mul bx t t mul mul add
+ cx t mul add x0 add ay t 3 exp mul
+ by t t mul mul add cy t mul add
+ y0 add 3 ay t t mul mul mul 2
+ by t mul mul add cy add 3 ax t t mul mul mul
+ 2 bx t mul mul add cx add atan /NAngle ED
+ /Y ED /X ED
+} def
+%
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+
+/NCCoor {
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def
+ /LPutPos { LPutVar LPutLine } def
+ /HPutPos { LPutVar HPutLine } def
+ /VPutPos { LPutVar VPutLine } def
+ LPutVar
+} def
+%
+/NCLine {
+ NCCoor
+ tx@Dict begin
+ ArrowA CP 4 2 roll
+ ArrowB
+ lineto pop pop
+ end
+} def
+%
+/NCLines {
+ false NArray
+ n 0 eq
+ { NCLine }
+ { 2 copy yA sub exch xA sub Atan /AngleA ED
+ n 2 mul dup index exch index yB sub exch xB sub
+ Atan /AngleB ED
+ GetEdgeA GetEdgeB
+ /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def
+ mark LPutVar
+ tx@Dict begin false Line end
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+ } ifelse
+} def
+%
+/NCCurve {
+ GetEdgeA
+ GetEdgeB
+ xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+%
+/NCAngles {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform pop
+ xB2 yB2 mtrx transform exch pop
+ mtrx itransform
+ /y0 ED /x0 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def } def
+%
+/NCAngle {
+ GetEdgeA GetEdgeB GetArmB
+ /mtrx AngleA matrix rotate def
+ xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+ /y0 ED /x0 ED
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 x0 y0 xA1 yA1
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCBar {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx itransform pop
+ xB2 yB2 mtrx itransform pop
+ sub dup 0 mtrx transform
+ 3 -1 roll 0 gt
+ { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+ { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse
+ mark
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+/NCDiag {
+ /lineAngle ED
+ GetEdgeA GetEdgeB GetArmA GetArmB mark
+ lineAngle abs 0 gt {
+ /xTemp xA2 10 add def
+ /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
+ /dY1 yTemp yA2 sub def
+ /dX1 xTemp xA2 sub def
+ /dY2 yB2 yB1 sub def
+ /dX2 xB2 xB1 sub def
+ dX1 abs 0.01 lt {
+ /m2 dY2 dX2 div def
+ /xB2 xA2 def
+ /yB2 xA2 xB1 sub m2 mul yB1 add def
+ }{
+ dX2 abs 0.01 lt {
+ /m1 dY1 dX1 div def
+ /xB2 xB1 def
+ /yB2 xB1 xA2 sub m1 mul yA2 add def
+ }{%
+ /m1 dY1 dX1 div def
+ /m2 dY2 dX2 div def
+ /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
+ /yB2 xB2 xA2 sub m1 mul yA2 add def
+ } ifelse
+ } ifelse
+ } if
+ ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetEdgeB GetArmA GetArmB mark
+% ArmB 0 ne { xB1 yB1 } if
+% xB2 yB2 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCDiagg {
+ /lineAngle ED
+ GetEdgeA GetArmA
+ lineAngle abs 0 gt
+ { lineAngle }
+ { yB yA2 sub xB xA2 sub Atan 180 add } ifelse
+ /AngleB ED
+ GetEdgeB mark
+ lineAngle abs 0 gt {
+ /dY2 yA2 yA1 sub def
+ /dX2 xA2 xA1 sub def
+ lineAngle abs 90 eq {
+ /m2 dY2 dX2 div def
+ /yA2 xB xA2 sub m2 mul yA2 add def
+ /xA2 xB def
+ }{
+ /m1 lineAngle dup sin exch cos div def % tan alpha
+ dX2 abs 0.01 lt {
+ /yA2 xA1 xB sub m1 mul yB add def
+ /xA2 xA1 def
+ }{%
+ /m2 dY2 dX2 div def
+ /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
+ /yA2 xA2 xB sub m1 mul yB add def
+ } ifelse
+ } ifelse
+ } if
+ xB1 yB1 xA2 yA2
+ ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+%
+% GetEdgeA GetArmA
+% yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+% GetEdgeB
+% mark
+% xB1 yB1 xA2 yA2
+% ArmA 0 ne { xA1 yA1 } if
+% tx@Dict begin false Line end
+% /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
+% /LPutPos { LPutLines } def
+% /HPutPos { HPutLines } def
+% /VPutPos { VPutLines } def
+} def
+%
+/NCLoop {
+ GetEdgeA GetEdgeB GetArmA GetArmB
+ /mtrx AngleA matrix rotate def
+ xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED
+ /xB3 xB2 yB2 mtrx transform pop def
+ xB3 yA3 mtrx itransform /yB3 ED /xB3 ED
+ xA3 yA3 mtrx itransform /yA3 ED /xA3 ED
+ mark ArmB 0 ne { xB1 yB1 } if
+ xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if
+ tx@Dict begin false Line end
+ /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { HPutLines } def
+ /VPutPos { VPutLines } def
+} def
+%
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+%
+/NCCircle {
+ NodeSepA 0 NodeA 0 GetEdge pop
+ 2 div dup 2 exp r r mul sub abs sqrt
+ atan 2 mul /a ED
+ r AngleA 90 add PtoC yA add exch xA add
+ exch 2 copy
+ /LPutVar [ 4 2 roll r AngleA ] cvx def
+ /LPutPos {
+ LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC
+ 3 -1 roll add
+ /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+ r AngleA 90 sub a add AngleA 270 add a sub
+ tx@Dict begin
+ /angleB ED /angleA ED /r ED
+ /c 57.2957 r Div def
+ /y ED /x ED
+} def
+%
+/NCBox {
+ /d ED /h ED
+ /AngleB yB yA sub xB xA sub Atan def
+ /AngleA AngleB 180 add def
+ GetEdgeA GetEdgeB
+ /dx d AngleB sin mul def
+ /dy d AngleB cos mul neg def
+ /hx h AngleB sin mul neg def
+ /hy h AngleB cos mul def
+ /LPutVar [
+ xA1 hx add yA1 hy add xB1 hx add yB1 hy add
+ xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def
+ /LPutPos { LPutLines } def
+ /HPutPos { xB yB xA yA LPutLine } def
+ /VPutPos { HPutPos } def
+ mark
+ LPutVar tx@Dict begin false Polygon end
+} def
+%
+/NCArcBox {
+ /l ED neg /d ED /h ED /a ED
+ /AngleA yB yA sub xB xA sub Atan def
+ /AngleB AngleA 180 add def
+ /tA AngleA a sub 90 add def
+ /tB tA a 2 mul add def
+ /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+ /x0 xA r tA cos mul add def
+ /y0 yA r tA sin mul add def
+ /c 57.2958 r div def
+ /AngleA AngleA a sub 180 add def
+ /AngleB AngleB a add 180 add def
+ GetEdgeA GetEdgeB
+ /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def
+ /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def
+ l 0 eq {
+ x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn
+ }{
+ x0 y0 translate
+ /tA AngleA l c mul add def
+ /tB AngleB l c mul sub def
+ 0 0 r h add tA tB arc r h add
+ AngleB PtoC r d add
+ AngleB PtoC 2 copy
+ 6 2 roll l arcto 4 { pop } repeat
+ r d add tB PtoC l arcto 4 { pop } repeat
+ 0 0 r d add tB tA arcn r d add
+ AngleA PtoC r h add
+ AngleA PtoC 2 copy 6 2 roll
+ l arcto 4 { pop } repeat
+ r h add tA PtoC l arcto 4 { pop } repeat
+ } ifelse
+ closepath
+ /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def
+ /LPutPos {
+ LPutVar /d ED /h ED
+ /AngleB ED /AngleA ED
+ /r ED /y0 ED /x0 ED
+ t 1 le {
+ r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC
+ }{t 2 lt {
+ /NAngle AngleB 180 add def r 2 t sub
+ h mul t 1 sub d mul add add AngleB PtoC
+ }{
+ t 3 lt {
+ r d add AngleB 3 t sub mul AngleA 2 t sub
+ mul add dup 90 sub /NAngle ED PtoC
+ }{
+ /NAngle AngleA 180 add def
+ r 4 t sub d mul t 3 sub h mul add add AngleA PtoC
+ } ifelse
+ } ifelse
+ } ifelse
+ y0 add /Y ED x0 add /X ED
+ } def
+ /HPutPos { LPutPos } def
+ /VPutPos { LPutPos } def
+} def
+%
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+%
+/LPutCoor {
+ NAngle
+ tx@Dict begin /NAngle ED end
+ gsave
+ CM STV
+ CP Y sub neg exch X sub neg exch moveto
+ setmatrix CP
+ grestore
+} def
+%
+/LPut {
+ tx@NodeDict /LPutPos known
+ { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse
+ LPutCoor
+} def
+%
+/HPutAdjust {
+ Sin Cos mul 0 eq
+ { 0 }
+ { d Cos mul Sin div flag not { neg } if
+ h Cos mul Sin div flag { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { r add neg }{ l add } ifelse
+ X add /X ED
+} def
+%
+/VPutAdjust {
+ Sin Cos mul
+ 0 eq
+ { 0 }
+ { l Sin mul Cos div flag { neg } if
+ r Sin mul Cos div flag not { neg } if
+ 2 copy gt { pop } { exch pop } ifelse
+ } ifelse
+ s add flag { d add } { h add neg } ifelse
+ Y add /Y ED
+} def
+%
+%
+end
+%
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-math.pro 0 0
+% -*- Mode: Postscript -*-
+% pst-math.pro --- PostScript header file pst-math.pro
+%
+% Author : Christophe JORSSEN
+% Author : Herbert Voß <hvoss@tug.org>
+% Created the : Sat 20 March 2004
+% Last Mod : $Date: 2010/10/02 $
+% Version : 0.62 $
+%
+/PI 3.14159265359 def
+/ENeperian 2.71828182846 def
+%
+/DegToRad {PI mul 180 div} bind def
+/RadToDeg {180 mul PI div} bind def
+%
+/COS {RadToDeg cos} bind def
+/SIN {RadToDeg sin} bind def
+/TAN {dup SIN exch COS Div} bind def
+/tan {dup sin exch cos Div} bind def
+/ATAN {neg -1 atan 180 sub DegToRad} bind def
+/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
+/acos {dup dup mul neg 1 add sqrt exch atan} bind def
+/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
+/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
+%
+/EXP {ENeperian exch exp} bind def
+%
+/COSH {dup EXP exch neg EXP add 2 div} bind def
+/SINH {dup EXP exch neg EXP sub 2 div} bind def
+/TANH {dup SINH exch COSH div} bind def
+/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
+/ASINH {dup dup mul 1 add sqrt add ln} bind def
+/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
+%
+%/SINC {dup SIN exch Div} bind def
+/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def
+
+/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
+%
+/GAMMA { 2 dict begin % hv 2007-08-30
+ /z exch def
+ 1.000000000190015 % p(0)
+ 0 1 5 { % on stack is 0 1 2 3 4 5
+ dup % n-1 n-1
+ [ 76.18009172947146
+ -86.50532032941677
+ 24.0140982483091
+ -1.231739572450155
+ 0.1208650973866179E-2
+ -0.5395239384953E-5 ] exch get exch % p(n) n-1
+ 1 add z add div % p(n)/(z+n)
+ add % build the sum
+ } for
+ Pi 2 mul sqrt z div mul
+ z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul
+ end } bind def
+%
+/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
+ 0 1 5 {
+ [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
+ .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
+ 4 -1 roll 1 add dup 5 1 roll div add} for
+ 4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
+/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
+%
+/HORNER {aload length
+ dup 2 add -1 roll
+ exch 1 sub {
+ dup 4 1 roll
+ mul add exch
+ } repeat
+ pop
+} bind def
+%
+/BESSEL_J0 {dup abs 8 lt {
+ dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
+ exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
+ Div}
+ {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index COS mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul}
+ ifelse} bind def
+%
+/BESSEL_Y0 {dup 8 lt {
+ dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
+ exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
+ Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
+ {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup
+ [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
+ 3 index SIN mul
+ exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+/BESSEL_J1 {dup abs 8 lt {
+ dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
+ exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
+ Div}
+ {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index COS mul
+ exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul}
+ ifelse} bind def
+%
+/BESSEL_Y1 {dup 8 lt {
+ dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
+ exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
+ Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
+ {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup
+ [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
+ 3 index SIN mul
+ exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
+ 4 -1 roll COS mul 3 -1 roll mul add mul}
+ ifelse} bind def
+%
+% En cours...
+/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
+ exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
+ mul 3 -1 roll mul 2 index sub pstack} for
+ } ifelse } ifelse } bind def
+%
+/SIMPSON { 1 dict begin %% on stack a b var f ierr Dominik Rodriguez
+ 3 index 5 index sub % compute h
+ 1 % a b var f ierr h n
+ 4 index 7 index def 3 index exec % a b var f ierr h n f(a)
+ 5 index 7 index def 4 index exec add % a b var f ierr h n f(a)+f(b)
+ 5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
+ exch 1 index 4 mul add 0 % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
+ { % a b var f ierr h n old Estim NbLoop
+ 5 -1 roll 2 div dup 6 1 roll % h<-h/2
+ 5 -1 roll 2 mul 5 1 roll % n<-2n
+ % a b var f ierr h n old Estim NbLoop h
+ 2 div 10 index add 0 % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
+ 5 index {
+ 1 index 10 index exch def 8 index exec add exch 6 index add exch
+ } repeat % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
+ exch pop % a b var f ierr h n old Estim NbLoop New
+ 2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
+ 4 -1 roll 2 mul 1 index sub 4 1 roll % a b var f ierr h n Estim NbLoop New Diff
+ exch 4 1 roll % a b var f ierr h n old Estim NbLoop Diff
+ 5 index 6 div mul abs 6 index lt { exit } if
+ 1 add dup 9 eq { exit } if
+ } loop % a b var f ierr h n old Estim NbLoop
+ exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
+end
+} def
+% ------------------------------------ math stuff ----------------------------------
+%
+% Matrix A in arrays of rows A[[row1][row2]...]
+% with [row1]=[a11 a12 ... b1]
+% returns on stack solution vector X=[x1 x2 ... xn]
+/SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b)
+ 10 dict begin % hold all ocal
+ /A exch def
+ /Rows A length def % Rows = number of rows
+ /Cols A 0 get length def % Cols = number of columns
+ /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1]
+ /col 0 def
+ /row 0 def
+ /PR Rows array def % PR[c] = pivot row for row row
+ { % starts the loop, find pivot entry in row r
+ col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit
+ /pRow row def % pRow = pivot row
+ /max A row get col get abs def % get A[row[col]], first A[0,0]
+ row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1
+ /j exch def % index counter
+ /x A j get col get abs def % get A[j[r]]
+ x max gt { % x>max, then save position
+ /pRow j def
+ /max x def
+ } if
+ } for % now we have the row with biggest A[0,1]
+ % with pRow = the pivot row
+ max 0 gt { % swap entries pRow and row in i
+ /tmp Index row get def
+ Index row Index pRow get put
+ Index pRow tmp put % and columns pRow and row in A
+ /tmp A row get def
+ A row A pRow get put
+ A pRow tmp put % pivot
+ /row0 A row get def % the pivoting row
+ /p0 row0 col get def % the pivot value
+ row 1 add 1 Rows 1 sub { % start for loop
+ /j exch def
+ /c1 A j get def
+ /p c1 col get p0 div def
+ c1 col p put % subtract (p1/p0)*row[i] from row[j]
+ col 1 add 1 Cols 1 sub { % start for loop
+ /i exch def
+ c1 dup i exch % c1 i c1
+ i get row0 i get p mul sub put
+ } for
+ } for
+ PR row col put
+ /col col 1 add def
+ /row row 1 add def
+ }{ % all zero entries
+ /row row 1 add def % continue loop with same row
+ } ifelse
+ } loop
+ /X A def % solution vector
+ A Rows 1 sub get dup
+ Cols 1 sub get exch
+ Cols 2 sub get div
+ X Rows 1 sub 3 -1 roll put % X[n]
+ Rows 2 sub -1 0 { % for loop to calculate X[i]
+ /xi exch def % current index
+ A xi get % i-th row
+ /Axi exch def
+ /sum 0 def
+ Cols 2 sub -1 xi 1 add {
+ /n exch def
+ /sum sum Axi n get X n get mul add def
+ } for
+ Axi Cols 1 sub get % b=Axi[Cols-1]
+ sum sub % b-sum
+ Axi xi get div % b-sum / Axi[xi]
+ X xi 3 -1 roll put % X[xi]
+ } for
+ X
+ end
+} def
+%
+/c@_0 2.515517 def
+/c@_1 0.802853 def
+/c@_2 0.010328 def
+/d@_1 1.432788 def
+/d@_2 0.189269 def
+/d@_3 0.001308 def
+/norminv {
+ 5 dict begin
+ neg 1 add 1 exch div ln 2 mul sqrt
+ /t exch def
+ /t2 t dup mul def
+ /t3 t2 t mul def
+ c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add
+ d@_2 t2 mul add d@_3 t3 mul add div neg t add
+ end
+} def
+%end{norminv Michael Sharpe}
+%
+%
+% END pst-math.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-3d.pro 0 0
+%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
+% PostScript prologue for pst-3d.tex.
+% Version 0.01, 2010/01/01
+%
+/tx@3Ddict 300 dict def
+tx@3Ddict begin
+%
+/SetMatrixThreeD {
+ dup sin /e ED cos /f ED
+ /p3 ED /p2 ED /p1 ED
+ p1 0 eq
+ { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
+ p3 p2 abs
+ }
+ { p2 0 eq
+ { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
+ p3 p1 abs
+ }
+ { p1 dup mul p2 dup mul add sqrt dup
+ p1 exch div /a ED
+ p2 exch div neg /b ED
+ p3 p1 a div
+ }
+ ifelse
+ }
+ ifelse
+ atan dup sin /c ED cos /d ED
+ /Matrix3D
+ [
+ b f mul c a mul e mul sub
+ a f mul c b mul e mul add
+ d e mul
+ b e mul neg c a mul f mul sub
+ a e mul neg c b mul f mul add
+ d f mul
+ ] def
+} def
+%
+/ProjThreeD {
+ /z ED /y ED /x ED
+ Matrix3D aload pop
+ z mul exch y mul add exch x mul add
+ 4 1 roll
+ z mul exch y mul add exch x mul add
+ exch
+} def
+%
+/SetMatrixEmbed {
+ SetMatrixThreeD
+ Matrix3D aload pop
+ /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
+ SetMatrixThreeD
+ [
+ Matrix3D aload pop
+ z3 mul exch z2 mul add exch z1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ Matrix3D aload pop
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ x3 mul exch x2 mul add exch x1 mul add
+ 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
+ x3 mul exch x2 mul add exch x1 mul add 4 1 roll
+ z3 mul exch z2 mul add exch z1 mul add
+ ]
+ concat
+} def
+%
+/TMSave {
+ tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
+ /TMatrix [ TMatrix CM ] cvx def
+} def
+%
+/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+%
+/TMChange {
+ TMSave
+ /cp [ currentpoint ] cvx def % ??? Check this later.
+ CM
+ CP T STV
+ CM matrix invertmatrix % Inv(M')
+ matrix concatmatrix % M Inv(M')
+ exch exec
+ concat cp moveto
+} def
+%
+end % of tx@3Ddict
+%%
+%% End of file `pst-3d.pro'.
+
+%%EndProcSet
+%%BeginProcSet: pstricks-add.pro 0 0
+%% $Id: pstricks-add.pro 328 2010-05-24 15:56:43Z herbert $
+% PostScript prologue for pstricks-add.tex.
+% Version 0.23, 2009/12/17
+%
+/tx@addDict 410 dict def tx@addDict begin
+%%
+realtime srand % set random generator
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GTriangle {
+ gsave
+ /mtrx CM def
+ /colorA ED /colorB ED /colorC ED % save the colors
+ /yA ED /xA ED % save the origin
+ xA yA translate
+ rotate % \psk@gangle
+ /yB ED /xB ED /yC ED /xC ED % save other coordinates
+ /ds [ % save data in a array
+ 0 0 0 colorA aload pop % fd x y xr xg xb
+ 0 xB xA sub yB yA sub colorB aload pop
+ 0 xC xA sub yC yA sub colorC aload pop
+% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD
+ ] def
+ newpath
+ <<
+ /ShadingType 4 % single Gouraud
+ /ColorSpace [ /DeviceRGB ]
+ /DataSource ds
+ >>
+ shfill
+ closepath
+ mtrx
+ setmatrix grestore} def
+%
+/RGBtoCMYK { % on stack r g b -> C M Y K
+ 3 dict begin
+ /Blue ED /Green ED /Red ED
+ 1 Red sub % Cyan
+ 1 Green sub % Magenta
+ 1 Blue sub % Yellow
+ 0 % Black
+ end
+} def
+%
+/CMYKtoGRAY { % on stack c m y k -> gray
+ exch 0.11 mul add
+ exch 0.59 mul add
+ exch 0.3 mul add
+ dup 1 gt { pop 1 } if
+ neg 1 add
+} def
+%
+/RGBtoGRAY { % on stack r g b -> gray
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+} def
+%
+/HSBtoGRAY {
+ 6 dict begin
+ /b exch def
+ /s exch def 6 mul dup cvi dup
+ /i exch def sub
+ /f exch def
+ /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
+ F i get { s mul neg 1 add b mul} forall
+ 0.11 mul
+ exch 0.59 mul add
+ exch 0.3 mul add
+ end
+} def
+%
+%% convertisseur longueur d'onde ->R,G,B Manuel Luque
+%% lambda max=780 nanometres
+%% lambda min=380 nanometres
+%% adaptation de :
+%% http://www.physics.sfasu.edu/astro/color.html
+%% www.efg2.com/lab
+%
+/Gamma 0.8 def
+/calculateRGB {
+ lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
+ lambda 380 ge {lambda 439 le {
+ /R {lambda 440 sub neg 440 380 sub div} def
+ /Red R factor mul Gamma exp def
+ /G 0 def
+ /Green G factor mul Gamma exp def
+ /B 1 def
+ /Blue B factor mul Gamma exp def} if
+ } if
+ lambda 440 ge { lambda 489 le {
+ /G {lambda 440 sub 490 440 sub div} def
+ /Green G factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /B 1 def
+ /Blue B factor mul Gamma exp def } if
+ } if
+ lambda 490 ge {lambda 509 le {
+ /B {lambda 510 sub neg 510 490 sub div} def
+ /Blue B factor mul Gamma exp def
+ /R 0 def /Red 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 510 ge {lambda 579 le {
+ /R {lambda 510 sub 580 510 sub div } def
+ /Red R factor mul Gamma exp def
+ /Blue 0 def
+ /G 1 def
+ /Green G factor mul Gamma exp def } if
+ } if
+ lambda 580 ge {lambda 644 le {
+ /G {lambda 645 sub neg 645 580 sub div } def
+ /Green G factor mul Gamma exp def
+ /Blue 0 def
+ /R 1 def
+ /Red R factor mul Gamma exp def } if
+ } if
+ lambda 645 ge { lambda 780 le {
+ /Red 1 factor mul Gamma exp def
+ /Blue 0 def
+ /Green 0 def } if
+ } if
+} def
+%
+/factor {
+ lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
+ lambda 420 ge {lambda 700 le { 1 } if } if
+ lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
+} def
+%
+/wavelengthToRGB { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+} def % now the colors are saved in Red Green Blue
+%
+/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ calculateRGB
+ Red Green Blue RGBtoGRAY
+} def % now the gray color is on the stack
+%
+/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
+ cvi /lambda exch def % no floating point here
+ gsave
+ calculateRGB Red Green Blue RGBtoCMYK
+ /Black ED /Yellow ED /Magenta ED /Cyan ED
+ grestore
+} def % now the colors are saved in Cyan Magenta Yellow Black
+%
+/axfill {
+ 8 dict begin
+ /xw exch def /nl exch def
+ /C1 exch def /y1 exch def/x1 exch def
+ /C0 exch def /y0 exch def/x0 exch def
+ << /ShadingType 2
+ /ColorSpace /DeviceRGB
+ /Coords [ x0 y0 x1 y1 ]
+ /EmulatorHints [ xw 2 div dup ]
+ /Function <<
+ /FunctionType 2
+ /Domain [0 1]
+ /C0 C0
+ /C1 C1
+ /N 1
+ >>
+ >> shfill
+ end
+} bind def
+%
+%/amplHand {.8} def
+%/dtHand 2 def
+/varHand { rand sin amplHand mul add } def
+/MovetoByHand { moveto } def
+%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def
+/LinetoByHand { 4 dict begin
+ /y1 ED /x1 ED
+ currentpoint /y0 ED /x0 ED
+ x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
+ 0 dtHand dEnd { dup
+ x1 x0 sub mul dEnd div x0 add varHand exch
+ y1 y0 sub mul dEnd div y0 add varHand lineto
+ } for
+% /x0 x1 def /y0 y1 def
+ end
+} def
+%
+end
+%
+% END pstricks-add.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-func.pro 0 0
+%% $Id: pst-func.pro 355 2010-06-21 10:02:44Z herbert $
+%%
+%% This is file `pst-func.pro',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-func'
+%%
+%% Herbert Voss <hvoss@tug.org>
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-func' is a PSTricks package to plot special math functions
+%%
+%%
+%% version 0.13 / 2010-06-21 Herbert Voss
+%
+/tx@FuncDict 100 dict def
+tx@FuncDict begin
+%
+/eps1 1.0e-05 def
+/eps2 1.0e-04 def
+/eps8 1.0e-08 def
+/Pi2 1.57079632679489661925640 def
+/CEuler 0.5772156649 def % Euler-Mascheroni constant
+%
+/factorial { % n on stack, returns n!
+ dup 0 eq { 1 }{
+ dup 1 gt { dup 1 sub factorial mul } if }
+ ifelse } def
+%
+/MoverN { % m n on stack, returns the binomial coefficient m over n
+ 2 dict begin
+ /n exch def /m exch def
+ n 0 eq { 1 }{
+ m n eq { 1 }{
+ m factorial n factorial m n sub factorial mul div } ifelse } ifelse
+ end
+} def
+%
+/Pascal [
+ [ 1 ] % 0
+ [ 1 1 ] % 1
+ [ 1 2 1 ] % 2
+ [ 1 3 3 1 ] % 3
+ [ 1 4 6 4 1 ] % 4
+ [ 1 5 10 10 5 1 ] % 5
+ [ 1 6 15 20 15 6 1 ] % 6
+ [ 1 7 21 35 35 21 7 1 ] % 7
+ [ 1 8 28 56 70 56 28 8 1 ] % 8
+ [ 1 9 36 84 126 126 84 36 9 1 ] % 9
+] def
+%
+/GetBezierCoor { % t on stack
+ 10 dict begin % hold all local
+ /t ED
+ /t1 1 t sub def % t1=1-t
+ /Coeff Pascal BezierType get def % get the coefficients
+ 0 0 % initial values for x y
+ BezierType -1 0 { % BezierType,...,2,1,0
+ /I ED % I=BezierType,...,2,1,0
+ /J BezierType I sub def % J=0,1,2,...,BezierType
+ /T t I exp Coeff J get mul def % coeff(J)*t^I
+ /T1 t1 J exp def % t1^J
+ Points I dup add 1 add get % y(2*I+1)
+ T mul T1 mul add % the y coordinate
+ exch % y x
+ Points I dup add get % x(2*I)
+ T mul T1 mul add % the x coordinate
+ exch % x y
+ } for % x y on stack
+ end
+} def
+%
+/BezierCurve { % on stack [ coors psk@plotpoints BezierType
+% 10 dict begin
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+ /tStart ED
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+} def
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+ /Sum arg def
+ /sign -1 def
+ /index 3 def
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+ Sum add /Sum exch def
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+ /index index 2 add def
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+} def
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+} def
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+ /index 2 def
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+ /sign sign neg def
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+} def
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+} def
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+%
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+ /Iter 0 def
+ {
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+ Nx func' /FS exch def % f'(Nx)
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+ } loop
+ Nx % the returned value ist the zero point
+} def
+
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+ exch 0 get % b a
+ neg exch neg % -a -b
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+} def
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+cleartomark
+{restore}if
+%%EndFont
+%%BeginFont: CMR8
+%!PS-AdobeFont-1.0: CMR8 003.002
+%%Title: CMR8
+%Version: 003.002
+%%CreationDate: Mon Jul 13 16:17:00 2009
+%%Creator: David M. Jones
+%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
+%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR8.
+% This Font Software is licensed under the SIL Open Font License, Version 1.1.
+% This license is in the accompanying file OFL.txt, and is also
+% available with a FAQ at: http://scripts.sil.org/OFL.
+%%EndComments
+FontDirectory/CMR8 known{/CMR8 findfont dup/UniqueID known{dup
+/UniqueID get 5000791 eq exch/FontType get 1 eq and}{pop false}ifelse
+{save true}{false}ifelse}{false}ifelse
+11 dict begin
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
+/FontName /CMR8 def
+/FontBBox {-36 -250 1070 750 }readonly def
+/UniqueID 5000791 def
+/PaintType 0 def
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.3 0.3 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.3 0.3 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 762 664 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
+a
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+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.2 0.2 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.2 0.2 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
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+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
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+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.2 0.2 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
+/arrowlength exch def 4 copy /y1 ED /x1 ED /y2 ED /x2 ED /Alpha y2
+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.2 0.2 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 762 664 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
+a
+tx@Dict begin /Func (-2.00+((0.3)*t)*(1/sqrt(1+((-2.00)-2*(-0.5))^2))|-0.5+((0.3)*t)*(1/sqrt(1+((-2.00)-2*(-0.5))^2))*((-2.00)-2*(-0.5))
+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.8 0.8 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha y2 y1 sub x2 x1 sub Atan
+def /ArrowPos 0. def /dArrowPos 0.5 abs def 1. cvi { /ArrowPos ArrowPos
+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
+mul add ArrowInside pop pop } repeat }{ /ArrowPos 0. def /dArrowPos
+1. 1 gt {1.0 1. 1.0 add div }{0.5 } ifelse def 1. cvi { /ArrowPos
+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.8 0.8 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
+@endspecial 762 664 a
+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
+a
+tx@Dict begin /Func (-1.7+((0.3)*t)*(1/sqrt(1+((-1.7)-2*(-0.5))^2))|-0.5+((0.3)*t)*(1/sqrt(1+((-1.7)-2*(-0.5))^2))*((-1.7)-2*(-0.5))
+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.9 0.9 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
+1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0
+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
+setlinejoin false NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ()
+length 0 gt { 1.5 2. CLW mul add dup 1.4 mul exch 0.4 mul neg add
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+y1 sub x2 x1 sub Atan def ArrowA x1 Alpha cos arrowlength mul add y1
+Alpha sin arrowlength mul add /n n 1 sub def n { 4 copy /y1 ED /x1
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+dArrowPos add def x1 Alpha cos ArrowPos mul add y1 Alpha sin ArrowPos
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+ArrowPos dArrowPos add def x2 x1 sub ArrowPos mul x1 add y2 y1 sub
+ArrowPos mul y1 add ArrowInside pop pop } repeat } ifelse pop pop Lineto
+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.9 0.9 setrgbcolor
+ 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore
+end
+
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+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
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+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.95 0.95
+ setrgbcolor /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale
+ false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul
+/a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg
+a neg rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow
+ } def /ArrowInside { } def [ tx@NodeDict begin tx@NodeDict /N@P1
+known { /N@P1 load GetCenter } { 0 0 } ifelse end tx@NodeDict begin
+tx@NodeDict /N@P0 known { /N@P0 load GetCenter } { 0 0 } ifelse end
+ /Lineto /lineto load def 0 setlinejoin false NArray n 0 eq not
+{ n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup
+1.4 mul exch 0.4 mul neg add /arrowlength exch def 4 copy /y1 ED /x1
+ED /y2 ED /x2 ED /Alpha y2 y1 sub x2 x1 sub Atan def ArrowA x1 Alpha
+cos arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub
+def n { 4 copy /y1 ED /x1 ED /y2 ED /x2 ED x1 y1 0.5 1 gt { /Alpha
+y2 y1 sub x2 x1 sub Atan def /ArrowPos 0. def /dArrowPos 0.5 abs
+def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x1 Alpha cos ArrowPos
+mul add y1 Alpha sin ArrowPos mul add ArrowInside pop pop } repeat
+}{ /ArrowPos 0. def /dArrowPos 1. 1 gt {1.0 1. 1.0 add div }{0.5 }
+ifelse def 1. cvi { /ArrowPos ArrowPos dArrowPos add def x2 x1 sub
+ArrowPos mul x1 add y2 y1 sub ArrowPos mul y1 add ArrowInside pop pop
+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
+n { Lineto } repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave
+0.8 SLW 1 0.95 0.95 setrgbcolor 1. .setopacityalpha 0 setlinejoin
+0 setlinecap stroke grestore end
+
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+tx@Dict begin /t0 0 def /t1 1 def t1 t0 sub end 1 div /dt exch def
+ 762 664 a 762 664
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+) AlgParser cvx def end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow
+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.95 0.95
+ setrgbcolor /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale
+ false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul dup /h ED mul
+/a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg
+a neg rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow
+ } def /ArrowInside { } def [ tx@NodeDict begin tx@NodeDict /N@P1
+known { /N@P1 load GetCenter } { 0 0 } ifelse end tx@NodeDict begin
+tx@NodeDict /N@P0 known { /N@P0 load GetCenter } { 0 0 } ifelse end
+ /Lineto /lineto load def 0 setlinejoin false NArray n 0 eq not
+{ n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup
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+cos arrowlength mul add y1 Alpha sin arrowlength mul add /n n 1 sub
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+} repeat } ifelse pop pop Lineto } repeat }{ ArrowA /n n 2 sub def
+n { Lineto } repeat } ifelse CP 4 2 roll ArrowB L pop pop } if gsave
+0.8 SLW 1 0.95 0.95 setrgbcolor 1. .setopacityalpha 0 setlinejoin
+0 setlinecap stroke grestore end
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+) AlgParser cvx def end
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+tx@Dict begin tx@NodeDict begin { /t 0 dt 0 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P0 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a 762 664 a
+tx@Dict begin tx@NodeDict begin { /t 0 dt 1 mul add def Func 28.5
+mul exch 28.5 mul exch } false /N@P1 10 {InitPnode } /NodeScale {}
+def NewNode end end
+ 762 664 a @beginspecial
+@setspecial
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+1. 1. scale false 0.4 1.4 1.5 2. CLW mul add dup 2 div /w ED mul
+dup /h ED mul /a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0
+0 L w h L w neg a neg rlineto gsave fill grestore grestore 0 h a sub
+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.95 0.95
+ setrgbcolor /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale
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+/a ED { 0 h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg
+a neg rlineto gsave fill grestore grestore 0 h a sub moveto EndArrow
+ } def /ArrowInside { } def [ tx@NodeDict begin tx@NodeDict /N@P1
+known { /N@P1 load GetCenter } { 0 0 } ifelse end tx@NodeDict begin
+tx@NodeDict /N@P0 known { /N@P0 load GetCenter } { 0 0 } ifelse end
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+{ n 1 eq { 0 0 /n 2 def } if () length 0 gt { 1.5 2. CLW mul add dup
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
+2 roll ArrowB L pop pop } if gsave 0.8 SLW 1 0.4 0.4 setrgbcolor
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+) AlgParser cvx def end
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+def NewNode end end
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+moveto EndArrow } def /ArrowInside { } def 0.8 SLW 1 0.6 0.6 setrgbcolor
+ /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.4
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+ 762 664 a @beginspecial
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
+load GetCenter } { 0 0 } ifelse end /Lineto /lineto load def 0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+def NewNode end end
+ 762 664 a @beginspecial
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+h T 1 -1 scale } if gsave w neg h moveto 0 0 L w h L w neg a neg rlineto
+gsave fill grestore grestore 0 h a sub moveto EndArrow } def /ArrowInside
+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+) AlgParser cvx def end
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+{ } def [ tx@NodeDict begin tx@NodeDict /N@P1 known { /N@P1 load GetCenter
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+} repeat }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse CP 4
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+} { 0 0 } ifelse end tx@NodeDict begin tx@NodeDict /N@P0 known { /N@P0
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diff --git a/info/pstricks_calcnotes/README b/info/pstricks_calcnotes/README
new file mode 100644
index 0000000000..41cc0adf3d
--- /dev/null
+++ b/info/pstricks_calcnotes/README
@@ -0,0 +1,11 @@
+This package presents three applications of PSTricks for making LaTeX lecture notes in
+Calculus.
+
+Application 1: Drawing approximations to the area under a graph by rectangles.
+Application 2: Drawing the vector field of an ordinary differential equation of order one.
+ (The remarks on this application give a way of coloring arrows properly for a vector field.)
+Application 3: Drawing partitions of a simply connected plane domain.
+ (There is a modified version of this application: AppThreePDF.pdf or AppThreePS.ps.)
+
+Author: Le Phuong Quan
+License: lppl
diff --git a/info/pstricks_calcnotes/ThreeAppsPDF.pdf b/info/pstricks_calcnotes/ThreeAppsPDF.pdf
new file mode 100644
index 0000000000..cbca59039f
--- /dev/null
+++ b/info/pstricks_calcnotes/ThreeAppsPDF.pdf
Binary files differ