diff options
author | Karl Berry <karl@freefriends.org> | 2009-11-13 14:30:47 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2009-11-13 14:30:47 +0000 |
commit | 6b6e76c3af4749246c999e2c6c6166a437c5d9cb (patch) | |
tree | c4b3f869163634e91c31c7961f3e2d028d462d38 /Master/texmf-dist | |
parent | ad927497ce54afc88641e38d368c1130a198f40a (diff) |
new pstricks package pst-knot 0.2 (12nov09)
git-svn-id: svn://tug.org/texlive/trunk@16000 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist')
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-knot/Changes | 10 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-knot/README | 12 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.bib | 141 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.pdf | bin | 0 -> 66578 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.tex | 148 | ||||
-rw-r--r-- | Master/texmf-dist/dvips/pst-knot/pst-psm.pro | 1815 | ||||
-rw-r--r-- | Master/texmf-dist/source/generic/pst-knot/Makefile | 70 | ||||
-rw-r--r-- | Master/texmf-dist/tex/generic/pst-knot/pst-knot.tex | 65 | ||||
-rw-r--r-- | Master/texmf-dist/tex/latex/pst-knot/pst-knot.sty | 8 |
9 files changed, 2269 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-knot/Changes b/Master/texmf-dist/doc/generic/pst-knot/Changes new file mode 100644 index 00000000000..c3b8c07cf62 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-knot/Changes @@ -0,0 +1,10 @@ +..... pst-knot.tex +0.01 2009-11-07 initial version + +..... pst-knot.pro +0.01 2009-11-07 initial version + +..... pst-fun.sty + 2009-11-07 first version + + diff --git a/Master/texmf-dist/doc/generic/pst-knot/README b/Master/texmf-dist/doc/generic/pst-knot/README new file mode 100644 index 00000000000..bdb06be8c2c --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-knot/README @@ -0,0 +1,12 @@ +pst-knot: plotting special knots + +Save the files pst-knot.sty|tex in a directory, which is part of your +local TeX tree. The pro file should go into $TEXMF/dvips/pstricks/ +Then do not forget to run texhash to update this tree. +For more information see the documentation of your LATEX distribution +on installing packages into your local TeX system or read the +TeX Frequently Asked Questions: +(http://www.tex.ac.uk/cgi-bin/texfaq2html?label=instpackages). + +PSTricks is PostScript Tricks, the documentation cannot be run +with pdftex, use the sequence latex->dvips->ps2pdf.
\ No newline at end of file diff --git a/Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.bib b/Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.bib new file mode 100644 index 00000000000..aa2a55a632f --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.bib @@ -0,0 +1,141 @@ +%% -*-bibtex-*- +@STRING{tugboat = {TUGboat} } +@STRING{beiprogramm = {{\TeX}-Beiprogramm} } +@STRING{bretter = {Bretter, die die Welt bedeuten} } +@STRING{dtk = {{D}ie {\TeX}nische {K}om{\"o}die} } +@STRING{editorial = {Editorial} } +@STRING{fremdebuehne = {Von fremden B{\"u}hnen} } +@STRING{fundus = {Aus dem Fundus} } +@STRING{hinterbuehne = {Hinter der B{\"u}hne} } +@STRING{leserbrief = {Leserbrief(e)} } +@STRING{magazin = {Magazin} } +@STRING{rezension = {Rezensionen} } +@STRING{schonimmer = {Was Sie schon immer {\"u}ber {\TeX} wissen wollten \dots} } +@STRING{theaterkasse = {Von der Theaterkasse} } +@STRING{theatertage = {{\TeX}-Theatertage} } + +@Article{ dtk02.2:jackson.voss:plot-funktionen, + author = {Laura E. Jackson and Herbert Vo{\ss}}, + title = {Die {P}lot-{F}unktionen von {\texttt{pst-plot}}}, + journal = dtk, + year = 2002, + volume = {2/02}, + altvolume = 2, + altnumber = 14, + month = jun, + pages = {27--34}, + annote = bretter, + keywords = {}, + abstract = { Im letzten Heft wurden die mathematischen Funktionen von + \PS~im Zusammenhang mit dem {\LaTeX}-Paket + \texttt{pst-plot} zum Zeichnen von Funktionen beschrieben + und durch Beispiele erl{\"a}utert. In diesem Teil werden + die bislang nur erw{\"a}hnten Plot-Funktionen f{\"u}r + externe Daten behandelt. } +} + +@Article{ dtk02.1:voss:mathematischen, + author = {Herbert Vo{\ss}}, + title = {Die mathematischen {F}unktionen von {P}ost{S}cript}, + journal = dtk, + year = 2002, + volume = {1/02}, + altvolume = 1, + altnumber = 14, + month = mar, + pages = {}, + annote = bretter, + keywords = {}, + abstract = { \PS, faktisch genauso alt wie {\TeX}, ist im + Verh{\"a}ltnis dazu allgemein noch weniger bekannt, wenn es + darum geht zu beurteilen, was es denn nun im eigentlichen + Sinne ist. Au{\ss}erdem wird h{\"a}ufig vergessen, dass + sich mit den \PS-Funktionen viele Dinge erledigen lassen, + bei denen sonst auf externe Programme zur{\"u}ckgegriffen + wird. Dies wird im Folgenden f{\"u}r die mathematischen + Funktionen im Zusammenhang mit dem Paket \texttt{pst-plot} + gezeigt. } +} + +@Book{companion, + author = {Michel Goosens and Frank Mittelbach and Sebastian Rahtz and Denis Roegel and Herbert Vo{\ss}}, + title = {The {\LaTeX} {G}raphics {C}ompanion}, + publisher = {{Addison-Wesley Publishing Company}}, + edition = 2, + year = {2007}, + address = {Reading, Mass.} +} + +@Book{PSTricks2, + author = {Herbert Vo\ss}, + title = {\texttt{PSTricks} -- {G}rafik f\"ur \TeX{} und \LaTeX}, + edition = {4.}, + publisher = {DANTE -- Lehmanns}, + year = {2007}, + address = {Heidelberg/Hamburg} +} + +@Book{LaTeXRef, + author = {Herbert Vo\ss}, + title = {\LaTeX\ Referenz}, + edition = {1.}, + publisher = {DANTE -- Lehmanns}, + year = {2007}, + address = {Heidelberg/Hamburg} +} +@Article{girou:01:, + author = {Denis Girou}, + title = {Pr\'esentation de {PST}ricks}, + journal = {Cahier {GUT}enberg}, + year = 1994, + volume = {16}, + month = apr, + pages = {21-70} +} + +@Article{girou:02:, + author = {{Timothy van} Zandt and Denis Girou}, + title = {Inside {PST}ricks}, + journal = TUGboat, + year = 1994, + volume = {15}, + month = sep, + pages = {239-246} +} + +@Book{PostScript, + Author = {Kollock, Nikolai G.}, + Title = {Post{S}cript richtig eingesetzt: vom {K}onzept zum + praktischen {E}insatz}, + Publisher = {IWT}, + Address = {Vaterstetten}, + year = 1989, +} + +@Manual{pstricks, + Title = {PSTricks - {\PS} macros for generic {\TeX}}, + Author = {{Timothy van} Zandt}, + Organization = {}, + Address = {\url{http://www.tug.org/application/PSTricks}}, + Note = {}, + year = 1993 +} + +@Manual{pst-plot, + Title = {\texttt{pst-plot}: Plotting two dimensional functions and data}, + Author = {{Timothy van} Zandt}, + Organization = {}, + Address = {\url{CTAN:graphics/pstricks/generic/pst-plot.tex}}, + Note = {}, + year = 1999 +} + +@Manual{multido, + Title = {\texttt{multido.tex} - a loop macro, that supports fixed-point addition}, + Author = {{Timothy van} Zandt}, + Organization = {}, + Address = {\url{CTAN:/graphics/pstricks/generic/multido.tex}}, + Note = {}, + year = 1997 +} + diff --git a/Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.pdf b/Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.pdf Binary files differnew file mode 100644 index 00000000000..252505e68a8 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.pdf diff --git a/Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.tex b/Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.tex new file mode 100644 index 00000000000..3a96773f79d --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-knot/pst-knot-doc.tex @@ -0,0 +1,148 @@ +%% $Id: pst-knot-doc.tex 137 2009-10-08 18:15:14Z herbert $ +\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false, + smallheadings, headexclude,footexclude,oneside]{pst-doc} +\usepackage[utf8]{inputenc} +\usepackage{pst-knot} +\let\pstKnotFV\fileversion +\renewcommand\bgImage{% +\begin{pspicture}(-2,-2)(2,2) + \psKnot[knotscale=2,linewidth=5pt,linecolor=blue](0,0){5-1} +\end{pspicture} +} +\lstset{pos=t,wide=false,language=PSTricks, + morekeywords={psKnot},basicstyle=\footnotesize\ttfamily} +% +\begin{document} + +\title{\texttt{pst-knot}} +\subtitle{Plotting special knots; v.\pstKnotFV} +\author{Herbert Vo\ss} +\docauthor{} +\date{\today} +\maketitle + +\tableofcontents + +\section{introduction} +This is the very first try of drawing knots. The package uses the \PS\ +subroutines from the file \LFile{psMath.pro} from Matthias Buch-Kromann.) +Currentlx there is only one macro with two mandatory arguments, the origin +of the image and the knot type. The following list shows all available knot types. + +\begin{BDef} +\Lcs{psKnot}\OptArgs\Largr{\CAny}\Largb{knot type} +\end{BDef} + + +\begin{LTXexample} +\begin{pspicture}[showgrid=true](-2,-2)(2,2) + \psKnot[linewidth=3pt,linecolor=red](0,0){0-1} +\end{pspicture} +\end{LTXexample} + +\begin{LTXexample}[pos=t] +\begin{pspicture}[showgrid=true](-2,-2)(8,2) + \psKnot[linewidth=3pt,linecolor=red](0,0){3-1} + \psKnot[linewidth=3pt,linecolor=blue](4,0){4-1} +\end{pspicture} +\end{LTXexample} + +\begin{LTXexample}[pos=t] +\begin{pspicture}(-2,-2)(8,2) + \psKnot[linewidth=3pt,linecolor=blue](0,0){5-1} + \psKnot[linewidth=3pt,linecolor=blue](4,0){5-2} +\end{pspicture} +\end{LTXexample} + +\begin{LTXexample}[pos=t] +\begin{pspicture}(-2,-2)(10,2) + \psKnot[linewidth=3pt,linecolor=blue](0,0){6-1} + \psKnot[linewidth=3pt,linecolor=blue](4,0){6-2} + \psKnot[linewidth=3pt,linecolor=blue](8,0){6-3} +\end{pspicture} +\end{LTXexample} + +\begin{LTXexample} +\begin{pspicture}(-2,-2)(10,2) + \psKnot[linewidth=3pt,linecolor=red](0,0){7-1} + \psKnot[linewidth=3pt,linecolor=blue](4,0){7-2} + \psKnot[linewidth=3pt,linecolor=green](8,0){7-3} +\end{pspicture} +\end{LTXexample} + +\begin{LTXexample} +\begin{pspicture}(-2,-2)(10,2) + \psKnot[linewidth=3pt,linecolor=red](0,0){7-4} + \psKnot[linewidth=3pt,linecolor=green](4,0){7-5} + \psKnot[linewidth=3pt,linecolor=blue](8,0){7-6} +\end{pspicture} +\end{LTXexample} + +\begin{LTXexample} +\begin{pspicture}[showgrid=true](-2,-2)(2,2) + \psKnot[linewidth=3pt,linecolor=blue](0,0){7-7} +\end{pspicture} +\end{LTXexample} + +\section{Special settings} +There exists three special optional arguments for the macro \Lcs{psKnot}. + +\subsection{Scaling} +The image can be scaled with \Lkeyword{scale}, which can take one or two +values for x and y scaling. For only one value it is scaled for x and y +with the same value. The default is 1 1. + +\begin{LTXexample}[pos=t] +\begin{pspicture}(-4,-4)(4,4) + \psKnot[linewidth=5pt,linecolor=blue,knotscale=2](0,0){6-1} +\end{pspicture} +\end{LTXexample} + +\subsection{Border color} +The background color of the border can be controlled by \Lkeyword{knotbgcolor} +with only a numerical value of $[0..1]$ for a grayscale color. It makes +only sense for a colored background to get the same color for the crossing. + +\begin{LTXexample}[pos=t] +\begin{pspicture}(-2,-2)(6,2) + \psframe[fillcolor=black!20,fillstyle=solid](-2,-2)(6,2) + \psKnot[linewidth=5pt,linecolor=red!50](0,0){7-4} + \psKnot[linewidth=5pt,linecolor=red!50, + knotbgcolor=0.8](4,0){7-4} +\end{pspicture} +\end{LTXexample} + +Pay attention that black!20 is the same as 0,8 of gray. + +\subsection{Border width} +The width of the border is controlled by the keyword \Lkeyword{knotborder} and +it is preset to 2 as a factor to the current linewidth. +It must at least be the currentlinewidth (1.0). + +\begin{LTXexample}[pos=t] +\begin{pspicture}(-2,-2)(6,2) + \psKnot[linewidth=3pt,linecolor=cyan!60](0,0){6-3} + \psKnot[linewidth=3pt,linecolor=red!50, + knotborder=5](4,0){6-3} +\end{pspicture} +\end{LTXexample} + + +\clearpage +\section{List of all optional arguments for \nxLPack{pst-knot}} + +\xkvview{family=pst-knot,columns={key,type,default}} + + +\bgroup +\raggedright +\nocite{*} +\bibliographystyle{plain} +\bibliography{\jobname} +\egroup + +\printindex + +\end{document} + + diff --git a/Master/texmf-dist/dvips/pst-knot/pst-psm.pro b/Master/texmf-dist/dvips/pst-knot/pst-psm.pro new file mode 100644 index 00000000000..de68cc2a60d --- /dev/null +++ b/Master/texmf-dist/dvips/pst-knot/pst-psm.pro @@ -0,0 +1,1815 @@ +%% psMath.pro (c) Aug 28, 1996 Matthias T. Kromann +%% version 0.01 2009/11/07 changes to knot subroutines +%% (hv) +/tx@KnotDict 11 dict def +tx@KnotDict begin +/PSMsysd 200 dict def +/PSMusrd 200 dict def +/PSMtexd 200 dict def +/PSMinit { + PSMtexd begin + PSMsysd begin + PSMusrd begin + line-std + Times setfontfamily 10 setfontsize 0 setfontstyle setupfont + -1 0 TeXsetfill +} def +/PSMclose { end end end } def +/PSMreload { PSMclose (psm.pro) run PSMinit } def +/PSMni { (not implemented) = } def +% ----------------------------------------------------------------- +PSMsysd begin + /bdef {bind def} bind def + /xdef {exch def} bdef + /lidef { + 0 begin /ini xdef /vars xdef cvlit dup /value xdef + length 3 add array /obj xdef + /obj load 0 vars dict begin ini currentdict end put + /obj load 1 {begin} putinterval + /obj load 2 /value load putinterval + /obj load dup length 1 sub {end} putinterval + /obj load cvx end def + } def + /lidef load 0 4 dict put + /ldef { {} lidef } def + /pt {1 mul} def + /mm {2.845 mul} def + /cm {28.45 mul} def + /inch {72.27 mul} def + /un {1 mm mul} def + /black { 0 setgray } def + /white { 1 setgray } def + /gray { 0.5 setgray } def + /darkgray { 0.25 setgray } def + /lightgray { 0.75 setgray } def + /red { 1 0 0 setrgbcolor } def + /green { 0 1 0 setrgbcolor } def + /blue { 0 0 1 setrgbcolor } def + /cyan { 0 1 1 setrgbcolor } def + /magenta { 1 0 1 setrgbcolor } def + /yellow { 1 1 0 setrgbcolor } def + /gold { 0.93 0.93 0.4 setrgbcolor } def + /thin { 0.5 setlinewidth } def + /medium { 1 setlinewidth } def + /thick { 2 setlinewidth } def + /lw-std { thin } def + /lw-dec { currentlinewidth 2 div setlinewidth } def + /lw-inc { currentlinewidth 2 mul setlinewidth } def + /nodash { [] 0 setdash } def + /dash { [2 2] 0 setdash } def + /line-std { lw-std nodash 0 setgray } def +% ----------------------------------------------------------------- +PSMtexd begin + /ISOfont { % font ISOfont + /isofont xdef /font xdef + font findfont + dup length dict begin + { 1 index /FID ne {def} {pop pop} ifelse + } forall + /Encoding ISOLatin1Encoding def + currentdict + end + isofont exch definefont pop + } 2 ldef + /Times-Roman /Times-Roman-ISOLatin1 ISOfont + /Times-Bold /Times-Bold-ISOLatin1 ISOfont + /Times-Italic /Times-Italic-ISOLatin1 ISOfont + /Times-BoldItalic /Times-BoldItalic-ISOLatin1 ISOfont + /Times [(ptm) /Times-Roman-ISOLatin1 /Times-Bold-ISOLatin1 + /Times-Italic-ISOLatin1 /Times-BoldItalic-ISOLatin1] def + /Helvetica /Helvetica-ISOLatin1 ISOfont + /Helvetica-Bold /Helvetica-Bold-ISOLatin1 ISOfont + /Helvetica-Oblique /Helvetica-Oblique-ISOLatin1 ISOfont + /Helvetica-BoldOblique /Helvetica-BoldOblique-ISOLatin1 ISOfont + /Helvetica [(phv) /Helvetica-ISOLatin1 /Helvetica-Bold-ISOLatin1 + /Helvetica-Oblique-ISOLatin1 /Helvetica-BoldOblique-ISOLatin1] def + /Symbol [(psy) /Symbol /Symbol /Symbol /Symbol] def + /getfontfamily {PSMtexd /fontfamily get} def + /setfontfamily {PSMtexd /fontfamily 3 -1 roll put} def + /getfontsize {PSMtexd /fontsize get} def + /setfontsize {PSMtexd /fontsize 3 -1 roll put} def + /getfontstyle {PSMtexd /fontstyle get} def + /setfontstyle {PSMtexd /fontstyle 3 -1 roll put} def + /setupfont { + font 0 getfontfamily 0 get putinterval + font 3 getfontstyle 1 add 1000 mul fontsize cvi add + fontext cvs putinterval + PSMtexd font cvn known not { + PSMtexd font cvn getfontfamily getfontstyle 1 add get + findfont getfontsize scalefont put } if + font cvn cvx exec setfont + } 2 { /font 7 string def /fontext 4 string def } lidef +end +% ----------------------------------------------------------------- +/pi 3.1415926535 def +/sqr {dup mul} def +/sgn {dup 0 gt {pop 1} {0 lt {-1} {0} ifelse} ifelse} def +/min + { /B xdef /A xdef + A type /arraytype eq {/a A 0 get def} {/a A def} ifelse + B type /arraytype eq {/b B 0 get def} {/b B def} ifelse + a b gt {B} {A} ifelse + } 4 ldef + /max + { /B xdef /A xdef + A type /arraytype eq {/a A 0 get def} {/a A def} ifelse + B type /arraytype eq {/b B 0 get def} {/b B def} ifelse + a b gt {A} {B} ifelse + } 4 ldef +/acos {dup sqr 1 exch sub sqrt exch atan} def +/asin {dup sqr 1 exch sub sqrt atan} def +/extrema + { /fct xdef /t2 xdef /t1 xdef + /t t1 def /ft t1 fct def + 1/T t1 def /fT t1 fct def + t1 t2 t1 sub 200 div t2 + { /x xdef /fx x fct def + fx ft lt {/t x def /ft fx def} if + fx fT gt {/T x def /fT fx def} if + } for + t T + } 9 ldef +/p2r* + { /v xdef aload pop /phi xdef /r xdef + phi cos r mul phi sin r mul v astore + } 3 ldef +/p2r {2 array p2r*} def +/r2p* + { /v xdef aload pop /y xdef /x xdef + x x mul y y mul add sqrt y x atan v astore + } 3 ldef +/r2p {2 array r2p*} def +/rotpnt* + { /v xdef /angle xdef aload pop /y xdef /x xdef + angle cos x mul angle sin y mul sub + angle sin x mul angle cos y mul add v astore + } 4 ldef +/rotpnt {2 array rotpnt*} def +/p2l* + { /v xdef aload pop /qy xdef /qx xdef aload pop /py xdef /px xdef + /a py qy sub def /b qx px sub def + a b a qx mul b qy mul add v astore + } 7 ldef +/p2l {3 array p2l*} def +/l2p* + { /v xdef aload pop /c2 xdef /b2 xdef /a2 xdef + aload pop /c1 xdef /b1 xdef /a1 xdef + /det a1 b2 mul a2 b1 mul sub def + c1 b2 mul c2 b1 mul sub det div + a1 c2 mul a2 c1 mul sub det div + v astore + } 8 ldef +/l2p {2 array l2p*} def +/altitude* + { /r xdef /C xdef /B xdef /A xdef + A B l p2l* pop + A B v vsub* 90 v rotpnt* C v vadd* C m p2l* pop + l m r l2p* + } 7 {/v 2 array def /l 3 array def /m 3 array def} lidef +/altitude {2 array altitude*} def +/angle + { pnt2num /qy exch def /qx exch def + pnt2num /py exch def /px exch def + qy py sub qx px sub 2 copy abs exch abs add 0 eq + {pop pop -360} {atan} ifelse + } 4 ldef +/vaddsub* + { /addsub xdef /uv xdef /v xdef /u xdef /i 0 def + u {v i get addsub /i i 1 add def} forall + uv astore + } 5 ldef +/vadd* {{add} vaddsub*} def +/vadd {dup length array {add} vaddsub*} def +/vsub* {{sub} vaddsub*} def +/vsub {dup length array {sub} vaddsub*} def +/smuldiv* + { /muldiv xdef /As xdef /A xdef /s xdef + A {s muldiv} forall As astore + } 4 ldef +/smul* + { 3 1 roll dup type /arraytype eq not {exch} if + 3 -1 roll {mul} smuldiv*} def +/smul + { dup type /arraytype eq not {exch} if dup length array + {mul} smuldiv*} def +/sdiv* + { 3 1 roll dup type /arraytype eq not {exch} if + 3 -1 roll {div} smuldiv*} def +/sdiv + { dup type /arraytype eq not {exch} if dup length array + {div} smuldiv*} def +/norm {0 exch {dup mul add} forall sqrt} def +/ip + { /B xdef /A xdef /i 0 def + 0 A {B i get mul add /i i 1 add def} forall + } 3 ldef +/v2u* {exch dup norm 3 -1 roll sdiv*} def +/v2u {dup norm sdiv} def +/dist + { /B xdef /A xdef /i 0 def + 0 A {B i get sub dup mul add /i i 1 add def} forall sqrt + } 3 ldef +/cp* + { /AxB xdef + aload pop /b3 xdef /b2 xdef /b1 xdef + aload pop /a3 xdef /a2 xdef /a1 xdef + a2 b3 mul a3 b2 mul sub + a3 b1 mul a1 b3 mul sub + a1 b2 mul a2 b1 mul sub + AxB astore + } 7 ldef +/cp {3 array cp*} def +/tvec* + { /C xdef /B xdef /A xdef /t xdef /i 0 def + A { dup B i get exch sub t mul add + /i i 1 add def + } forall + C astore + } 5 ldef +/tvec {dup length array tvec*} def +/nullmatrix + {/n xdef /m xdef n {m array} repeat n array astore } 2 ldef +/mget {exch 3 1 roll get exch get} bdef +/mput {4 1 roll exch 4 1 roll get 3 1 roll put} bdef +/mstore + { /M xdef /i M length 1 sub def + M length {M i get astore pop /i i 1 sub def} repeat + } 2 ldef +/madd* + { /AB xdef /B xdef /A xdef + 0 1 A length 1 sub + {/i xdef A i get B i get AB i get vadd* pop} for AB + } 4 ldef +/madd + { /B xdef /A xdef A B A 0 get length B length nullmatrix madd* + } 2 ldef +/msub* + { /AB xdef /B xdef /A xdef + 0 1 A length 1 sub + {/i xdef A i get B i get AB i get vsub* pop} for AB + } 4 ldef +/msub + { /B xdef /A xdef A B A 0 get length B length nullmatrix msub* + } 2 ldef +/msmul* + { /Ms xdef dup type /arraytype eq {exch} if + /s xdef /M xdef /i 0 def + M {s Ms i get smul* pop /i i 1 add def} forall Ms + } 5 ldef +/msmul + { dup type /arraytype eq not {exch} if /M xdef + M M 0 get length M length nullmatrix msmul* + } 1 ldef +/msdiv* + { /Ms xdef dup type /arraytype eq {exch} if + /s xdef /M xdef /i 0 def + M {s Ms i get sdiv* pop /i i 1 add def} forall Ms + } 5 ldef +/msdiv + { dup type /arraytype eq not {exch} if /M xdef + M M 0 get length M length nullmatrix msdiv* + } 1 ldef +/mmul* + { /AB xdef /B xdef /A xdef + /m A 0 get length def /n A length def /r B length def + 0 1 r 1 sub + { /j xdef + 0 1 m 1 sub + { /i xdef 0 + 0 1 n 1 sub + { /k xdef A i k mget B k j mget mul add} for + } for + } for + AB mstore AB + } 9 ldef +/mmul + { /B xdef /A xdef A B A 0 get length B length nullmatrix mmul* + } 2 ldef +/mvmul* + { /Mv xdef /v xdef /M xdef + /m M 0 get length def /n M length def + 0 1 m 1 sub + { /i xdef 0 + 0 1 n 1 sub + { /j xdef M i j mget v j get mul add + } for + } for + Mv astore + } 7 ldef +/mvmul {exch dup 0 get length array exch 3 1 roll mvmul*} def +/minv {PSMni} def +/minvmul {PSMni} def +/mtrace + { /M xdef /i 0 def + 0 M {i get add /i i 1 add def} forall + } 2 ldef +/mtrans* + { /TM xdef /M xdef /m M 0 get length def /n M length def + 0 1 m 1 sub + { /i xdef + 0 1 n 1 sub {M i 3 -1 roll mget} for + } for + TM mstore TM + } 5 ldef +/mtrans {/M xdef M M length M 0 get length nullmatrix mtrans*} 1 ldef +/m2v {/M xdef [M {aload pop} forall]} 1 ldef +/v2mc {1 array astore} def +/v2mr + { dup length /n xdef {1 array astore} forall n array astore + } 1 ldef +/dot-size 1.5 def +/pnt2numx + { /n xdef n 1 sub index type exec + } 5 + { /integertype {} def /realtype {} def + /arraytype + { n -1 roll dup + 0 get type /arraytype eq + { 0 get aload pop} + { dup length 2 eq + { aload pop} { p 3D* aload pop} ifelse + } ifelse + n 1 add 2 roll + } def + /p 2 array def + } lidef +/pnt2num {1 pnt2numx} def +/pnt2vctx* + { /p xdef /n xdef n 1 sub index type exec + } 5 + { /integertype {n 1 add -2 roll p astore n 1 roll} def + /realtype {integertype} def + /arraytype + { n -1 roll dup + 0 get type /arraytype eq + { 0 get } + { dup length 2 eq {} {p 3D*} ifelse + } ifelse + aload pop p astore n 1 roll + } def + } lidef +/pnt2vctx {2 array pnt2vctx*} def +/pnt2vct* {1 exch pnt2vctx*} def +/pnt2vct {1 pnt2vctx} def +/-moveto /moveto load def +/-rmoveto /rmoveto load def +/-lineto /lineto load def +/-rlineto /rlineto load def +/-arc /arc load def +/-arcn /arcn load def +/-arcto /arcto load def +/-curveto /curveto load def +/-rcurveto /rcurveto load def +/Moveto {aload pop -moveto} def +/rMoveto {aload pop -rmoveto} def +/Lineto {aload pop -lineto} def +/rLineto {aload pop -rlineto} def +/moveto {pnt2num -moveto} def +/rmoveto {pnt2num -rmoveto} bdef +/lineto {pnt2num -lineto} bdef +/rlineto {pnt2num -rlineto} bdef +/line {pnt2num 3 pnt2numx 4 2 roll -moveto -lineto} def +/lines {dup 0 get moveto {lineto} forall} def +/xline + { /dB xdef /dA xdef B pnt2vct* pop A pnt2vct* pop + B A BA vsub* BA v2u* + dA neg A' smul* A A' vadd* Moveto + BA dB B' smul* B B' vadd* Lineto + } 9 + { /A 2 array def /B 2 array def /BA 2 array def + /A' 2 array def /B' 2 array def + } lidef +/arc {4 pnt2numx -arc} def +/arcn {4 pnt2numx -arcn} def +/curve + { 1 pnt2numx 3 pnt2numx 5 pnt2numx 7 pnt2numx + 8 -2 roll -moveto -curveto} def +/curveto {1 pnt2numx 3 pnt2numx 5 pnt2numx -curveto} def +/dotx {newpath pnt2num dot-size 0 360 -arc} def +/dot-bullet {gsave dotx fill grestore} def +/dot-circ {gsave dotx stroke grestore} def +/dot {dot-bullet} def +/perpsign + { /rsize xdef /B xdef /A xdef + B A v vsub* v v2u* rsize v smul* pop + v 90 h rotpnt* rsize sgn h smul* pop + A Moveto h rlineto v rlineto h -1 smul rlineto + closepath B lineto + } 5 {/v 2 array def /h 2 array def} lidef +/turtle-init {PSMsysd /turtle-angle 3 -1 roll put Moveto pendown} def +/pendown {PSMsysd /turtle-state {rlineto} put} def +/penup {PSMsysd /turtle-state {rmoveto} put} def +/fwd + { dup PSMsysd /turtle-angle get dup 3 1 roll cos mul + 3 1 roll sin mul PSMsysd /turtle-state get exec + } def +/bwd {neg fwd} def +/lht + { PSMsysd /turtle-angle get add PSMsysd /turtle-angle + 3 -1 roll put + } def +/rht {neg lht} def +/box + { pnt2num /by xdef /bx xdef pnt2num /ay xdef /ax xdef + ax ay -moveto ax by -lineto + bx by -lineto bx ay -lineto closepath + } 4 ldef +/circle {newpath 2 pnt2numx 0 360 -arc closepath} def +/ellipsearc + { newpath /a2 xdef /a1 xdef /yr xdef /xr xdef + pnt2num /oy xdef /ox xdef + /mtrx matrix currentmatrix def + ox oy translate xr yr scale 0 0 1 a1 a2 -arc + mtrx setmatrix + } 7 ldef +/ellipse {0 360 ellipsearc closepath} def +/arrow {currentlinewidth 3.5 mm 40 0.7 arrowx} def +/varrow {currentlinewidth 2.5 mm 40 1 arrowx} def +/arcarrow {currentlinewidth 3.5 mm 45 0.7 arcarrowx} def +/varcarrow {currentlinewidth 2.5 mm 40 1 arcarrowx} def +/sarcarrow {currentlinewidth 2 mm 45 0.7 arcarrowx} def +/arrowx + { /rhead xdef 2 div /a xdef /hlen xdef 2 div /lw xdef + head pnt2vct* pop tail pnt2vct* pop + head tail vsub r2p aload pop /dir xdef + /shaftl exch hlen rhead mul sub def + /wingsz hlen a cos div def + /lwing [wingsz dir 180 sub a sub] p2r head vadd def + /rwing [wingsz dir 180 sub a add] p2r head vadd def + /ltail [lw dir 90 add] p2r tail vadd def + /rtail [lw dir 90 sub] p2r tail vadd def + /lshaft [shaftl dir] p2r ltail vadd def + /rshaft [shaftl dir] p2r rtail vadd def + head Moveto lwing Lineto lshaft Lineto ltail Lineto + rtail Lineto rshaft Lineto rwing Lineto closepath + } 16 {/head 2 array def /tail 2 array def} lidef +/arcarrowx + { /rhead xdef 2 div /a xdef /hlen xdef 2 div /lw xdef + /ha xdef /ta xdef /r xdef O pnt2vct* pop + ta ha gt /clockw xdef + clockw {/hlen hlen neg def /lw lw neg def} if + /head [r ha] p2r O vadd def + /rheada 1 rhead add 0.5 mul def + /ang 90 hlen rheada mul r div 28.6479 mul add def + /wingsz hlen a cos div def + /iwing [wingsz ha ang sub a sub] p2r head vadd def + /owing [wingsz ha ang sub a add] p2r head vadd def + /shafta ha hlen rhead mul r div 57.29578 mul sub def + head Moveto iwing Lineto + O aload pop r lw sub shafta ta clockw {-arc} {-arcn} ifelse + O aload pop r lw add ta shafta clockw {-arcn} {-arc} ifelse + owing Lineto closepath + } 16 {/O 2 array def} lidef +/bboxray2p + { /phi xdef /P xdef + aload pop /ury xdef /urx xdef /lly xdef /llx xdef + /ray P [1 phi] p2r vadd P p2l def /P' P def + phi cos 0.05 gt {/P' ray [1 0 urx] l2p def} if + phi cos -0.05 lt {/P' ray [1 0 llx] l2p def} if + phi sin 0.05 gt {/P' P' ray [0 1 ury] l2p P closestne def} if + phi sin -0.05 lt {/P' P' ray [0 1 lly] l2p P closestne def} if + P' + } 9 ldef +/closestne + { /P xdef /P2 xdef /P1 xdef + /d1 P1 P dist def /d2 P2 P dist def + d1 0 eq + { P2 } + { d2 0 eq {P1} + {d1 d2 lt {P1} {P2} ifelse} ifelse + } ifelse + } 5 ldef +/cdbbox + { /cd xdef + /pnt cd 0 get def /lbl cd 1 get def + /bbox [lbl TeXbbox] def + /dy 3 def /dhx 5 def /dhy 3 def + /x pnt 0 get bbox 0 get bbox 2 get add 2 div sub def + /y pnt 1 get dy sub def + /bbox bbox [x dhx sub y dhy sub x dhx add y dhy add] vadd def + bbox [x y] + } 9 ldef +/cdarrowpts + { /cd2 xdef /cd1 xdef + /pnt1 cd1 0 get def /lbl1 cd1 1 get def + /pnt2 cd2 0 get def /lbl2 cd2 1 get def + /bbox1 cd1 cdbbox pop def + /bbox2 cd2 cdbbox pop def + /angle pnt2 pnt1 vsub r2p 1 get def + /tail bbox1 pnt1 angle bboxray2p def + /head bbox2 pnt2 angle 180 add bboxray2p def + tail head + PSMsysd begin + /cdarrowhead xdef + /cdarrowtail xdef + end + tail head + } 11 ldef +/cdarrow-lw 0.3 def +/cdarrow {cdarrowpts cdarrow-std} def +/cdarrow-std + { /head xdef /tail xdef + /u head tail vsub v2u 2.5 smul def + /up u 90 rotpnt def + gsave + newpath cdarrow-lw setlinewidth + tail head u cdarrow-lw smul 0.5 smul vsub line + stroke nodash + [head u vsub up vadd head head u vsub up vsub] + lines stroke + grestore + head moveto +} 4 ldef +/cdarrow-eq + { cdarrowpts /head xdef /tail xdef + /orth head tail vsub 90 rotpnt v2u def + tail orth vadd head orth vadd line stroke + tail orth vsub head orth vsub line stroke + head Moveto + head Moveto + } 2 ldef +/cdarrow-surj + { cdarrowpts /head xdef /tail xdef + gsave + newpath cdarrow-lw setlinewidth + tail head cdarrow-std stroke + tail + tail head dist dup 1.5 sub exch div + tail head tvec + cdarrow-std stroke + grestore + head Moveto + } 2 ldef +/cdarrow-incl + { cdarrowpts /head xdef /tail xdef + /u head tail vsub v2u 2 smul def + /up u 90 rotpnt def + gsave + newpath cdarrow-lw setlinewidth + tail u vadd up vadd + tail up vadd + tail + tail u vadd curve + tail u vadd head cdarrow-std stroke + grestore + head Moveto + } 4 ldef +/cdarrow-line + { cdarrowpts + dup 3 1 roll + gsave newpath line stroke grestore + Moveto + } def +/cdarrow-down {cdarrow-up} def +/cdarrow-up + { cdarrowpts /head xdef /tail xdef + /u head tail vsub v2u def /v [u aload pop exch neg] def + tail v 2 smul vadd head v 2 smul vadd cdarrow-std + } 4 ldef +/cdentry {2 array astore dup cdlbl} def +/cdlbl + { /cd xdef /lbl cd 1 get def + cd cdbbox Moveto pop lbl TeX + } 3 ldef +/cdarrowlbl + { /ypos xdef /xpos xdef /lbl xdef + lbl 0.5 cdarrowtail cdarrowhead tvec xpos ypos label + } 3 ldef +/cdpnt + { dup type dup /integertype eq exch /realtype eq or not + {0.5} if + cdarrowtail cdarrowhead tvec + } def +/cdlist % ListOfWords cdentry dx dy => ListOfCDentry +{ 0 begin + /dy xdef /dx xdef + 0 get [0 dy neg] vadd /P xdef + /L xdef + /n L length def + /N n array def + /width 0 L {stringwidth pop add} forall n 1 sub dx mul add def + /x width 2 div neg def + 0 1 n 1 sub + { /i xdef + /w L i get stringwidth pop def + N i [P [w 2 div x add 0] vadd L i get] put + /x x w add dx add def + } for + N + end + { dup 1 get cvn exch dup cdlbl def + } forall +} def +/cdlist load 0 12 dict put +/cdsuper % [cdpnt1 cdpnt2 ... cdpntn] => pnt +{ /list xdef + % Find initial xmin, xmax, ymin + /pnt list 0 get 0 get def + /xmin pnt 0 get def + /xmax pnt 0 get def + /ymax pnt 1 get def + + % Find xmin, xmax, ymin + list { + 0 get /pnt xdef + /x pnt 0 get def + /y pnt 1 get def + x xmin lt {/xmin x def} if + x xmax gt {/xmax x def} if + y ymax gt {/ymax y def} if + } forall + + % Return super point + [xmin xmax add 2 div ymax vspace add] +} 8 ldef + +/3Dinit + { PSMsysd begin + /3Ddist xdef /3Dcenter xdef /3Dfocal xdef + /3Dnormal 3Dfocal 3Dcenter vsub v2u def + /3Dorigo 3Ddist 3Dnormal smul 3Dcenter vadd def + /3Dex 3Dnormal [0 0 1] cp def + 3Dex norm 1e-8 lt + {/3Dex [1 0 0] def} {/3Dex 3Dex v2u def} ifelse + /3Dey 3Dex 3Dnormal cp def + /3Dmatrix [3Dex 3Dey 3Dnormal] mtrans def + end + } def +/3D* + { /p' xdef /p xdef + PSMsysd begin + p 3Dcenter p" vsub* + dup 3Dnormal ip p" sdiv* + 3Dnormal p" vsub* + 3Ddist p" smul* + 3Dmatrix exch p" mvmul* + aload pop pop p' astore + end + } 3 {/p" 3 array def} lidef +/3D {2 array 3D*} def +/P2L* + { /line xdef /p' xdef /p xdef + p' p p" vsub* aload pop + p aload pop + line astore + } 4 {/p" 3 array def} lidef +/P2L {6 array P2L*} def +/LP2P* + { /p xdef aload pop /d xdef n astore pop aload pop + p0 astore pop r astore pop + /s d n p0 ip sub n r ip div def + r s r smul* + p0 p vadd* + } 6 {/n 3 array def /r 3 array def /p0 3 array def} lidef +/LP2P {3 array LP2P*} def +/PL2P* + { /pi xdef aload pop p0 astore pop r astore pop /p xdef + r p p0 n vsub* n cp* aload pop + n p0 ip + pi astore + } 6 {/n 3 array def /r 3 array def /p0 3 array def} lidef +/PL2P {4 array PL2P*} def +/s2r* + { /p xdef aload pop /theta xdef /phi xdef /r xdef + r theta sin mul phi cos mul + r theta sin mul phi sin mul + r theta cos mul + p astore + } 4 ldef +/s2r {3 array s2r*} def +/r2s* + { /p xdef aload pop /z xdef /y xdef /x xdef + x sqr y sqr add z sqr add sqrt + y x atan + dup y exch sin z mul atan + p astore + } 4 ldef +/r2s {3 array r2s*} def +/3Dpoints2gcircle* + { /C xdef /ey xdef /ex xdef + /ex' C 0 get def /ey' C 1 get def /ez' C 2 get def + ex ey ez cp* ez v2u* pop + ez ex ey' cp* pop + ex aload pop ex' astore pop + ez aload pop ez' astore pop + C + } 7 {/ez 3 array def} lidef +/3Dpoints2gcircle {3 3 nullmatrix 3Dpoints2gcircle*} def +/3Dgcircle-t2p* + { /p xdef /t xdef + t cos t sin 0 p' astore p mvmul* + } 3 {/p' 3 array def} lidef +/3Dgcircle-t2p {3 array 3Dgcircle-t2p*} def +/3Dgcircle-p2t + { exch M mtrans* exch v mvmul* + aload pop pop exch atan + } 2 {/M 3 3 nullmatrix def /v 3 array def} lidef +/3Dgcircle-draw + { /tmax xdef /tmin xdef /M xdef + M tmin v 3Dgcircle-t2p* moveto + tmin tmax { M exch v 3Dgcircle-t2p*} plot + } 5 {/v 3 array def} lidef +PSMtexd begin +/TeX-mm false def +/TeX-script 0.65 def +/TeX-lower 0.2 def +/TeX-raise 0.25 def +/TeXshow {show} def +/TeX-tok +{ /s xdef + s length 0 eq + { () () } + { /s0 s 0 get def + 47 s0 eq 123 s0 eq or + { s0 47 eq + { /n 1 def + s { /sn xdef + sn 64 gt sn 91 lt and + sn 96 gt sn 123 lt and or + {/n n 1 add def} {n 1 ne {exit} if} ifelse + } forall + s n s length n sub getinterval /S xdef + S length 0 eq not + { S 0 get 32 eq + {/S S 1 S length 1 sub getinterval def} if + } if S + s 0 n getinterval + } if + s0 123 eq + { /n 0 def /bl 0 def + s { dup + 123 eq {/bl bl 1 add def} if + 125 eq {/bl bl 1 sub def} if + /n n 1 add def + bl 0 eq {exit} if + } forall + s n s length n sub getinterval + s 1 n 2 sub getinterval + } if + } + { s 1 s length 1 sub getinterval s 0 1 getinterval + } ifelse + } ifelse +} 5 ldef +/PSMtexld 3 dict def PSMtexld begin /TeXnest 0 def end +/TeX +{ /TeXnest where {pop} {PSMtexld begin} ifelse + /TeXnest TeXnest 1 add def + TeX-tok /tok xdef /tail xdef + tok length dup 0 eq exch 1 gt or + { tok length 0 eq + { tail length 0 eq not {{tail TeX}} {{}} ifelse} + { tok 0 get 47 eq + {{tail tok 1 tok length 1 sub getinterval cvn cvx + PSMtexd exch get exec TeX}} + {{tail tok TeX TeX}} + ifelse + } ifelse + } + { + % Both text and math mode + ($) tok eq {{tail PSMtexd begin /TeX-mm TeX-mm not def + getfontstyle 2 xor setfontstyle setupfont end TeX}} if + (_) tok eq {{tail subscript TeX}} if + (^) tok eq {{tail supscript TeX}} if + + % Math mode only + TeX-mm { + ( ) tok eq {{tail TeX}} if + (=) tok eq {{tail spc tok romanshow spc TeX}} if + (+) tok eq {{tail spc tok romanshow spc TeX}} if + (-) tok eq {{tail spc (\261) romanshow spc TeX}} if + (()0123456789[]:) tok search {pop pop pop {tok romanshow + tail TeX}} {pop} ifelse + (_^$ =+-()0123456789[]:) tok search {pop pop pop} + {pop {tail tok TeXshow TeX}} ifelse + } { + (_$^) tok search {pop pop pop} + {pop {tail tok TeXshow TeX}} ifelse + } ifelse + } ifelse + bind exec + /TeXnest TeXnest 1 sub def + TeXnest 0 eq {end} if +} def +/romanshow + { getfontstyle 0 setfontstyle setupfont exch TeXshow + setfontstyle setupfont + } def +/subsup {gsave 0 -1 rmoveto subscript grestore supscript} def +/lit {TeX-tok show} def +/subscript + { 0 getfontsize PSMtexd /TeX-lower get mul neg rmoveto script + 0 getfontsize PSMtexd /TeX-lower get mul rmoveto + } def +/supscript + { 0 getfontsize PSMtexd /TeX-raise get mul rmoveto script + 0 getfontsize PSMtexd /TeX-raise get mul neg rmoveto + } def +/script + { getfontsize PSMtexd /TeX-script get mul setfontsize setupfont + TeX-tok TeX getfontsize TeX-script div setfontsize setupfont + } def +/overline + { TeX-tok dup TeXbbox + /ury xdef /urx xdef pop /llx xdef + gsave llx ury 1 add rmoveto urx llx sub 0 rlineto + 0.5 setlinewidth stroke grestore TeX + } 3 ldef +/spc {getfontsize 0.2 mul 0 rmoveto} bdef +/nspc {getfontsize -0.2 mul 0 rmoveto} bdef +/phantom {TeX-tok gsave TeX grestore} def +/roman + { TeX-tok {TeX 1 setfontstyle setupfont} dup 1 + PSMtexd /fontstyle get put + 0 setfontstyle setupfont exec + } def +/bold + { TeX-tok {TeX 1 setfontstyle setupfont} dup 1 + PSMtexd /fontstyle get put + getfontstyle 1 or setfontstyle setupfont exec + } def +/italic + { TeX-tok {TeX 1 setfontstyle setupfont} dup 1 + PSMtexd /fontstyle get put + getfontstyle 2 or setfontstyle setupfont exec + } def +/symbol + { TeX-tok {TeX 1 setfontfamily getfontsize 0.825 div + setfontsize setupfont} dup 1 PSMtexd /fontfamily get put + Symbol setfontfamily getfontsize 0.825 mul setfontsize + setupfont exec + } def +/symbol-show + { TeX-tok {show 1 setfontfamily getfontsize 0.825 div + setfontsize setupfont} dup 1 PSMtexd /fontfamily get put + Symbol setfontfamily getfontsize 0.825 mul setfontsize + setupfont exec + } def +/xlabel + { /vpos xdef /hpos xdef /dy xdef /dx xdef pnt2vct /pnt xdef /lbl xdef + lbl () ne + { lbl TeXbbox /ury xdef /urx xdef /lly xdef /llx xdef + pnt Moveto dx dy rmoveto + hpos 0 eq not {llx neg 0 rmoveto hpos 1 sub urx llx sub + 2 div mul neg 0 rmoveto} if + vpos 0 eq not {0 lly neg rmoveto 0 vpos 1 sub ury lly sub + 2 div mul neg rmoveto} if + fill? { gsave currentpoint newpath moveto + llx filldist sub lly filldist sub rmoveto + urx llx sub filldist 2 mul add 0 rlineto + 0 ury lly sub filldist 2 mul add rlineto + llx urx sub filldist 2 mul sub 0 rlineto + closepath fillcol setgray fill grestore } if + lbl TeX + } if + } 13 {/fill? false def /fillcol 1 def /filldist 3 def} lidef +/label + { /vpos xdef /hpos xdef + /dx [1 1 0 -1] hpos get def + /dy [1 1 0 -1] vpos get def + /dabs dx abs dy abs add sqrt def + dabs 0 eq not {/dabs 4 dabs div def} if + dx dabs mul dy dabs mul hpos vpos xlabel + } 5 ldef +/TeXsetfill + { /xlabel load 0 get begin + /filldist xdef + dup 0 lt {pop /fill? false def} + {/fillcol xdef /fill? true def} ifelse + end + } def +/TeXbbox + { TeXbbdict begin + /llx 1e30 def /lly 1e30 def /urx -1e30 def /ury -1e30 def + gsave newpath 0 0 moveto TeX grestore + llx lly itransform urx ury itransform + /ury xdef /urx xdef /lly xdef /llx xdef + llx urx gt {llx urx /llx xdef /urx xdef} if + lly ury gt {lly ury /lly xdef /ury xdef} if + llx lly urx ury end + } def +/TeXbbdict 14 dict def +TeXbbdict begin + /show {false charpath currentpoint maxbbox moveto} def + /stroke {maxbbox} def + /fill {maxbbox} def + /maxbbox + { gsave TeXbbdict begin + flattenpath pathbbox + transform /ury' xdef /urx' xdef + transform /lly' xdef /llx' xdef + /llx llx' urx' min llx min def + /lly lly' ury' min lly min def + /urx urx' llx' max urx max def + /ury ury' lly' max ury max def + end grestore newpath + } def +end +/alpha {(a) symbol pop} def /Alpha {(A) symbol pop} def +/beta {(b) symbol pop} def /Beta {(B) symbol pop} def +/chi {(c) symbol pop} def /Chi {(C) symbol pop} def +/delta {(d) symbol pop} def /Delta {(D) symbol pop} def +/epsilon{(e) symbol pop} def /Epsilon{(E) symbol pop} def +/phi {(f) symbol pop} def /Phi {(F) symbol pop} def +/gamma {(g) symbol pop} def /Gamma {(G) symbol pop} def +/eta {(h) symbol pop} def /Eta {(H) symbol pop} def +/iota {(i) symbol pop} def /Iota {(I) symbol pop} def +/phi1 {(j) symbol pop} def /theta1 {(J) symbol pop} def +/kappa {(k) symbol pop} def /Kappa {(K) symbol pop} def +/lambda {(l) symbol pop} def /Lambda {(L) symbol pop} def +/mu {(m) symbol pop} def /Mu {(M) symbol pop} def +/nu {(n) symbol pop} def /Nu {(N) symbol pop} def +/omicron{(o) symbol pop} def /Omicron{(O) symbol pop} def +/pi {(p) symbol pop} def /Pi {(P) symbol pop} def +/theta {(q) symbol pop} def /Theta {(Q) symbol pop} def +/rho {(r) symbol pop} def /Rho {(R) symbol pop} def +/sigma {(s) symbol pop} def /Sigma {(S) symbol pop} def +/tau {(t) symbol pop} def /Tau {(T) symbol pop} def +/upsilon{(u) symbol pop} def /Upsilon{(U) symbol pop} def +/omega1 {(v) symbol pop} def /sigma1 {(V) symbol pop} def +/omega {(w) symbol pop} def /Omega {(W) symbol pop} def +/xi {(x) symbol pop} def /Xi {(X) symbol pop} def +/psi {(y) symbol pop} def /Psi {(Y) symbol pop} def +/zeta {(z) symbol pop} def /Zeta {(Z) symbol pop} def +/do {TeX-tok cvx exec} def +/prime {(\242) symbol pop} def +/dprime {(\262) symbol pop} def +/tensor {(\304) symbol pop} def +/oplus {(\305) symbol pop} def +/isom {(\100) symbol pop} def +/in {(\316) symbol pop} def +/times {(\264) symbol pop} def +/union {(\310) symbol pop} def +/intsct {(\307) symbol pop} def +/into {(\256) symbol pop} def +/slash {(/) show} def +/ul {(_) show} def +/lbr {({) show} def +/rbr {(}) show} def +/exists {(\044) symbol-show pop} def +/all {(\042) symbol pop} def +/lnot {(\330) symbol pop} def +/land {(\331) symbol pop} def +/lor {(\332) symbol pop} def +/iff {(\333) symbol pop} def +/implies {(\336) symbol pop} def +/perp {(\136) symbol pop} def +/prod + { gsave currentpoint translate + [0.2 -0.57] getfontsize smul Moveto (P) symbol pop grestore + 0.9 getfontsize mul 0 rmoveto + } def +/Prod + { getfontsize dup 1.5 mul setfontsize setupfont prod + setfontsize setupfont + } def +/dlim +{ getfontstyle 0 setfontstyle setupfont + /P1 [currentpoint] def (lim) show + /P2 [currentpoint] def /un {getfontsize mul} def + gsave newpath P1 [0 -0.2 un] vadd P2 [-0.2 un -0.2 un] vadd + 0.05 un setlinewidth 0 0.12 un 90 0 xArrow stroke grestore + setfontstyle setupfont +} 3 ldef +/ilim +{ getfontstyle 0 setfontstyle setupfont + /P1 [currentpoint] def (lim) show + /P2 [currentpoint] def /un {getfontsize mul} def + gsave newpath P1 [0 -0.2 un] vadd P2 [-0.2 un -0.2 un] vadd exch + 0.05 un setlinewidth 0 0.12 un 90 0 xArrow stroke grestore + setfontstyle setupfont + } 3 ldef +/coprod +{ gsave currentpoint translate 1 -1 scale + [0.2 -0.57] getfontsize smul Moveto (P) symbol pop grestore + 0.9 getfontsize mul 0 rmoveto +} def +/Coprod +{ getfontsize dup 1.5 mul setfontsize setupfont coprod + setfontsize setupfont +} def +/ell +{ gsave currentpoint translate newpath + getfontsize 1000 div dup scale 35 112 moveto + 101 173 245 319 299 474 curveto 363 652 271 735 160 295 curveto + 130 178 95 -87 263 59 curveto 342 127 357 100 301 49 curveto + 134 -81 35 57 112 346 curveto 215 726 429 718 317 440 curveto + 251 277 124 165 58 101 curveto 11 58 -3 78 35 112 curveto + closepath fill grestore 0.5 getfontsize mul 0 rmoveto +} def +end +/CSmaxplots 20000 def +/CSminplots 20 def +/CSmaxdev 5 def +/CSplot0 {moveto} def +/CSplot {lineto} def +%/CSpnt0 2 array def +%/CSplot0 {2 copy moveto CSpnt0 astore pop gsave CSpnt0 dot grestore} def +%/CSplot {2 copy lineto CSpnt0 astore pop gsave CSpnt0 dot grestore} def +/CS-xmarks 20 def +/CS-ymarks 15 def +/CS-xbase 1 def +/CS-ybase 1 def +/CS-axismarklen 4 def +/CSxlabel {CS-xun div cvi CS-xmul mul s cvs exch 2 3 label} def +/CSylabel {CS-yun div cvi CS-ymul mul s cvs exch 1 2 label} def +/CS-xunitname () def +/CS-yunitname () def +/CS-labelfontsize 6 def +/CS-dimsfontsize 8 def +/CS-axismarklen 4 def +/CSunits + { /base xdef /idealn xdef /tmax xdef /tmin xdef + % Make the first, rough guess -- probably too small + /unit tmax tmin sub abs base div log 3 div floor 1 sub + 1000 exch exp base mul def + % Now multiply unit by 2,5,10,... until too big, and pick best + /best 1 rating def + 0 1 idealn dup add log floor 3 add + { 10 exch exp /e xdef + /best best + [ 2 e mul dup rating exch] max + [ 5 e mul dup rating exch] max + [10 e mul dup rating exch] max + def + best 1 get 10 e mul ne {exit} if + } for + % OK, now find the best unit, and new tmin and tmax + /unit best 1 get unit mul tmax tmin sub sgn mul def + /tmin tmin unit div floor unit mul def + /tmax tmax unit div ceiling 1 add unit mul def + /origo tmax tmin mul 0 gt {tmin} {0} ifelse def + /mult best 1 get dup 500 gt {1000 div} if cvi def + tmin tmax unit origo mult + } 12 + { % How good is the choice of unit? This routine measures it! + /rating % k => n(2*idealn-n) where n=dt/(unit*k) + { tmax tmin sub abs exch div unit div dup + idealn dup add exch sub mul + } def + } lidef +/CSframe % [xmin ymin] [xmax ymax] => - + { PSMsysd begin + aload pop /CS-fymax xdef /CS-fxmax xdef + aload pop /CS-fymin xdef /CS-fxmin xdef + end + } def +[0 mm 0 mm] [80 mm 50 mm] CSframe +/CSinit % xmin xmax ymin ymax => - + { CS-ymarks CS-ybase CSunits + PSMsysd begin + /CS-ymul xdef /CS-yorigo xdef /CS-yun xdef /CS-ymax xdef /CS-ymin xdef + end + CS-xmarks CS-xbase CSunits + PSMsysd begin + /CS-xmul xdef /CS-xorigo xdef /CS-xun xdef /CS-xmax xdef /CS-xmin xdef + /CS-sx CS-fxmax CS-fxmin sub CS-xmax CS-xmin sub div def + /CS-sy CS-fymax CS-fymin sub CS-ymax CS-ymin sub div def + /CS-tx CS-fxmin CS-sx CS-xmin mul sub def + /CS-ty CS-fymin CS-sy CS-ymin mul sub def + /CS-xaxis [CS-xmax CS-yorigo cs] def + /CS-yaxis [CS-xorigo CS-ymax cs] def + end + } def +/cs {pnt2num CS-sy mul CS-ty add exch CS-sx mul CS-tx add exch} def +/CSaxes + { gsave [CS-xorigo CS-ymin cs] [CS-xorigo CS-ymax cs] arrow fill + [CS-xmin CS-yorigo cs] [CS-xmax CS-yorigo cs] arrow fill + grestore + } def +/CSaxismarks + { CS-xmin CS-xun dup CS-xmax exch sub + { gsave 0 cs moveto CS-axismarklen dup -2 div 0 exch rmoveto + 0 exch rlineto stroke grestore } for + CS-ymin CS-yun dup CS-ymax exch sub + { gsave 0 exch cs moveto CS-axismarklen dup -2 div 0 rmoveto + 0 rlineto stroke grestore } for + } def +/sconcat % s1 s2 => s + { /s2 xdef /s1 xdef + s1 length s2 length add string dup + 0 s1 putinterval dup s1 length s2 putinterval + } 2 ldef +/CSaxislabels % - => - +{ /fs getfontsize def + CS-labelfontsize setfontsize setupfont + /dx (-9999) stringwidth pop CS-sx CS-xun mul div 1.5 mul def + /dy CS-labelfontsize CS-sy CS-yun mul div 1.5 mul def + /dx [1 2 5 10 20] {dup dx lt {pop} {exit} ifelse} forall CS-xun mul def + /dy [1 2 5 10 20] {dup dy lt {pop} {exit} ifelse} forall CS-yun mul def + CS-xorigo dx add dx CS-xmax dx 0.6 mul sub + {/x xdef [x 0 cs] x CSxlabel} for + CS-xorigo dx sub dx neg CS-xmin dx 0.1 mul sub + {/x xdef [x 0 cs] x CSxlabel} for + CS-yorigo dy add dy CS-ymax dy 0.6 mul sub + {/y xdef [0 y cs] y CSylabel} for + CS-yorigo dy sub dy neg CS-ymin dy 0.1 mul sub + {/y xdef [0 y cs] y CSylabel} for + /xexp CS-xun CS-xbase div CS-xmul div log round cvi def + /yexp CS-yun CS-ybase div CS-ymul div log round cvi def + CS-dimsfontsize setfontsize setupfont + xexp 0 eq + {()} {($\26410^{) xexp s cvs sconcat (}$ ) sconcat} ifelse + CS-xunitname sconcat CS-xaxis -8 -6 1 3 xlabel + yexp 0 eq + {()} {($\26410^{) yexp s cvs sconcat (}$ ) sconcat} ifelse + CS-yunitname sconcat CS-yaxis 6 -2 1 3 xlabel + fs setfontsize setupfont +} 7 {/s 20 string def} lidef + +/plot + { /fct xdef /tmax xdef /tmin xdef + /dtmin tmax tmin sub CSmaxplots div def + /dtmax tmax tmin sub CSminplots div def + /t tmin def /dt dtmax def + % Initialize + t fct pnt2num /y xdef /x xdef x y CSplot0 + /dev x y t dtmin 10 div add fct pnt2num angle def + % Start plotting + { % Predicted point + /tp t dt add dup tmax sub dt mul 0 lt not {pop tmax} if def + tp fct pnt2num /yp xdef /xp xdef + /devp x y xp yp angle def + % Test for correct change in dev + devp dev sub abs CSmaxdev lt dt abs dtmin abs lt or + { /x xp def /y yp def /t tp def /dev devp def /dt dt 1.2 mul def + x y CSplot tp tmax eq {exit} if } + { /dt dt 2 div def } + ifelse + } loop + } 15 ldef +/plimits +{ /pfct xdef /tmax xdef /tmin xdef + /xmin 1e36 def /xmax -1e36 def + /ymin 1e36 def /ymax -1e36 def + tmin tmax tmin sub cs-plots div tmax + { /t xdef t pfct aload pop /y xdef /x xdef + x xmin lt {/xmin x def} {x xmax gt {/xmax x def} if } ifelse + y ymin lt {/ymin y def} {y ymax gt {/ymax y def} if } ifelse + } for + xmin xmax ymin ymax +} 7 ldef +% +/knot-bgcolour 1 def +/knot-bgline {currentlinewidth 5 mul setlinewidth} def +/knot-line {1 setlinewidth} def +/chequer-line 0 def +/chequer-bg 1 def +/chequer-fill 0 def +/braid-dx 20 def +/braid-v 0 def +/braid-angle 0 def +/braid-dot {pop} def +/spline{ + /spline xdef + spline 0 get dup 0 get exch 1 get moveto + spline {aload pop 8 -2 roll pop pop curveto} forall +} 1 ldef +/splinestroke {spline stroke} def +/msplinestroke{ + /spline xdef + /n spline length def + 0 2 n 1 sub { + /i xdef + spline i get aload pop 8 -2 roll moveto curveto + spline i 1 add n mod get aload pop 8 -2 roll pop pop + curveto + } for + stroke +} 3 ldef +/splinesplit + { aload pop + /y3 xdef /x3 xdef /y2 xdef /x2 xdef + /y1 xdef /x1 xdef /y0 xdef /x0 xdef + [ x0 + y0 + x1 x0 add 2 div + y1 y0 add 2 div + x2 x1 add x1 add x0 add 4 div + y2 y1 add y1 add y0 add 4 div + x2 x1 add 3 mul x3 add x0 add 8 div + y2 y1 add 3 mul y3 add y0 add 8 div + ] + [ x2 x1 add 3 mul x3 add x0 add 8 div + y2 y1 add 3 mul y3 add y0 add 8 div + x3 x2 x2 add add x1 add 4 div + y3 y2 y2 add add y1 add 4 div + x3 x2 add 2 div + y3 y2 add 2 div + x3 + y3 + ] + } 8 ldef +/crossings2spline + { aload pop pop /v2 xdef /a2 xdef aload pop /y2 xdef /x2 xdef + aload pop pop /v1 xdef /a1 xdef aload pop /y1 xdef /x1 xdef + [ x1 + y1 + x1 a1 cos v1 mul add + y1 a1 sin v1 mul add + x2 a2 cos v1 mul sub + y2 a2 sin v1 mul sub + x2 + y2 + ] + } 8 ldef +/countsplines + { /C xdef /upper 0 def /lower 0 def + C { 3 get 0 lt + {/lower lower 2 add def} {/upper upper 2 add def} ifelse + } forall + C 0 get 3 get 0 lt + {/lower lower 1 sub def} {/upper upper 1 sub def} ifelse + C dup length 1 sub get 3 get 0 lt + {/lower lower 1 sub def} {/upper upper 1 sub def} ifelse + lower upper + } 3 ldef +/crossings2layer + { /C xdef + C countsplines array /upperlayer xdef array /lowerlayer xdef + /upper 0 def /lower 0 def + /first true def + [ C + { first + { /prev xdef /first false def } + { /curr xdef + prev curr crossings2spline /spline xdef + spline splinesplit /currspline xdef /prevspline xdef + prev 3 get 0 lt + { lowerlayer lower prevspline put + /lower lower 1 add def } + { upperlayer upper prevspline put + /upper upper 1 add def } + ifelse + curr 3 get 0 lt + { lowerlayer lower currspline put + /lower lower 1 add def } + { upperlayer upper currspline put + /upper upper 1 add def } + ifelse + /prev curr def spline + } ifelse + } forall + ] /layer xdef + C 0 get 3 get 0 lt + { lowerlayer aload length 1 roll lowerlayer astore pop } + { upperlayer aload length 1 roll upperlayer astore pop } + ifelse + layer lowerlayer upperlayer + } 12 ldef +% +/drawcrossings{ + crossings2layer + /upperlayer xdef + /lowerlayer xdef + /layer xdef + layer splinestroke + gsave knot-bgcolour setgray knot-bgline upperlayer msplinestroke grestore + upperlayer msplinestroke +} 3 ldef +/knot{ + /crossings xdef + [ crossings aload 0 get ] drawcrossings +} 1 ldef +/chequerboard + { /crossings xdef [ crossings aload 0 get ] crossings2layer + /upperlayer xdef /lowerlayer xdef spline closepath + gsave chequer-fill 0 lt not + {chequer-fill setgray eofill} if grestore + gsave chequer-bg setgray knot-bgline stroke grestore + chequer-line setgray stroke + gsave chequer-bg setgray knot-bgline upperlayer msplinestroke + grestore chequer-line setgray upperlayer msplinestroke + } 3 ldef +/string-s2angle + { /s2 xdef /s1 xdef + s1 -2 eq {/s1 -1 def} if + s1 2 eq {/s1 1 def} if + s2 -2 eq {/s2 -1 def} if + s2 2 eq {/s2 1 def} if + s1 s2 eq + {45 s1 mul neg} + { s1 s2 neg eq {0} {s1 s2 add braid-angle mul neg} ifelse } + ifelse + } 2 ldef +/stroke-string +{ /s xdef /i xdef + /n s length def /j 0 def + /angle1 0 def + /s [s aload pop 0] def + /x1 i braid-dx mul def + /y1 j braid-dx mul def + x1 y1 moveto + [ 0 1 n 1 sub + { /j xdef + /s1 s j get def + /s2 s j 1 add get def + /angle2 s1 s2 string-s2angle def + s1 0 gt {/i i 1 add def} if + s1 0 lt {/i i 1 sub def} if + /x4 i braid-dx mul def + /y4 j 1 add braid-dx mul def + [x1 y1] [braid-v braid-dx mul angle1 90 add] p2r vadd + aload pop /y2 xdef /x2 xdef + [x4 y4] [braid-v braid-dx mul angle2 270 add] p2r vadd + aload pop /y3 xdef /x3 xdef + x2 y2 x3 y3 x4 y4 curveto + s1 abs 2 eq {[x2 y2 x3 y3 x4 y4 x1 y1]} if + /x1 x4 def + /y1 y4 def + /angle1 angle2 def + } for + ] + knot-line stroke +} 16 ldef +/braid2string +{ /braid xdef /i xdef + [ braid + { /j xdef /s 0 def /ii i def + i j abs eq + {/ii i 1 add def /s j 0 gt { 2} { 1} ifelse def} if + i j abs 1 add eq j abs 0 gt and + {/ii i 1 sub def /s j 0 gt {-1} {-2} ifelse def} if + /i ii def s + } forall + ] +} 5 ldef +/braid +{ /braid xdef /n xdef + [ 1 1 n + { dup braid braid2string stroke-string + } for + ] { { aload pop moveto curveto + gsave knot-bgline 1 setgray stroke grestore stroke + } forall + } forall + /y1 0 def /y2 braid length braid-dx mul def + 1 1 n + { braid-dx mul /x xdef [x y1] braid-dot [x y2] braid-dot + } for +} 5 ldef +/knot-0-1 {[currentpoint] 12.5 mm circle stroke} def +/hopf-link +{ /cpoint [currentpoint] def /angle 60 def /radius 10 mm def + /A cpoint [angle cos radius mul neg 0] vadd def + /B cpoint [angle cos radius mul 0] vadd def + /dtheta gsave knot-bgline currentlinewidth grestore radius + div 57.2958 mul def + /theta1 angle dtheta add def /theta2 angle dtheta sub def + A Moveto [radius theta1] p2r rMoveto + A radius theta1 theta2 Arc + B Moveto [radius theta1 180 sub] p2r rMoveto + B radius theta1 180 sub theta2 180 sub Arc +} 8 ldef +/knot-3-1 +{ /A [10 mm -90] p2r [currentpoint] vadd def + /B [10 mm 30] p2r [currentpoint] vadd def + /C [10 mm 150] p2r [currentpoint] vadd def + /v 5 mm def /w 15 mm def + [ [A 45 v -1] [B 75 w 1] [C 285 v -1] + [A -45 w 1] [B 165 v -1] [C 195 w 1] ] +} 5 ldef +/knot-4-1 +{ /A [currentpoint] def + /B A [12 mm 90] p2r vadd def + /C A [12 mm 240] p2r vadd def + /D A [12 mm 300] p2r vadd def + /u 4 mm def /v 8 mm def /w 12 mm def + [ [A 45 u -1] [B 135 w 1] [C -30 u -1] + [D 40 w 1] [B 225 u -1] [A -45 u 1] + [D -90 v -1] [C 90 u 1] ] +} 7 ldef +/knot-5-1 +{ /O [currentpoint] def + /A O [10 mm -90] p2r vadd def + /B O [10 mm -18] p2r vadd def + /C O [10 mm 54] p2r vadd def + /D O [10 mm 126] p2r vadd def + /E O [10 mm 198] p2r vadd def + /v 5 mm def /w 10 mm def + [ [A 36 v 1] [B 36 w -1] [C 180 v 1] + [D 180 w -1] [E 324 v 1] [A 324 w -1] + [B 468 v 1] [C 468 w -1] [D 612 v 1] + [E 612 w -1] ] +} 8 ldef +/knot-5-2 +{ /A [currentpoint] def + /B A [13 mm 90] p2r vadd def + /C A [9 mm 225] p2r vadd def + /D A [13 mm -90] p2r vadd def + /E A [9 mm -45] p2r vadd def + /u 4 mm def /v 9 mm def /w 13 mm def + [ [A 45 v -1] [B 135 w 1] [C -45 u -1] + [D -45 v 1] [E 135 u -1] [A 135 v 1] + [B 45 w -1] [E 225 u 1] [D 225 v -1] + [C 45 u 1] ] +} 8 ldef +/knot-6-1 +{ /A [currentpoint] def + /B A [13 mm 90] p2r vadd def + /C A [13 mm 210] p2r vadd def + /D C [10 mm -45] p2r vadd def + /F A [13 mm -30] p2r vadd def + /E F [10 mm 225] p2r vadd def + /u 4 mm def /v 10 mm def /w 13 mm def + [ [A 45 u -1] [B 135 w 1] [C -45 u -1] + [D -45 u 1] [E 45 u -1] [F 45 w 1] + [B 225 u -1] [A -45 u 1] [F -45 v -1] + [E 135 u 1] [D 225 v -1] [C 45 u 1] ] +} 9 ldef +/knot-6-2 +{ /A [currentpoint] def + /B A [10 mm 45] p2r vadd def + /C A [10 mm 135] p2r vadd def + /D A [10 mm -45] p2r vadd def + /E D [10 mm 225] p2r vadd def + /F A [10 mm 225] p2r vadd def + /u 3 mm def /v 7 mm def /w 10 mm def + [ [A 45 u 1] [B 90 v -1] [C -90 u 1] + [A -45 u -1] [D -45 v 1] [E 135 u -1] + [F 135 w 1] [C 0 u -1] [B 0 w 1] + [D 225 u -1] [E 225 v 1] [F 45 u -1] ] +} 9 ldef +/knot-6-3 +{ /A [currentpoint] def + /B A [10 mm 150] p2r vadd def + /C A [10 mm 30] p2r vadd def + /D A [ 7 mm -90] p2r vadd def + /E D [10 mm 225] p2r vadd def + /F D [10 mm -45] p2r vadd def + /u 4 mm def /v 7 mm def /w 10 mm def + [ [A 180 u 1] [B 90 v -1] [C -90 u 1] + [D 225 u -1] [E -90 v 1] [F 90 u -1] + [D 135 u 1] [A 90 u -1] [B 200 v 1] + [E 0 u -1] [F 0 v 1] [C 180 u -1] ] +} 9 ldef +/knot-7-1 +{ /O [currentpoint] def /da 360 7 div def + /A O [11 mm da 0 mul 90 sub] p2r vadd def + /B O [11 mm da 1 mul 90 sub] p2r vadd def + /C O [11 mm da 2 mul 90 sub] p2r vadd def + /D O [11 mm da 3 mul 90 sub] p2r vadd def + /E O [11 mm da 4 mul 90 sub] p2r vadd def + /F O [11 mm da 5 mul 90 sub] p2r vadd def + /G O [11 mm da 6 mul 90 sub] p2r vadd def + /u 4 mm def /v 8 mm def + [ [A 25.7 u 1] [B 25.7 v -1] [C 128.6 u 1] + [D 128.6 v -1] [E 231.4 u 1] [F 231.4 v -1] + [G 334.3 u 1] [A 334.3 v -1] [B 437.1 u 1] + [C 437.1 v -1] [D 540.0 u 1] [E 540.0 v -1] + [F 643.9 u 1] [G 643.9 v -1] ] +} 11 ldef +/knot-7-2 +{ /A [currentpoint] def + /B A [8 mm 90] p2r vadd def + /O A [8 mm -90] p2r vadd def + /C O [8 mm 30] p2r vadd def + /D O [8 mm -30] p2r vadd def + /E O [8 mm -90] p2r vadd def + /F O [8 mm 210] p2r vadd def + /G O [8 mm 150] p2r vadd def + /u 3 mm def /v 8 mm def /w 12 mm def + [ [A 150 u 1] [B 30 w -1] [C 250 u 1] + [D -70 v -1] [E 130 u 1] [F 170 v -1] + [G 10 u 1] [A 50 u -1] [B 150 w 1] + [G -70 u -1] [F 250 v 1] [E 50 u -1] + [D 10 v 1] [C 170 u -1] ] +} 11 ldef +/knot-7-3 +{ /A [currentpoint] def + /B A [ 7 mm 90] p2r vadd def + /C B [ 7 mm 90] p2r vadd def + /D A [10 mm -30] p2r vadd def + /E D [ 7 mm 225] p2r vadd def + /G A [10 mm 210] p2r vadd def + /F G [ 7 mm -45] p2r vadd def + /u 4 mm def /v 10 mm def /w 13 mm def + [ [A 45 u -1] [B 135 u 1] [C 45 w -1] + [D 225 u 1] [E 225 u -1] [F 135 u 1] + [G 135 w -1] [C -45 u 1] [B 225 u -1] + [A -45 u 1] [D -45 v -1] [E 135 u 1] + [F 225 v -1] [G 45 u 1] ] +} 10 ldef +/knot-7-4 +{ /A [currentpoint] def + /B A [10 mm 120] p2r vadd def + /C A [10 mm 180] p2r vadd def + /D A [10 mm 240] p2r vadd def + /E A [10 mm 300] p2r vadd def + /F A [10 mm 360] p2r vadd def + /G A [10 mm 420] p2r vadd def + /u 4 mm def /v 7 mm def /w 10 mm def + [ [A 120 u 1] [B 120 w -1] [C -60 u 1] + [D -60 v -1] [E 60 u 1] [F 60 w -1] + [G 240 u 1] [A 240 u -1] [D 240 w 1] + [C 60 u -1] [B 60 v 1] [G -60 u -1] + [F -60 w 1] [E 120 u -1] ] +} 10 ldef +/knot-7-5 +{ /A [currentpoint] def + /B A [ 7 mm 90] p2r vadd def + /C B [ 7 mm 120] p2r vadd def + /D B [ 7 mm 60] p2r vadd def + /E A [ 7 mm -45] p2r vadd def + /F E [ 7 mm 225] p2r vadd def + /G A [ 7 mm 225] p2r vadd def + /u 5 mm def /v 10 mm def /w 15 mm def + [ [A 45 u 1] [B 135 u -1] [C 90 u 1] + [D -90 u -1] [B 225 u 1] [A -45 u -1] + [E -45 v 1] [F 135 u -1] [G 135 w 1] + [C 5 u -1] [D -5 w 1] [E 225 u -1] + [F 225 v 1] [G 45 u -1] ] +} 10 ldef +/knot-7-6 + { /A [currentpoint] def + /B A [ 7 mm 75] p2r vadd def + /C B [ 7 mm 105] p2r vadd def + /D A [10 mm 180] p2r vadd def + /E A [10 mm 240] p2r vadd def + /F A [10 mm -60] p2r vadd def + /G A [10 mm 0] p2r vadd def + /u 5 mm def /v 10 mm def /w 15 mm def + [ [A 60 u -1] [B 90 u 1] [C 135 w -1] + [D -60 u 1] [E -60 u -1] [F 60 u 1] + [G 60 w -1] [C 225 u 1] [B 0 u -1] + [G -60 v 1] [F 120 u -1] [A 120 u 1] + [D 240 v -1] [E 60 u 1] ] + } 10 ldef +/knot-7-7 + { /O [currentpoint] def + /A O [ 4 mm 180] p2r vadd def + /B A [ 8 mm 60] p2r vadd def + /C O [12 mm 0] p2r vadd def + /D C [ 8 mm 240] p2r vadd def + /E A [ 8 mm 240] p2r vadd def + /F O [12 mm 180] p2r vadd def + /G O [ 4 mm 0] p2r vadd def + /u 5 mm def /v 8 mm def /w 12 mm def + [ [A 60 u -1] [B 60 w 1] [C 240 u -1] + [D 240 v 1] [E 120 u -1] [F 120 w 1] + [B -60 u -1] [G -60 u 1] [D -60 v -1] + [C 180 u 1] [G 180 u -1] [A 180 u 1] + [F 180 v -1] [E 60 u 1] ] + } 11 ldef +/art +{ /A [currentpoint] def + /B A [ 8 mm 90] p2r vadd def + /C B [ 8 mm 90] p2r vadd def + /D A [13 mm 210] p2r vadd def + /E D [10 mm -45] p2r vadd def + /F A [13 mm -30] p2r vadd def + /G F [10 mm 225] p2r vadd def + /u 4 mm def /v 10 mm def /w 13 mm def + A dot B dot C dot D dot E dot F dot G dot + [ [A 45 u -1] [B 135 u 1] [C 45 w -1] + [D -45 u 1] [E -45 u -1] [F 135 u 1] + [G 135 w -1] [C -45 u 1] [B 225 u -1] + [A -45 u 1] [D -45 v -1] [E 45 u 1] + [F 225 v -1] [G 45 u 1] ] +} 10 ldef +/chemdist 6 mm def +/chempoints 20 array def +/chemlabels 50 array def +% general procedures +/cheminit % pnt angle => - +{ /chemangle xdef /chempoint xdef + chempoints 0 0 put + chemlabels 0 0 put + 1 1 TeXsetfill +} def +/chemclose +{ chemlabels 1 chemlabels 0 get getinterval + {aload pop exch 2 2 label} forall +} def +/atom % label +{ /lbl xdef chemlabels [chempoint lbl] spush +} def +/bondlines % pnta pntb n => - +{ gsave + newpath /n xdef line /c 0 def /lw currentlinewidth def + n 2 mul 1 sub -2 0 + { gsave lw mul setlinewidth c setgray stroke /c 1 c sub def + grestore + } for + grestore +} 3 ldef +/spush % stack any => - +{ /a xdef /s xdef /n s 0 get 1 add def s 0 n put s n a put +} 3 ldef +/spop % stack => top element +{ /s xdef /n s 0 get def s n get s 0 n 1 sub put +} 2 ldef +/xbond % angle n length => - + { /l xdef /n xdef /a xdef + chempoint + /chemangle chemangle a add def + /chempoint chempoint [l chemangle] p2r vadd def + chempoint n bondlines + } def +/chempush {chempoints [chempoint chemangle] spush} def +/single {1 chemdist xbond} def +/double {2 chemdist xbond} def +/triple {3 chemdist xbond} def +/single* {chempush single} def +/double* {chempush double} def +/triple* {chempush triple} def +/back +{ chempoints spop aload pop + /chemangle xdef /chempoint xdef +} def +/benzene +{ chempoint [chemdist chemangle] p2r vadd + chemdist 3 sqrt 2 div mul 2 sub circle stroke + -60 single* 5 {60 single*} repeat +} def + +% DATA TYPES +% +% label: string +% node: [xcenter ybaseline label] +% leaf: [label] +% branch: [label node1 ... noden] +% tree: leaf | node | [label tree1 ... treen] +% ctree: a tree, but not a branch, leaf or node +% +% METHOD +% +% The program takes a tree and returns its top node. +% a tree as above. The program applies the following rules to +% the tree: +% +% 1 a) It is a label; leave it. +% b) It is a node; leave it. +% +% 2 a) It is a leaf; draw it and return node. +% b) It is a branch; draw it and return top node. +% +% 3 It is a tree; process each entry separately and +% astore the tree into a branch; then reprocess it. + +% MAIN + +/tree % tree => node +{ dup treetype % tree treetype + cvx exec +} def + +% TREETYPE CASES + +/TeXstringwidth {TeXbbox pop exch pop exch sub 0} def +/treelabel { } def + +/node { } def + +/leaf % [string] => node +{ aload pop % string + currentpoint pop % string x1 + 1 index TeX currentpoint % string x1 x2 y + 3 1 roll add 2 div exch % string x y + 3 -1 roll 3 array astore % [x y string] + hspace 0 rmoveto +} def + +/branch % [string node1 node2 ... noden] => node +{ dup length 1 sub /n exch def % branch + dup aload pop % branch string node1 ... noden + 1 get n 1 sub % branch string node1 ... noden-1 yn n-1 + { exch 1 get max + } repeat + vspace add % branch string y + 2 index dup % branch string y branch branch + 1 get 0 get exch n get 0 get % branch string y x1 xn + add 2 div exch 3 -1 roll % branch string x y + 3 array astore exch % node branch + dup 0 1 index 1 get put % node [node1 node1 ... noden] + { 1 index nodeline + } forall + dup aload pop 3 1 roll % node string x y + 2 index TeXstringwidth pop 2 div % node string x y sw/2 + 3 -1 roll exch sub exch % node string x y + gsave moveto TeX grestore % node +} def + +/ctree % [string tree1 ... treen] => node +{ dup length 1 sub 1 1 3 -1 roll % ctree 1 1 n + { 1 index exch dup 2 index % ctree ctree i i ctree + exch get % ctree ctree i treei + tree % ctree ctree i nodei + put % ctree + } for + branch +} def + +/nodeline % node1 node => - +{ gsave + aload pop pop vspace- sub moveto + aload pop pop vspace+ add lineto stroke + grestore +} def + +% TREETYPE TESTS: tree => bool + +/node? +{ dup type /arraytype eq + { 0 get type dup + /integertype eq exch /realtype eq or + } + { pop false + } ifelse +} def + +/treetype +{ dup type /stringtype eq % tree bool + { pop /treelabel % /treelabel + } + { dup 0 get dup type /stringtype eq % tree tree_0 bool + { pop dup length % tree length + dup 1 eq % tree length bool + { pop pop /leaf % /leaf + } + { 1 sub 1 1 % tree length-1 1 1 + 3 -1 roll true % tree 1 1 length-1 true + 4 1 roll % tree true 1 1 length-1 + { 2 index % tree bool i tree + exch get % tree bool tree_i + node? and % tree bool + } for + {pop /branch} {pop /ctree} ifelse + } ifelse + } + { pop pop /node % /node + } ifelse + } ifelse +} def + + +% CREATE AN ISO-LATIN1 ENCODED TIMES FONT +%/TimesRoman findfont +%dup length dict begin +% {1 index /FID ne {def} {pop pop} ifelse} forall +% /Encoding ISOLatin1Encoding def +% currentdict +%end +%/TimesRoman-ISOLatin1 exch definefont pop +%/TimesRoman-ISOLatin1 findfont fontsize scalefont setfont + +% DEFAULTS +/hspace 10 def +/vspace 20 def +/vspace+ 10 def +/vspace- 3.33 def + +% Define procedures +/yxline % P Q +{ aload pop /y2 xdef /x2 xdef + aload pop /y1 xdef /x1 xdef + x1 y1 moveto x1 y2 lineto x2 y2 lineto +} 4 ldef + +/nextline {/nextpnt nextpnt [0 -15] vadd def} def + +/Root % Label Pnt +{ 10 dict begin + /rootpnt xdef /rootlabel xdef + rootlabel rootpnt 2 -3 1 0 xlabel + /nextpnt rootpnt [20 0] vadd def + /rootpnt nextpnt [-5 -5] vadd def + nextline +} def + +/Subtree % Label +{ rootpnt nextpnt yxline stroke + nextpnt Root +} def + +/Endtree +{ nextpnt 1 get + end + nextpnt 0 get exch + 2 array astore /nextpnt xdef +} def + +/Endroot +{ end nextline +} def + +/Node % Label +{ rootpnt nextpnt yxline stroke + nextpnt 2 -3 1 0 xlabel + nextline +} def + +%% Trees +/words {[0 0] ( ) cdentry hspace vspace cdlist} def +/cat {dup type /stringtype eq {[0 0]} {[0 vspace] smul} ifelse + 3 -1 roll cdsuper vadd exch cdentry def} def +/trans {/vspace -10 def exch cdsuper exch cdentry} 1 ldef +/lex {gsave 2 setlinewidth cdarrow-line grestore} def +/head {gsave 2 setlinewidth cdarrow-line grestore} def +/comp {cdarrow-line} def +/adj {[3 1] 0 setdash cdarrow-line nodash} def +/landing {[1 3] 0 setdash cdarrow-line nodash} def +/filler {landing (_{fill}) 0.5 cdpnt 2 2 label} def +end +end diff --git a/Master/texmf-dist/source/generic/pst-knot/Makefile b/Master/texmf-dist/source/generic/pst-knot/Makefile new file mode 100644 index 00000000000..fec35e5e0cf --- /dev/null +++ b/Master/texmf-dist/source/generic/pst-knot/Makefile @@ -0,0 +1,70 @@ + +# `Makefile' for `pst-coil.pdf', hv, 2006/08/11 + +.SUFFIXES : .tex .ltx .dvi .ps .pdf .eps + +PACKAGE = pst-knot + +MAIN = $(PACKAGE)-doc + +LATEX = latex + +ARCHNAME = $(MAIN)-$(shell date +%y%m%d) + +ARCHFILES = $(PACKAGE).sty $(PACKAGE).tex $(PACKAGE).pro $(MAIN).tex README Changes Makefile + +TDS = ~/PSTricks/PSTricks-TDS + +all : doc clean + +doc: $(MAIN).pdf + +$(MAIN).pdf : $(MAIN).ps + GS_OPTIONS=-dAutoRotatePages=/None ps2pdf $< + +$(MAIN).ps : $(MAIN).dvi + dvips $< + +$(MAIN).dvi : $(MAIN).tex + $(LATEX) $< + $(LATEX) $< + if ! test -f $(basename $<).glo ; then touch $(basename $<).glo; fi + if ! test -f $(basename $<).idx ; then touch $(basename $<).idx; fi + makeindex -s gglo.ist -t $(basename $<).glg -o $(basename $<).gls \ + $(basename $<).glo + makeindex -t $(basename $<).ilg -o $(basename $<).ind \ + $(basename $<).idx + bibtex $(basename $<) + $(LATEX) $< + $(LATEX) $< + +clean : + $(RM) $(addprefix $(MAIN), .log .aux .blg .bbl .glg .glo .gls .ilg .idx .ind .tmp .toc .out ) + $(RM) $(addprefix $(MAIN), .dvi .ps) + +veryclean : clean + $(RM) $(addprefix $(MAIN), .pdf .bbl .blg) + +arch : + zip $(ARCHNAME).zip $(ARCHFILES) + +tds: + cp -u Changes $(TDS)/doc/generic/$(PACKAGE)/ + cp -u README $(TDS)/doc/generic/$(PACKAGE)/ + cp -u $(MAIN).pdf $(TDS)/doc/generic/$(PACKAGE)/ +# + cp -u Changes $(TDS)/tex/latex/$(PACKAGE)/ + cp -u $(PACKAGE).sty $(TDS)/tex/latex/$(PACKAGE)/ +# + cp -u Changes $(TDS)/tex/generic/$(PACKAGE)/ + cp -u $(PACKAGE).tex $(TDS)/tex/generic/$(PACKAGE)/ +# + cp -u Changes $(TDS)/dvips/$(PACKAGE)/ + cp -u *.pro $(TDS)/dvips/$(PACKAGE)/ +# + cp -u Changes $(TDS)/source/$(PACKAGE)/ + cp -u $(MAIN).tex $(TDS)/source/$(PACKAGE)/ + cp -u $(MAIN).bib $(TDS)/source/$(PACKAGE)/ + cp -u Makefile $(TDS)/source/$(PACKAGE)/ + +# EOF diff --git a/Master/texmf-dist/tex/generic/pst-knot/pst-knot.tex b/Master/texmf-dist/tex/generic/pst-knot/pst-knot.tex new file mode 100644 index 00000000000..ea222af4b4c --- /dev/null +++ b/Master/texmf-dist/tex/generic/pst-knot/pst-knot.tex @@ -0,0 +1,65 @@ +%% +%% This is file `pst-knot.tex', +%% +%% IMPORTANT NOTICE: +%% +%% Package `pst-knot.tex' +%% +%% Herbert Voss <herbert -> dante.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-knot' is a PSTricks package for knot macros +%% +%% +\csname PSTknotLoaded\endcsname +\let\PSTknotLoaded\endinput +% Requires PSTricks +\ifx\PSTricksLoaded\endinput\else\input pstricks.tex\fi +\ifx\PSTXKeyLoaded\endinput\else\input pst-xkey.tex \fi +% +\edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax +% interface to the `xkeyval' package +\pst@addfams{pst-knot} + +\def\fileversion{0.01} +\def\filedate{2009/11/07} +\message{`PST-knot' v\fileversion, \filedate\space (hv)} +% +\SpecialCoor +\pstheader{pst-psm.pro} +% +\define@key[psset]{pst-knot}{knotborder}[2]{\def\psk@knot@border{#1 }} +\define@key[psset]{pst-knot}{knotbgcolor}[1]{\def\psk@knot@bgcolor{#1 }} +\define@key[psset]{pst-knot}{knotscale}[1 1]{\pst@getscale{#1}\psk@knot@scale} +\psset[pst-knot]{knotborder=2,knotbgcolor=1,knotscale=1} +% +\def\psKnot{\def\pst@par{}\pst@object{psKnot}} +\def\psKnot@i(#1)#2{\expandafter\psKnot@ii(#1)#2} +\def\psKnot@ii(#1)#2-#3{% + \addto@par{border=.5\pslinewidth}% + \begin@ClosedObj% + \pst@getcoor{#1}\pst@tempA% + \addto@pscode{ + \pst@tempA\space moveto + tx@KnotDict begin + PSMinit + /rgb {} def /gray {} def /cmyk {} def + \pst@number\pslinewidth SLW + \pst@usecolor\pslinecolor + \psk@knot@scale + /knot-bgline { CLW \psk@knot@border mul SLW } def + /knot-bgcolour \psk@knot@bgcolor def + knot-#2-#3 \ifnum#2=0 \else knot \fi + end + }% + \end@ClosedObj} +% +\catcode`\@=\PstAtCode\relax +% +%% END: pst-knot.tex +\endinput +% diff --git a/Master/texmf-dist/tex/latex/pst-knot/pst-knot.sty b/Master/texmf-dist/tex/latex/pst-knot/pst-knot.sty new file mode 100644 index 00000000000..d11f64db10a --- /dev/null +++ b/Master/texmf-dist/tex/latex/pst-knot/pst-knot.sty @@ -0,0 +1,8 @@ +\RequirePackage{pstricks} +\ProvidesPackage{pst-knot}[2009/11/07 package wrapper for + pst-knot.tex (hv)] +\input{pst-knot.tex} +\ProvidesFile{pst-knot.tex} + [\filedate\space v\fileversion\space `PST-knot' (hv)] +\IfFileExists{pst-psm.pro}{\@addtofilelist{pst-psm.pro}}{}% +\endinput |