pst-func 0.58 2008/12/08

git-svn-id: svn://tug.org/texlive/trunk@11831 c570f23f-e606-0410-a88d-b1316a301751

4 files changed, 163 insertions, 5 deletions

diff --git a/Master/texmf-dist/doc/generic/pst-func/Changes b/Master/texmf-dist/doc/generic/pst-func/Changes
index 2c6049860b8..d1d858b05fe 100644
--- a/Master/texmf-dist/doc/generic/pst-func/Changes
+++ b/Master/texmf-dist/doc/generic/pst-func/Changes
@@ -1,4 +1,8 @@
 ..... pst-func.tex
+0.58  2008-12-08  - add the ChebyshevT and ChebyshevU (first and second kind)
+                    the macros are only wrappers for the PS routines
+		  - take the optional argument comma from pstricks-add into
+                    account for \psPrintValue
 0.57  2008-11-13  - new optional argument for the step width of \psPlotImp
 0.56  2008-10-31  - fix bug with \psPoisson, thanks to Gerry Coombes
                   - index for the documentation
@@ -60,6 +64,7 @@
 
 
 ..... pst-func.pro
+0.10  2009-01-08  added ChebyshevT and ChebyshevU (first and second kind)
 0.09  2008-03-22  added Bernstein code for Bernstein polynomials
 0.08  2008-03-21  added BezierCurve code for Bezier curves of up to
 		    order 9 
diff --git a/Master/texmf-dist/doc/generic/pst-func/README b/Master/texmf-dist/doc/generic/pst-func/README
index 8006296267e..bc9e337e31e 100644
--- a/Master/texmf-dist/doc/generic/pst-func/README
+++ b/Master/texmf-dist/doc/generic/pst-func/README
@@ -41,4 +41,4 @@ CTAN server, f.ex. ftp://ftp.ctan.org
 PSTricks is PostScript Tricks, the documentation cannot be run
 with pdftex, use the sequence latex->dvips->ps2pdf.
 
-%% $Id: README 55 2008-11-14 12:01:12Z herbert $
+%% $Id: README 56 2008-11-14 15:55:45Z herbert $
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
index 3cecc9ab010..18fc3f85dda 100644
--- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
+++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
index 3f7b0a0a456..3b97fe8ed01 100644
--- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
+++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
@@ -1,9 +1,10 @@
-%% $Id: pst-func-doc.tex 55 2008-11-14 12:01:12Z herbert $
+%% $Id: pst-func-doc.tex 72 2009-01-08 22:00:47Z herbert $
 \documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,smallheadings
     headexclude,footexclude,oneside]{pst-doc}
 \usepackage[utf8]{inputenc}
 \usepackage{pst-func}
 \let\pstFuncFV\fileversion
+\usepackage{pstricks-add}
 \usepackage{pst-math}
 \lstset{pos=t,wide=true,language=PSTricks,
     morekeywords={psGammaDist,psChiIIDist,psTDist,psFDist,psBetaDist,psPlotImpl},basicstyle=\footnotesize\ttfamily}
@@ -53,6 +54,7 @@ and last but not least \url{http://mathworld.wolfram.com}
 
 \end{abstract}
 
+
 \section{\nxLcs{psBezier\#}}
 This macro can plot a B\'ezier spline from order 1 up to 9 which needs
 (order+1) pairs of given coordinates.
@@ -169,8 +171,159 @@ changed in the usual way.
 \end{pspicture}
 \endgroup
 
-
+\clearpage
 \section{Polynomials}
+
+\subsection{Chebyshev polynomials}
+
+The polynomials of the first (ChebyshevT) kind are defined through the identity
+
+\[ T_n(\cos\theta)=\cos(n\theta)\] 
+
+They can be obtained from the generating functions
+\begin{align}
+  g_1(t,x) &= \frac{1-t^2}{1-2xt+t^2}\\
+	   &= T_0(x)+2\sum_{n=1}^\infty T_n(x)t^n
+\end{align}
+
+and
+
+\begin{align}
+  g_2(t,x) &= \frac{1-xt}{1-2xt+t^2}\\
+           &= \sum_{n=0}^\infty T_n(x)t^n
+\end{align}
+
+The polynomials of second kind (ChebyshevU) can be generated by
+
+\begin{align}
+  g(t,x) &= \frac{1}{1-2xt+t^2}\\
+         &= \sum_{n=0}^\infty U_n(x)t^n
+\end{align}
+
+\LPack{pst-func} defines the \TeX-macros \Lcs{ChebyshevT} for the
+first kind and \Lcs{ChebyshevU} for the second kind of Chebyshev polynomials.
+These \TeX-macros cannot be used outside of PostScript, they are only wrappers
+for \verb+tx@FuncDict begin ChebyshevT end+ and the same for \Lcs{ChebyshevU}.
+
+\begin{center}
+\bgroup
+\psset{arrowscale=1.5,unit=3cm}
+\begin{pspicture}(-1.5,-1.5)(1.5,1.5)
+  \psaxes[ticks=none,labels=none]{->}(0,0)(-1.25,-1.25)(1.25,1.25)%
+    [Re$\{s_{21}\}$,0][Im$\{s_{21}\}$,90]
+  \pscircle(0,0){1}
+  \parametricplot[linecolor=blue,plotpoints=10000]{0}{1.5}{
+    /N 9 def
+    /x 2 N mul t \ChebyshevT def
+    /y 2 N mul 1 sub t \ChebyshevU def
+    x x 2 exp y 2 exp add div
+    y x 2 exp y 2 exp add div
+  }
+\end{pspicture}
+\egroup
+\end{center}
+
+\begin{lstlisting}
+\psset{arrowscale=1.5,unit=3cm}
+\begin{pspicture}(-1.5,-1.5)(1.5,1.5)
+  \psaxes[ticks=none,labels=none]{->}(0,0)(-1.25,-1.25)(1.25,1.25)%
+    [Re$\{s_{21}\}$,0][Im$\{s_{21}\}$,90]
+  \pscircle(0,0){1}
+  \parametricplot[linecolor=blue,plotpoints=10000]{0}{1.5}{
+    /N 9 def
+    /x 2 N mul t \ChebyshevT def
+    /y 2 N mul 1 sub t \ChebyshevU def
+    x x 2 exp y 2 exp add div
+    y x 2 exp y 2 exp add div
+  }
+\end{pspicture}
+\end{lstlisting}
+
+\begin{center}
+\bgroup
+\psset{xunit=4cm,yunit=3cm,plotpoints=1000}
+\begin{pspicture}(-1.2,-2)(2,1.5)
+  \psaxes[Dx=0.2]{->}(0,0)(-1.25,-1.2)(1.25,1.2)
+  \psset{linewidth=1.5pt}
+  \psplot[linestyle=dashed]{-1}{1}{1 x \ChebyshevT}
+  \psplot[linecolor=black]{-1}{1}{2 x \ChebyshevT}
+  \psplot[linecolor=black]{-1}{1}{3 x \ChebyshevT}
+  \psplot[linecolor=blue]{-1}{1}{4 x \ChebyshevT }
+  \psplot[linecolor=red]{-1}{1}{5 x \ChebyshevT }
+\end{pspicture}
+\egroup
+\end{center}
+
+
+
+\begin{lstlisting}
+\psset{xunit=4cm,yunit=3cm,plotpoints=1000}
+\begin{pspicture}(-1.2,-2)(2,1.5)
+  \psaxes[Dx=0.2]{->}(0,0)(-1.25,-1.2)(1.25,1.2)
+  \psset{linewidth=1.5pt}
+  \psplot[linestyle=dashed]{-1}{1}{1 x \ChebyshevT}
+  \psplot[linecolor=black]{-1}{1}{2 x \ChebyshevT}
+  \psplot[linecolor=black]{-1}{1}{3 x \ChebyshevT}
+  \psplot[linecolor=blue]{-1}{1}{4 x \ChebyshevT }
+  \psplot[linecolor=red]{-1}{1}{5 x \ChebyshevT }
+\end{pspicture}
+\end{lstlisting}
+
+\begin{center}
+\bgroup
+\psset{xunit=4cm,yunit=3cm,plotpoints=1000}
+\begin{pspicture*}(-1.5,-1.5)(1.5,1.5)
+  \psaxes[Dx=0.2]{->}(0,0)(-1.15,-1.1)(1.15,1.1)
+  \psset{linewidth=1.5pt}
+  \psplot[linecolor=black]{-1}{1}{2 x \ChebyshevU}
+  \psplot[linecolor=black]{-1}{1}{3 x \ChebyshevU}
+  \psplot[linecolor=blue]{-1}{1}{4 x \ChebyshevU }
+  \psplot[linecolor=red]{-1}{1}{5 x \ChebyshevU }
+\end{pspicture*}
+\egroup
+\end{center}
+
+
+
+\begin{lstlisting}
+\psset{xunit=4cm,yunit=3cm,plotpoints=1000}
+\begin{pspicture*}(-1.5,-1.5)(1.5,1.5)
+  \psaxes[Dx=0.2]{->}(0,0)(-1.15,-1.1)(1.15,1.1)
+  \psaxes[Dx=0.2]{->}(0,0)(-1.25,-1.2)(1.25,1.2)
+  \psset{linewidth=1.5pt}
+  \psplot[linecolor=black]{-1}{1}{2 x \ChebyshevU}
+  \psplot[linecolor=black]{-1}{1}{3 x \ChebyshevU}
+  \psplot[linecolor=blue]{-1}{1}{4 x \ChebyshevU }
+  \psplot[linecolor=red]{-1}{1}{5 x \ChebyshevU }
+\end{pspicture*}
+\end{lstlisting}
+
+\begin{center}
+\bgroup
+\psset{xunit=4cm,yunit=3cm,plotpoints=1000}
+\begin{pspicture}(-1.25,-1.2)(1.25,1.2)
+  \psaxes[Dx=0.2]{->}(0,0)(-1.25,-1.1)(1.25,1.1)
+  \psset{linewidth=1.5pt}
+  \psplot[linecolor=black]{-1}{1}{x ACOS 2 mul RadtoDeg cos}
+  \psplot[linecolor=black]{-1}{1}{x ACOS 3 mul RadtoDeg cos}
+  \psplot[linecolor=blue]{-1}{1}{x ACOS 4 mul RadtoDeg cos}
+  \psplot[linecolor=red]{-1}{1}{x ACOS 5 mul RadtoDeg cos}
+\end{pspicture}
+\egroup
+\end{center}
+
+\begin{lstlisting}
+\psset{xunit=4cm,yunit=3cm,plotpoints=1000}
+\begin{pspicture}(-1.25,-1.2)(1.25,1.2)
+  \psaxes[Dx=0.2]{->}(0,0)(-1.25,-1.2)(1.25,1.2)
+  \psset{linewidth=1.5pt}
+  \psplot[linecolor=black]{-1}{1}{x ACOS 2 mul RadtoDeg cos}
+  \psplot[linecolor=black]{-1}{1}{x ACOS 3 mul RadtoDeg cos}
+  \psplot[linecolor=blue]{-1}{1}{x ACOS 4 mul RadtoDeg cos}
+  \psplot[linecolor=red]{-1}{1}{x ACOS 5 mul RadtoDeg cos}
+\end{pspicture}
+\end{lstlisting}
+
 \subsection{\Lcs{psPolynomial}}
 The polynomial function is defined as
 %
@@ -1559,7 +1712,7 @@ There are the following new options:
   \makebox[1em]{\iA}
   \makebox[5em]{\psPrintValue[PSfont=Helvetica]{\iA\space sin}}
   \makebox[4em][r]{\psPrintValue[PSfont=Courier,fontscale=10,decimals=3]{\iA\space cos}}\hspace{1em}
-  \makebox[5em]{\psPrintValue[valuewidth=15,linecolor=blue,PSfont=AvantGarde]{\iA\space sqrt}}
+  \makebox[5em]{\psPrintValue[comma,valuewidth=15,linecolor=blue,PSfont=AvantGarde]{\iA\space sqrt}}
   \makebox[7em]{\psPrintValue[PSfont=Times-Italic]{\iA\space dup sin exch cos add}}
   \makebox[6em]{\psPrintValue[PSfont=Palatino-Roman]{\iA\space dup sin dup mul exch cos dup mul add}}\\}
 \end{center}
@@ -1574,7 +1727,7 @@ There are the following new options:
   \makebox[1em]{\iA}
   \makebox[5em]{\psPrintValue[PSfont=Helvetica]{\iA\space sin}}
   \makebox[4em][r]{\psPrintValue[PSfont=Courier,fontscale=10,decimals=3]{\iA\space cos}\hspace{1em}}
-  \makebox[5em]{\psPrintValue[valuewidth=15,linecolor=blue,PSfont=AvantGarde]{\iA\space sqrt}}
+  \makebox[5em]{\psPrintValue[comma,valuewidth=15,linecolor=blue,PSfont=AvantGarde]{\iA\space sqrt}}
   \makebox[7em]{\psPrintValue[PSfont=Times-Italic]{\iA\space dup sin exch cos add}}
   \makebox[6em]{\psPrintValue[PSfont=Palatino-Roman]{\iA\space dup sin dup mul exch cos dup mul add}}\\}
 \end{lstlisting}