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author | Karl Berry <karl@freefriends.org> | 2006-01-09 00:56:57 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2006-01-09 00:56:57 +0000 |
commit | f07bb53970ee2ecc53f81a206a3d3a67ef665e4a (patch) | |
tree | 6f57a1d62971db79e5ff023bdfd83b22cb971dc9 /Master/texmf-dist/doc/generic/pst-math | |
parent | 007f67a693e4d031fd3d792df8e4d5f43e2cb2e7 (diff) |
doc 6
git-svn-id: svn://tug.org/texlive/trunk@85 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/generic/pst-math')
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-math/README | 2 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-math/pst-math-doc.tex | 415 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/pst-math/pst-math.pdf | bin | 0 -> 162112 bytes |
3 files changed, 417 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-math/README b/Master/texmf-dist/doc/generic/pst-math/README new file mode 100644 index 00000000000..2ac88bb4551 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-math/README @@ -0,0 +1,2 @@ +Material in this directory is an enhancement of postscript math operators +to use with pstricks
\ No newline at end of file diff --git a/Master/texmf-dist/doc/generic/pst-math/pst-math-doc.tex b/Master/texmf-dist/doc/generic/pst-math/pst-math-doc.tex new file mode 100644 index 00000000000..aa40adde20e --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-math/pst-math-doc.tex @@ -0,0 +1,415 @@ +\documentclass[fleqn,10pt]{article} + +\usepackage{multicol} +\usepackage[a4paper,margin=1.5cm,includeheadfoot]{geometry} +\usepackage{fancyhdr} +\usepackage[baw,pstricks]{fvrb-ex} +\usepackage{pst-infixplot,pst-math} +\usepackage{amsmath,amssymb} +\usepackage{pstcol} +\makeatletter + +\renewcommand{\Begin@Example}{% +\parindent=0pt +\multiply\topsep by 2 \VerbatimEnvironment +\begin{VerbatimOut}[codes={\catcode`\£=12\catcode`\/=12\catcode`\&=12% + \catcode`\"=12}]{\jobname.tmp}} + +\renewcommand{\Below@Example}[1]{% +\VerbatimInput[gobble=0,commentchar=£,commandchars=/&",numbersep=3pt]% + {\jobname.tmp} +\catcode`\£=9\relax% +\NoHighlight@Attributes % To suppress possible highlighting +\ifFvrbEx@Grid\vspace{5pt}\fi +#1% +\ifFvrbEx@Grid\vspace{5pt}\fi +\par} + +\renewcommand{\SideBySide@Example}[1]{% +\@tempdimb=\FV@XRightMargin \advance\@tempdimb -5mm +\begin{minipage}[c]{\@tempdimb} + \fvset{xrightmargin=0pt} + \catcode`\£=9\relax% + \NoHighlight@Attributes % To suppress possible highlighting + #1 +\end{minipage}% +\@tempdimb=\textwidth \advance\@tempdimb -\FV@XRightMargin \advance\@tempdimb 5mm +\begin{minipage}[c]{\@tempdimb} + \VerbatimInput[gobble=0,commentchar=£,commandchars=/&",numbersep=3pt, + xleftmargin=5mm,xrightmargin=0pt]{\jobname.tmp} +\end{minipage}} + +% The \NoHighlight@Attributes from `hbaw' and `hcolors' packages +% must be modified too +\def\NoHighlight@Attributes{% +\catcode`\/=0\relax% +\catcode`\&=1\relax% +\catcode`\"=2\relax% +\def\HLa##1{##1}% +\def\HLb##1{##1}% +\def\HLc##1{##1}% +\def\HLd##1{##1}% +\def\HLe##1{##1}% +\def\HLf##1{##1}% +\def\HLBFa##1{##1}% +\def\HLBFb##1{##1}% +\def\HLBFc##1{##1}% +\def\HLBFd##1{##1}% +\def\HLBFe##1{##1}% +\def\HLBFf##1{##1}% +\def\HLITa##1{##1}% +\def\HLITb##1{##1}% +\def\HLITc##1{##1}% +\def\HLITd##1{##1}% +\def\HLITe##1{##1}% +\def\HLITf##1{##1}% +\def\HLCBBa##1{##1}% +\def\HLCBBb##1{##1}% +\def\HLCBBc##1{##1}% +\def\HLCBBd##1{##1}% +\def\HLCBBe##1{##1}% +\def\HLCBBf##1{##1}% +\def\HLCBBz##1{##1}% +\def\HLCBWa##1{##1}% +\def\HLCBWb##1{##1}% +\def\HLCBWc##1{##1}% +\def\HLCBWd##1{##1}% +\def\HLCBWe##1{##1}% +\def\HLCBWf##1{##1}% +\def\HLCBWz##1{##1}% +} + +\makeatother + +\fvset{numbers=none,frame=single,labelposition=topline,gobble=4} + +\DeclareRobustCommand\cs[1]{\texttt{\char`\\#1}} + +\newcommand{\MathPackage}{\textbf{`pst-math'}} + +\lhead{\MathPackage}\rhead{A PSTricks package for enhancing mathematical operators in PSTricks} +\pagestyle{fancy} + +\psset{subgriddiv=1,griddots=10}% +\showgrid + +\makeatletter + +\def\DefOfOperator{\@ifstar{\DefOfOperator@}{\DefOfOperator@@}} + +\def\DefOfOperator@#1#2#3#4{{\operator@font#1}:\left\{\begin{array}{ccc} #2&\to\\ +x&\mapsto\end{array}\right.} + +\def\DefOfOperator@@#1#2#3{{\operator@font#1}:\left\{\begin{array}{ccc} #2&\to\\ +x&\mapsto&{\operator@font#1}(x)\end{array}\right.} + +\makeatother + +\begin{document} + +\title{\MathPackage\\ A PSTricks package for enhancing mathematical operators in PSTricks\\ \normalsize ver. 0.2} +\author{Christophe \textsc{Jorssen} \texttt{<christophe.jorssen@libre.fr.invalid>}\\ \footnotesize `libre' is the french word for `free'} +\date{04/07/14} +\maketitle + +\setlength{\columnseprule}{0.6pt} +\begin{multicols}{2} +{\parskip 0pt \tableofcontents} +\end{multicols} + +\section{Trigonometry} + +\MathPackage{} introduces natural trigonometric postscript operators COS, SIN and TAN defined by +\[\DefOfOperator{cos}{\mathbb R}{[-1,1]}\] +\[\DefOfOperator{sin}{\mathbb R}{[-1,1]}\] +\[\DefOfOperator{tan}{\mathbb R\backslash\{k\frac{\pi}2,k\in\mathbb Z\}}{\mathbb R}\] +where $x$ is in \emph{radians}. TAN does \emph{not} produce PS error\footnote{TAN is defined with +Div PSTricks operator rather than with div PS operator.} when $x=k\frac{pi}{2}$. +\begin{center} +\begin{tabular}{c|c|c|c} + \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{COS}} & \textsf{\textsl{real}} & Return cosine of + \textsf{\textsl{num}} radians \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{SIN}} & \textsf{\textsl{real}} & Return sine of + \textsf{\textsl{num}} radians \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{TAN}} & \textsf{\textsl{real}} & Return tangent of + \textsf{\textsl{num}} radians +\end{tabular} +\end{center} + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \begin{pspicture}*(-5,-2)(5,2) + \SpecialCoor % For label positionning + \psaxes[labels=y,Dx=/HLCBWz&\pstPI2"]{->}% + (0,0)(-5,-2)(5,2) + \uput[-90](!/HLCBWz&PI" 0){$\pi$} + \uput[-90](!/HLCBWz&PI" neg 0){$-\pi$} + \uput[-90](!/HLCBWz&PI" 2 div 0){$\frac{\pi}2$} + \uput[-90](!/HLCBWz&PI" 2 div neg 0)% + {$-\frac{\pi}2$} + \psplot[linecolor=blue]{-5}{5}{x /HLCBWz&COS"} + \psplot[linecolor=red]{-5}{5}{x /HLCBWz&SIN"} + \psplot[linecolor=green]{-5}{5}{x /HLCBWz&TAN"} + \end{pspicture} +\end{SideBySideExample} + +\MathPackage{} introduces natural trigonometric postscript operators ACOS, ASIN and ATAN defined by +\[\DefOfOperator{acos}{[-1,1]}{[0,\pi]}\] +\[\DefOfOperator{asin}{[-1,1]}{[-\frac{\pi}2,\frac{\pi}2]}\] +\[\DefOfOperator{atan}{\mathbb R}{]-\frac{\pi}2,\frac{\pi}2[}\] + +\begin{center} +\begin{tabular}{c|c|c|c} + \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{ACOS}} & \textsf{\textsl{angle}} & Return arccosine of + \textsf{\textsl{num}} in radians \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{ASIN}} & \textsf{\textsl{angle}} & Return arcsine of + \textsf{\textsl{num}} in radians \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{ATAN}} & \textsf{\textsl{angle}} & Return arctangent of + \textsf{\textsl{num}} in radians \\ +\end{tabular} +\end{center} + +\textbf{Important :} ATAN is \emph{not} defined as PS operator atan. ATAN needs only \emph{one} +argument on the stack. + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \begin{pspicture}(-5,-2)(5,4) + \SpecialCoor % For label positionning + \psaxes[labels=x,Dy=/HLCBWz&\pstPI2"]{->}% + (0,0)(-5,-2)(5,4) + \uput[0](!0 /HLCBWz&PI"){$\pi$} + \uput[0](!0 /HLCBWz&PI" 2 div){$\frac{\pi}2$} + \uput[0](!0 /HLCBWz&PI" 2 div neg)% + {$-\frac{\pi}2$} + \psplot[linecolor=blue]{-1}{1}% + {x /HLCBWz&ACOS"} + \psplot[linecolor=red]{-1}{1}% + {x /HLCBWz&ASIN"} + \psplot[linecolor=green]{-5}{5}% + {x /HLCBWz&ATAN"} + \end{pspicture} +\end{SideBySideExample} + +\section{Hyperbolic trigonometry} + +\MathPackage{} introduces hyperbolic trigonometric postscript operators COSH, SINH and TANH defined +by +\[\DefOfOperator{cosh}{\mathbb R}{[1,+\infty[}\] +\[\DefOfOperator{sinh}{\mathbb R}{\mathbb R}\] +\[\DefOfOperator{tanh}{\mathbb R}{]-1,1[}\] +\begin{center} +\begin{tabular}{c|c|c|c} + \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{COSH}} & \textsf{\textsl{real}} & Return hyperbolic cosine of + \textsf{\textsl{num}} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{SINH}} & \textsf{\textsl{real}} & Return hyperbolic sine of + \textsf{\textsl{num}} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{TANH}} & \textsf{\textsl{real}} & Return hyperbolic tangent of + \textsf{\textsl{num}} +\end{tabular} +\end{center} + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \begin{pspicture}*(-5,-5)(5,5) + \psaxes{->}(0,0)(-5,-5)(5,5) + \psplot[linecolor=blue]{-5}{5}{x /HLCBWz&COSH"} + \psplot[linecolor=red]{-5}{5}{x /HLCBWz&SINH"} + \psplot[linecolor=green]{-5}{5}{x /HLCBWz&TANH"} + \end{pspicture} +\end{SideBySideExample} + +\MathPackage{} introduces reciprocal hyperbolic trigonometric postscript operators ACOSH, ASINH and +ATANH defined by +\[\DefOfOperator{acosh}{[1,+\infty[}{\mathbb R}\] +\[\DefOfOperator{asinh}{\mathbb R}{\mathbb R}\] +\[\DefOfOperator{atanh}{]-1,1[}{\mathbb R}\] +\begin{center} +\begin{tabular}{c|c|c|c} + \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{ACOSH}} & \textsf{\textsl{real}} & Return reciprocal hyperbolic cosine of + \textsf{\textsl{num}} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{ASINH}} & \textsf{\textsl{real}} & Return reciprocal hyperbolic sine of + \textsf{\textsl{num}} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{ATANH}} & \textsf{\textsl{real}} & Return reciprocal hyperbolic tangent of + \textsf{\textsl{num}} +\end{tabular} +\end{center} + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \begin{pspicture}(-5,-4)(5,4) + \psaxes{->}(0,0)(-5,-4)(5,4) + \psplot[linecolor=blue]{1}{5}% + {x /HLCBWz&ACOSH"} + \psplot[linecolor=red]{-5}{5}% + {x /HLCBWz&ASINH"} + \psplot[linecolor=green]{-.999}{.999}% + {x /HLCBWz&ATANH"} + \end{pspicture} +\end{SideBySideExample} + +\section{Other operators} + +\MathPackage{} introduces postscript operator EXP defined by +\[\DefOfOperator{exp}{\mathbb R}{\mathbb R}\] +\begin{center} +\begin{tabular}{c|c|c|c} + \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{EXP}} & \textsf{\textsl{real}} & Return exponential of + \textsf{\textsl{num}} +\end{tabular} +\end{center} + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \begin{pspicture}*(-5,-1)(5,5) + \psaxes{->}(0,0)(-5,-0.5)(5,5) + \psplot[linecolor=blue, + plotpoints=1000]{-5}{5}{x /HLCBWz&EXP"} + \end{pspicture} +\end{SideBySideExample} + +\MathPackage{} introduces postscript operator GAUSS defined by +\[\DefOfOperator*{gauss}{\mathbb R}{\mathbb R}{\displaystyle\frac{1}{\sqrt{2\pi\sigma^2}}\exp-\frac{(x-\overline x)^2}{2\sigma^2}}\] +\begin{center} +\begin{tabular}{c|c|c|c} + \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ + \hline + \textsf{\textsl{num}${}_1$} \textsf{\textsl{num}${}_2$} \textsf{\textsl{num}${}_3$} & + \textsf{\textbf{GAUSS}} & \textsf{\textsl{real}} & \parbox{4cm}{Return gaussian + of \textsf{\textsl{num}${}_1$} with mean \textsf{\textsl{num}${}_2$} and standart deviation \textsf{\textsl{num}${}_3$}} +\end{tabular} +\end{center} + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \psset{yunit=5} + \begin{pspicture}(-5,-.1)(5,1.1) + \psaxes{->}(0,0)(-5,-.1)(5,1.1) + \psplot[linecolor=blue, + plotpoints=1000]% + {-5}{5}{x 2 2 /HLCBWz&GAUSS"} + \psplot[linecolor=red, + plotpoints=1000]% + {-5}{5}{x 0 .5 /HLCBWz&GAUSS"} + \end{pspicture} +\end{SideBySideExample} + +\MathPackage{} introduces postscript operator SINC defined by +\[\DefOfOperator*{sinc}{\mathbb R}{\mathbb R}{\displaystyle\frac{\sin x}x}\] +\begin{center} +\begin{tabular}{c|c|c|c} + \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{SINC}} & \textsf{\textsl{real}} & Return cardinal sine of + \textsf{\textsl{num}} radians +\end{tabular} +\end{center} + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \psset{xunit=.25,yunit=3} + \begin{pspicture}(-20,-.5)(20,1.5) + \SpecialCoor % For label positionning + \psaxes[labels=y,Dx=/HLCBWz&\pstPI1"]{->}% + (0,0)(-20,-.5)(20,1.5) + \uput[-90](!/HLCBWz&PI" 0){$\pi$} + \uput[-90](!/HLCBWz&PI" neg 0){$-\pi$} + \psplot[linecolor=blue, + plotpoints=1000]{-20}{20}{x /HLCBWz&SINC"} + \end{pspicture} +\end{SideBySideExample} + +\MathPackage{} introduces postscript operator GAMMALN defined by +\[\DefOfOperator*{\ln\Gamma}{]0,+\infty[}{\mathbb R}{\ln\displaystyle\int_0^t t^{x-1}\mathrm e^{-t}\,\mathrm d t}\] +\begin{center} +\begin{tabular}{c|c|c|c} + \textbf{Stack} & \textbf{Operator} & \textbf{Result} & \textbf{Description} \\ + \hline + \textsf{\textsl{num}} & \textsf{\textbf{GAMMALN}} & \textsf{\textsl{real}} & Return logarithm of + $\Gamma$ function of \textsf{\textsl{num}} +\end{tabular} +\end{center} + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \begin{pspicture}(-.5,-.5)(6,6) + \psaxes{->}(0,0)(-.5,-.5)(6,6) + \psplot[linecolor=blue, + plotpoints=1000]{.1}{6}{x /HLCBWz&GAMMALN"} + \end{pspicture} +\end{SideBySideExample} + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \psset{xunit=.25,yunit=3} + \begin{pspicture}(-20,-.5)(20,1.5) + \psaxes[Dx=5,Dy=.5]{->}% + (0,0)(-20,-.5)(20,1.5) + \psplot[linecolor=blue, + plotpoints=1000]{-20}{20}% + {x /HLCBWz&BESSEL_J0"} + \psplot[linecolor=red, + plotpoints=1000]{-20}{20}% + {x /HLCBWz&BESSEL_J1"} + \end{pspicture} +\end{SideBySideExample} + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \psset{xunit=.5,yunit=3} + \begin{pspicture}*(-1.5,-.75)(19,1.5) + \psaxes[Dx=5,Dy=.5]{->}% + (0,0)(-1,-.75)(19,1.5) + \psplot[linecolor=blue, + plotpoints=1000]{0.0001}{20}% + {x /HLCBWz&BESSEL_Y0"} + \psplot[linecolor=red, + plotpoints=1000]{0.0001}{20}% + {x /HLCBWz&BESSEL_Y1"} + % \psplot[linecolor=green, + % plotpoints=1000]{0.0001}{20}% + % {x 2 /HLCBWz&BESSEL_Yn"} + \end{pspicture} +\end{SideBySideExample} + +\section{\texttt{Infix-RPN} and \texttt{pst-infixplot} support} + +You can now use the operators defined in \MathPackage{} with the infix notation, using the +\texttt{infix-RPN} package. The packages must be read in the fellowing order: + +\begin{Verbatim}[label={\LaTeX{} preamble}] + \usepackage{infix-RPN,pst-math} +\end{Verbatim} + +If you want to use \MathPackage{} with \texttt{pst-infixplot}, then read the packages in the +fellowing order: + +\begin{Verbatim}[label={\LaTeX{} preamble}] + \usepackage{pst-infixplot,pst-math} +\end{Verbatim} + +\begin{SideBySideExample}[xrightmargin=10.5cm] + \psset{xunit=.5,yunit=3} + \begin{pspicture}*(-1.5,-.75)(19,1.5) + \psaxes[Dx=5,Dy=.5]{->}% + (0,0)(-1,-.75)(19,1.5) + \psPlot[linecolor=red, + plotpoints=1000]{0.0001}{20}% + {BESSEL_Y0(x)-BESSEL_Y1(x)} + \end{pspicture} +\end{SideBySideExample} + +\section{Credits} + +Many thanks to Jacques L'helgoualc'h and Herbert Voss. + + +\end{document} diff --git a/Master/texmf-dist/doc/generic/pst-math/pst-math.pdf b/Master/texmf-dist/doc/generic/pst-math/pst-math.pdf Binary files differnew file mode 100644 index 00000000000..c05fee1491e --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-math/pst-math.pdf |