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authorKarl Berry <karl@freefriends.org>2006-01-11 23:51:58 +0000
committerKarl Berry <karl@freefriends.org>2006-01-11 23:51:58 +0000
commit798d600169392a065c68d8db9e3c59902086d6de (patch)
treef90e7716a2b9662fb33a31877115b93c3549d5e2 /Master/texmf-dist/source/latex/coordsys
parent82e14921eab1a3c28918c08088a8100535241645 (diff)
trunk/Master/texmf-dist/source/latex/coordsys
git-svn-id: svn://tug.org/texlive/trunk@202 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/source/latex/coordsys')
-rw-r--r--Master/texmf-dist/source/latex/coordsys/coordsys.dtx3260
-rw-r--r--Master/texmf-dist/source/latex/coordsys/coordsys.ins51
2 files changed, 3311 insertions, 0 deletions
diff --git a/Master/texmf-dist/source/latex/coordsys/coordsys.dtx b/Master/texmf-dist/source/latex/coordsys/coordsys.dtx
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--- /dev/null
+++ b/Master/texmf-dist/source/latex/coordsys/coordsys.dtx
@@ -0,0 +1,3260 @@
+% \iffalse
+% This is the coordsys package, coordsys.dtx
+% Copyright 2000--04 by Mogens Lemvig Hansen.
+%
+% Run first coordsys.ins then this file, coordsys.dtx,
+% through LaTeX and read the documentation in coordsys.dvi
+%
+% This program may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.2
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.2 or later is part of all distributions of LaTeX
+% version 2003/12/01 or later.
+%
+% This program consists of the files coordsys.dtx and coordsys.ins
+%
+%<*docdriver>
+\documentclass{ltxdoc}[1996/01/11]
+\usepackage{url,varioref,color,coordsys,logsys}
+\IfFileExists{eepic.sty}{\usepackage{epic,eepic}}{\relax}
+\CodelineIndex%\EnableCrossrefs
+\OnlyDescription
+\MakeShortVerb{\"}
+\makeatletter
+\newcommand{\nextlinelabel}[2][1]{\@bsphack
+ \@tempcnta\c@CodelineNo
+ \advance\@tempcnta#1\relax
+ \def\@currentlabel{\the\@tempcnta}\label{#2}%
+ \@esphack}
+\makeatother
+\begin{filecontents*}{parabola.put}
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+
+\begin{document} \DocInput{coordsys.dtx} \end{document}
+%</docdriver>
+% \fi
+% \CheckSum{2292}
+% \CharacterTable
+% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+% Digits \0\1\2\3\4\5\6\7\8\9
+% Exclamation \! Double quote \" Hash (number) \#
+% Dollar \$ Percent \% Ampersand \&
+% Acute accent \' Left paren \( Right paren \)
+% Asterisk \* Plus \+ Comma \,
+% Minus \- Point \. Solidus \/
+% Colon \: Semicolon \; Less than \<
+% Equals \= Greater than \> Question mark \?
+% Commercial at \@ Left bracket \[ Backslash \\
+% Right bracket \] Circumflex \^ Underscore \_
+% Grave accent \` Left brace \{ Vertical bar \|
+% Right brace \} Tilde \~}
+%
+% \def\fileversion{1.3} \def\filedate{2004/11/15} \def\docdate{\filedate}
+% \title{The \textsf{coordsys} and \textsf{logsys} Packages\thanks{This
+% file describes version \fileversion, \filedate.}}
+% \author{\copyright\ Mogens Lemvig Hansen\thanks{%
+% The \textsf{coordsys} and \textsf{logsys} packages are distributed under
+% the \LaTeX\ Project
+% Public License; please see Section~\ref{sec:license}.}\\
+% mlhansen@uniserve.com}
+% \date{\docdate}
+% \maketitle
+% \begin{abstract}
+% The \textsf{coordsys} package provides commands for typesetting
+% number lines (coordinate axes), coordinate systems, and grids
+% in the \textsf{picture} environment.
+% The \textsf{logsys} package extends the \textsf{coordsys} package by
+% providing logarithmic, semi-logarithmic, and double-logarithmic
+% coordinate systems and grids.
+% \end{abstract}
+%
+% \tableofcontents
+%
+% \section{Regular Coordinate Systems}
+% Load the \textsf{coordsys} package with the "\usepackage" command.
+% \begin{quote}
+% "\usepackage"\oarg{options}"{coordsys}"
+% \end{quote}
+% The \textsf{coordsys} package has three \meta{options},
+% \textsf{centred} (the default), \textsf{outside}, and \textsf{inside}, that
+% control the
+% appearance of tick marks; see Section~\ref{sec:tickstyle} on
+% page~\pageref{sec:tickstyle}.
+%
+% \subsection{One Dimension}
+% \DescribeMacro{\numbline}
+% The "\numbline" command typesets a number line. For example,
+% \begin{quote}
+% \begin{verbatim}
+% \begin{picture}(200,20)(-75,-15)
+% \numbline{-75}{125}
+% \end{picture}
+% \end{verbatim}
+% \begin{picture}(200,20)(-75,-15)
+% \numbline{-75}{125}
+% \end{picture}
+% \end{quote}
+% You should always use the "\numbline" command inside a
+% \textsf{picture} environment.
+% Do not forget to leave room for the labels on the number line.
+% In the following examples I omit the "\begin{picture}"
+% and "\end{picture}" commands to reduce clutter.
+%
+% The tick marks are by default separated by 10 units;
+% give "\numbline" an optional first argument to change that.
+% For example
+% \begin{quote}
+% \begin{verbatim}
+% \numbline[7]{-75}{125}
+% \end{verbatim}
+% \begin{picture}(200,20)(-75,-15)
+% \numbline[7]{-75}{125}
+% \end{picture}
+% \end{quote}
+%
+% \DescribeMacro{\numbline*}
+% The starred version of "\numbline" omits the labels.
+% \begin{quote}
+% \begin{verbatim}
+% \numbline*[7]{-75}{125}
+% \end{verbatim}
+% \begin{picture}(200,6)(-75,-3)
+% \numbline*[7]{-75}{125}
+% \end{picture}
+% \end{quote}
+%
+% Thus,
+% \begin{quote}
+% "\numbline"\oarg{spacing}\marg{from}\marg{to}\\
+% "\numbline*"\oarg{spacing}\marg{from}\marg{to}
+% \end{quote}
+% typeset\label{numblinesyntax} (horizontal) number lines
+% from \meta{from} to \meta{to} with
+% \meta{spacing}
+% units between the tick marks (the default is 10);
+% use the starred command to suppresses the labels.
+% All the arguments must be integers.
+%
+% \DescribeMacro{\vnumbline}\DescribeMacro{\vnumbline*}
+% The "\vnumbline" and "\vnumbline*" commands similarly
+% typeset vertical number lines.
+% \begin{quote}
+% "\vnumbline"\oarg{spacing}\marg{from}\marg{to}\\
+% "\vnumbline*"\oarg{spacing}\marg{from}\marg{to}
+% \end{quote}
+% The syntax is similar to that of the "\numbline" command
+% \vpageref[above]{numblinesyntax}.
+% \begin{quote}
+% \begin{minipage}{.2\linewidth}
+% \begin{picture}(20,100)(-17,20)
+% \vnumbline{20}{120}
+% \end{picture}
+% \end{minipage}
+% \qquad
+% \begin{minipage}{.6\linewidth}
+% \begin{verbatim}
+% \vnumbline{20}{120}
+% \end{verbatim}
+% \end{minipage}
+% \end{quote}
+%
+% \subsection{Two Dimensions}
+% \DescribeMacro{\coordsys}
+% Use the "\coordsys" command to typeset coordinate systems.
+% \begin{quote}
+% \begin{picture}(200,110)(-50,-50)
+% \coordsys(-50,-50)(150,60)
+% \put(75,25){\texttt{\textbackslash coordsys(-50,-50)(150,60)}}
+% \end{picture}
+% \end{quote}
+% \DescribeMacro{\coordsys*}
+% Thus,
+% \begin{quote}
+% "\coordsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\coordsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}
+% \end{quote}
+% typeset\label{coordsyssyntax} coordinate systems where
+% \parg{ll} is the lower-left corner
+% and \parg{ur} is the upper-right corner.
+% The optional argument \meta{h-spacing} gives the spacing between the
+% tick marks on the horizontal axis; the default is 10 units.
+% The optional argument \meta{v-spacing} gives the spacing between the
+% tick marks on the vertical axis; the default is to use the same
+% spacing as on the horizontal axis.
+% The starred version omits the labels.
+% All the arguments must be integers.
+%
+% Regular coordinate systems with intersecting axes are not always
+% appropriate, for example when the point $(0,0)$ is not in the range
+% of the coordinate system.
+% The \textsf{coordsys} package therefore provides some alternative
+% styles. All the coordinate-system-drawing commands have similar syntax.
+%
+% \DescribeMacro{\fcoordsys}\DescribeMacro{\fcoordsys*}
+% The "\fcoordsys" command typesets framed coordinate systems; that is, the
+% axes are at the left and bottom edges of the system.
+% \begin{quote}
+% "\fcoordsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\fcoordsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}
+% \end{quote}
+% The syntax is similar to that of the "\coordsys" command
+% \vpageref[above]{coordsyssyntax}.
+% \begin{quote}
+% \begin{picture}(220,125)(30,35)
+% \fcoordsys[5](50,50)(250,160)
+% \put(155,125){\texttt{\textbackslash fcoordsys[5](-50,-50)(150,60)}}
+% \end{picture}
+% \end{quote}
+%
+% \DescribeMacro{\bcoordsys}\DescribeMacro{\bcoordsys*}
+% The "\bcoordsys" command typesets boxed coordinate systems.
+% \begin{quote}
+% "\bcoordsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\bcoordsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}
+% \end{quote}
+% The syntax is similar to that of the "\coordsys" command
+% \vpageref[above]{coordsyssyntax}.
+% \begin{quote}
+% \begin{picture}(265,125)(-70,-65)
+% \bcoordsys[15][5](-50,-50)(195,60)
+% \put(-30,25){\texttt{\textbackslash bcoordsys[15][5](-50,-50)(195,60)}}
+% \end{picture}
+% \end{quote}
+%
+% \DescribeMacro{\window}\DescribeMacro{\window*}
+% The "\window" command typesets a plotting window as on a graphing
+% calculator.
+% \begin{quote}
+% "\window"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\window*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}
+% \end{quote}
+% The syntax is similar to that of the "\coordsys" command
+% \vpageref[above]{coordsyssyntax}.
+% \begin{quote}
+% \begin{picture}(302,127)(-107,-67)
+% \window(-50,-50)(195,60)
+% \put(15,25){\texttt{\textbackslash window(-50,-50)(195,60)}}
+% \end{picture}
+% \end{quote}
+% The labels will look nicer if you use the \textsf{amstext} package (which is
+% part of the \textsf{amsmath} package).
+%
+% \DescribeMacro{\coordgrid}
+% The "\coordgrid" command typesets a coordinate grid.
+% \begin{quote}
+% \begin{picture}(300, 125)
+% \coordgrid(0,0)(300,125)
+% \put(15,25){\texttt{\textbackslash coordgrid(0,0)(300,125)}}
+% \end{picture}
+% \end{quote}
+% The "\coordgrid" command does not print any labels
+% but you can superimpose a coordinate system.
+% \begin{quote}
+% \begin{verbatim}
+% \coordgrid[15][5](-50,-50)(195,60)
+% \coordsys[15][5](-50,-50)(195,60)
+% \end{verbatim}
+% \begin{picture}(245,110)(-50,-50)
+% \coordgrid[15][5](-50,-50)(195,60)
+% \coordsys[15][5](-50,-50)(195,60)
+% \end{picture}
+% \end{quote}
+% If you load the \textsf{color} package before the \textsf{coordsys}
+% package, the labels will be printed on a white background.
+%
+% Typesetting pretty grids with dotted lines is not easy.
+% If a grid does come out ugly, try to increase "\unitlength"
+% to allow for more dots between the lines.
+% You may also reduce the size of the dots;
+% see the "\gridstyle" command \vpageref[below]{gridstyle}.
+% \DescribeMacro{\coordgrid*}
+% Alternatively you can use the "\coordgrid*" command which
+% typesets a coordinate grid with solid lines. You could then use the
+% \textsf{color} package to colour the grid, say, gray; again, see
+% the "\gridstyle" command \vpageref[below]{gridstyle}.
+%
+% Thus,
+% \begin{quote}
+% "\coordgrid"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\coordgrid*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}
+% \end{quote}
+% typeset coordinate grids with a syntax similar to that of
+% the "\coordsys" command \vpageref[above]{coordsyssyntax}.
+% The starred version uses solid lines;
+% the un-starred version uses dotted lines.
+%
+% \DescribeMacro{\gridstyle}\label{gridstyle}
+% The default size of the dots is the with of "\thinlines"
+% and "\thicklines". If you intend to print your grids at a
+% sufficiently high resolution, you should reduce the size of the
+% dots by issuing a "\gridstyle" command. On my 600\,dpi printer,
+% these sizes look nice for points:
+% \begin{quote}
+% \begin{verbatim}
+% \gridstyle{\linethickness{0.24pt}}{\linethickness{0.48pt}}
+% \end{verbatim}
+% \gridstyle{\linethickness{0.24pt}}{\linethickness{0.48pt}}
+% \begin{picture}(245,110)(-50,-50)
+% \coordgrid[15][5](-50,-50)(195,60)
+% \coordsys[15][5](-50,-50)(195,60)
+% \end{picture}
+% \end{quote}
+% When I use solid lines, I can get away with half that,
+% \begin{quote}
+% \begin{verbatim}
+% \gridstyle{\linethickness{0.12pt}}{\linethickness{0.24pt}}
+% \end{verbatim}
+% \gridstyle{\linethickness{0.12pt}}{\linethickness{0.24pt}}
+% \begin{picture}(245,110)(-50,-50)
+% \coordgrid*[15][5](-50,-50)(195,60)
+% \coordsys[15][5](-50,-50)(195,60)
+% \end{picture}
+% \end{quote}
+%
+% If you make grids for the screen, I recommend using colour. For example,
+% \begin{quote}
+% \begin{verbatim}
+% \definecolor{gray}{gray}{0.5}
+% \definecolor{lightgray}{gray}{0.75}
+% \gridstyle{\thinlines\color{lightgray}}{\thinlines\color{gray}}
+% \coordgrid*(-109,-65)(200,100)
+% \coordsys(-109,-65)(200,100)
+% \end{verbatim}
+% \begin{picture}(245,110)(-50,-50)
+% \definecolor{gray}{gray}{0.5}
+% \definecolor{lightgray}{gray}{0.75}
+% \gridstyle{\thinlines\color{lightgray}}{\thinlines\color{gray}}
+% \coordgrid*[15][5](-50,-50)(195,60)
+% \coordsys[15][5](-50,-50)(195,60)
+% \end{picture}
+% \end{quote}
+%
+% In general,
+% \begin{quote}
+% "\gridstyle"\marg{thin declaration}\marg{thick declaration}
+% \end{quote}
+% Note that these are \emph{declarations}: the \meta{thin declarations}
+% apply also to the thick grid lines unless explicitly overruled by the
+% \meta{thick declaration}.
+% The current "\gridstyle" applies to all types of grids:
+% dotted, solid, regular, or logarithmic.
+% The default style is "\gridstyle{\thinlines}{\thicklines}".\label{defaultgridstyle}
+%
+%
+% \subsection{Bells and Whistles}
+% \subsubsection{Manual Labels}
+% \DescribeMacro{\sethlabel}\DescribeMacro{\setvlabel}
+% All the number-line and coordinate-system commands format the labels using
+% the commands "\sethlabel" (for labels on horizontal axes) and
+% "\setvlabel" (for labels on vertical axes). If you set labels manually,
+% you should use the same commands for a uniform appearance.
+% \begin{quote}
+% \begin{verbatim}
+% \numbline{-75}{125}
+% \put(125,0){\sethlabel{x}}
+% \end{verbatim}
+% \begin{picture}(200,20)(-75,-15)
+% \numbline{-75}{125}
+% \put(125,0){\sethlabel{x}}
+% \end{picture}
+% \end{quote}
+% The syntax is
+% \begin{quote}
+% "\sethlabel"\oarg{alignment}\marg{label}\\
+% "\setvlabel"\oarg{alignment}\marg{label}
+% \end{quote}
+% The \meta{label} is set in math mode.
+% The default \meta{alignment} is "[t]" for "\sethlabel" and
+% "[r]" for "\setvlabel". You may want to add to these defaults
+% (as in "\sethlabel[tl]"); you probably do not want to replace the
+% defaults.
+%
+% If you want your labels set in some other style, you must re-define
+% "\sethlabel" and "\setvlabel".
+%
+% \subsubsection{Thick Tick Density}
+% \DescribeMacro{\hthickratio}
+% \DescribeMacro{\vthickratio}
+% By default every fifth tick mark is thick. You can change that by
+% redefining
+% the commands "\hthickratio" and "\vthickratio".
+% \begin{quote}
+% \begin{verbatim}
+% \renewcommand{\hthickratio}{4}
+% \numbline[25]{0}{350}
+% \end{verbatim}
+% \setlength{\unitlength}{.3pt}
+% \begin{picture}(350,80)(0,-50)
+% \renewcommand{\hthickratio}{4}
+% \numbline[25]{0}{350}
+% \end{picture}
+% \end{quote}
+%
+% \subsubsection{Different Scales on the Two Axes}
+% \DescribeMacro{\rescaleby}
+% LaTeX\ (the \textsf{picture} environment) does not support different scales
+% on the two axes; "\unitlength" is used for both the
+% horizontal and the vertical direction.
+% However, you may create the \emph{appearance} of different scales by
+% scaling the labels on the axes.
+% Here is a coordinate system that has been rigged to contain the graph of
+% $y=x^2$ for $x$ between $-10$ and $10$.
+% \begin{quote}
+% \setlength{\unitlength}{5pt}
+% \rescaleby{10}{1}{\vlabel}
+% \begin{picture}(22,15)(-10,-3)
+% \coordsys[1](-10,0)(12,12)
+% \end{picture}
+% \begin{minipage}[b]{.5\linewidth}
+% \begin{verbatim}
+% \rescaleby{10}{1}{\vlabel}
+% \coordsys[1](-10,0)(12,12)
+% \end{verbatim}
+% \end{minipage}
+% \end{quote}
+% That is,
+% \begin{quote}
+% "\rescaleby"\oarg{opt}\marg{num}\marg{den}\marg{cmd}
+% \end{quote}
+% multiplies the labels by $\frac{\meta{num}}{\meta{den}}$;
+% both \meta{num} and \meta{den} should be positive integers.
+% If the optional argument is present, each label will also
+% be multiplied by \meta{opt} (which may be a non-integer).
+% The last argument, \meta{cmd}, must be one of "\hlabel"
+% or "\vlabel".
+%
+% The following coordinate system has been rigged for graphing $\sin$ or
+% $\cos$. Note that only that labels have been scaled;
+% the real coordinates of the small circle are still $(90,50)$.
+% \begin{quote}
+% \begin{verbatim}
+% \renewcommand{\hthickratio}{6}
+% \rescaleby[\pi]{1}{180}{\hlabel}
+% \rescaleby{1}{100}{\vlabel}
+% \coordsys[15][10](0,-100)(400,115)
+% \put(90,50){\circle{6}}
+% \end{verbatim}
+% \setlength{\unitlength}{.5pt}
+% \begin{picture}(435,215)(-35,-100)
+% \renewcommand{\hthickratio}{6}
+% \rescaleby[\pi]{1}{180}{\hlabel}
+% \rescaleby{1}{100}{\vlabel}
+% \coordsys[15][10](0,-100)(400,115)
+% \put(90,50){\circle{6}}
+% \end{picture}
+% \end{quote}
+%
+% \subsubsection{Different Styles of Tick Marks}
+% \label{sec:tickstyle}
+% \DescribeMacro{\tickstyle}
+% As you can affect the width of the dots or lines of a
+% "\coordgrid" with a "\gridstyle" command,
+% so you can affect the width of the tick marks with a
+% "\tickstyle" command:
+% \begin{quote}
+% "\tickstyle"\marg{thin declaration}\marg{thick declaration}
+% \end{quote}
+% Note that these are \emph{declarations}: the \meta{thin declarations}
+% apply also to the thick tick marks unless explicitly overruled by the
+% \meta{thick declaration}.\footnote{And the declarations that apply
+% to the thick tick marks spill over to the labels which maybe they
+% shouldn't, so let's not talk about that.}
+% The default style is
+% "\tickstyle{\thinlines}{\thicklines}".\footnote{When
+% I wrote \vpageref[above]{defaultgridstyle} that the default grid style is
+% \texttt{\textbackslash gridstyle\{\textbackslash thinlines\}\{\textbackslash
+% thicklines\}} I lied. The default grid style is the follow the current
+% \texttt{\textbackslash tickstyle}.}
+%
+% \DescribeMacro{\ticklength}
+% The "\ticklength" command controls the length of the tick marks.
+% \begin{quote}
+% \begin{verbatim}
+% \tickstyle{\thinlines\renewcommand{\ticklength}{4pt}}
+% {\thinlines\renewcommand{\ticklength}{8pt}}
+% \end{verbatim}
+% \tickstyle{\thinlines\renewcommand{\ticklength}{4pt}}
+% {\thinlines\renewcommand{\ticklength}{8pt}}
+% \begin{picture}(200,20)(-75,-15)
+% \numbline{-75}{125}
+% \end{picture}
+% \end{quote}
+% Note that the \emph{command} "\ticklength" must be changed with
+% "\renewcommand".
+%
+% If you prefer tick marks just on the outside of the coordinate axes, load
+% \textsf{coordsys} with the \textsf{outside} option.
+% \begin{quote}
+% \begin{verbatim}
+% \usepackage[outside]{coordsys}
+% \end{verbatim}
+% \makeatletter
+% \renewcommand{\vtickmark}{\makebox(0,0)[t]{\rule{\@wholewidth}{3pt}}}
+% \renewcommand{\htickmark}{\makebox(0,0)[r]{\rule{3pt}{\@wholewidth}}}
+% \makeatother
+% \begin{picture}(200,110)(-50,-50)
+% \coordsys(-50,-50)(150,60)
+% \end{picture}
+% \end{quote}
+%
+% Similarly, the \textsf{inside} option puts the tick marks on the inside of
+% the axes. The default option is \textsf{centred}.
+%
+%
+%
+% \section{Logarithmic Coordinate Systems}
+% Load the \textsf{logsys} package with the "\usepackage" command.
+% \begin{quote}
+% "\usepackage"\oarg{options}"{coordsys,logsys}"
+% \end{quote}
+% The \textsf{logsys} package supports the same options, \textsf{centred},
+% \textsf{outside}, and \textsf{inside}, as the \textsf{coordsys} package.
+%
+% \subsection{One Dimension}
+% \DescribeMacro{\logline}
+% The "\logline" command typesets a horizontal, logarithmic number line.
+% \begin{quote}
+% \begin{verbatim}
+% \logline{-60}{210}
+% \end{verbatim}
+% \begin{picture}(270,20)(-60,-15)
+% \logline{-60}{210}
+% \end{picture}
+% \end{quote}
+% The "\logline" command typesets only whole blocks of tick marks
+% (whole powers of $10$).
+% Making the axis long enough that the tick marks do not
+% collide with the arrow and yet not so long that it looks ridiculous is the
+% users responsibility.
+% The default distance between the thick tick marks (the powers of $10$) is
+% 50~units.
+% Therefore I made the axis above extend from $-60$ (a bit below $-50$ which
+% appears as $10^{-1} = \frac1{10}$) to $210$ (a bit above $200$ which appears
+% as $10^4$).
+%
+% \DescribeMacro{\logline*}
+% Thus,\label{loglinesyntax}
+% \begin{quote}
+% "\logline"\oarg{spacing}\marg{from}\marg{to}\\
+% "\logline*"\oarg{spacing}\marg{from}\marg{to}
+% \end{quote}
+% typeset horizontal, logarithmic number lines from \meta{from} to
+% \meta{to} with \meta{spacing} units between the powers of $10$; the default
+% is 50.
+% The starred version omits the labels.
+% All the arguments must be integers.
+%
+% The "\logline" command only typesets an axis; it does not change the
+% way \LaTeX\ and the \textsf{picture} environment interprets coordinates.
+% The equation below gives the relationship between the coordinate to
+% "\put", $x_p$, and the apparent coordinate, $x_a$.
+% \[
+% x_p = \meta{spacing} \log_{10} x_a.
+% \]
+% For example:
+% \begin{quote}
+% \begin{verbatim}
+% \logline[40]{-50}{210}
+% \put(87.04,10){\makebox(0,0)[b]{150}} % 40*log(150) = 87.04
+% \put(87.04,10){\vector(0,-1){10}}
+% \end{verbatim}
+% \begin{picture}(260, 40)(-50,-15)
+% \logline[40]{-50}{210}
+% \put(87.04,10){\makebox(0,0)[b]{150}} ^^A% 40*log(150) = 87.04
+% \put(87.04,10){\vector(0,-1){10}}
+% \end{picture}
+% \end{quote}
+%
+% \DescribeMacro{\vlogline}
+% \DescribeMacro{\vlogline*}
+% The vertical equivalent is "\vlogline":
+% \begin{quote}
+% "\vlogline"\oarg{spacing}\marg{from}\marg{to}\\
+% "\vlogline*"\oarg{spacing}\marg{from}\marg{to}
+% \end{quote}
+% The syntax is similar to that of the "\logline" command
+% \vpageref[above]{loglinesyntax}.
+%
+%
+% \subsection{Two Dimensions}
+% \DescribeMacro{\logsys}
+% Use the "\logsys" command to typeset logarithmic coordinate systems.
+% \begin{quote}
+% \begin{picture}(220,125)(-70,-65)
+% \logsys[5](-50,-50)(150,60)
+% \put(55,25){\texttt{\textbackslash logsys[5](-50,-50)(150,60)}}
+% \end{picture}
+% \end{quote}
+% \DescribeMacro{\logsys*}
+% Thus,
+% \begin{quote}
+% "\logsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\logsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}
+% \end{quote}
+% typeset coordinate systems with logarithmic vertical axis,
+% where \parg{ll} is the lower-left corner
+% and \parg{ur} is the upper-right corner.
+% The optional argument \meta{h-spacing} gives the spacing between the
+% tick marks on the horizontal axis; the default is 10 units.
+% The optional argument \meta{v-spacing} gives the spacing between the
+% thick tick marks (powers of $10$) on the vertical axis;
+% the default is 50 units.
+% The starred version omits the labels.
+% All the arguments must be integers.
+%
+% \DescribeMacro{\semilogsys}
+% Use the "\semilogsys" command to typeset semi-logarithmic
+% coordinate systems.
+% \begin{quote}
+% \begin{picture}(230,125)(-70,-65)
+% \semilogsys[25](-50,-50)(160,60)
+% \put(55,25){\texttt{\textbackslash semilogsys[25](-50,-50)(160,60)}}
+% \end{picture}
+% \end{quote}
+% \DescribeMacro{\semilogsys*}
+% Thus,
+% \begin{quote}
+% "\semilogsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\semilogsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}
+% \end{quote}
+% typeset coordinate systems with logarithmic horizontal axis,
+% where \parg{ll} is the lower-left corner
+% and \parg{ur} is the upper-right corner.
+% The optional argument \meta{h-spacing} gives the spacing between the
+% thick tick marks (powers of $10$) on the horizontal axis;
+% the default is 50 units.
+% The optional argument \meta{v-spacing} gives the spacing between the
+% tick marks on the vertical axis;
+% the default is 10 units.
+% The starred version omits the labels.
+% All the arguments must be integers.
+%
+% \DescribeMacro{\loglogsys}
+% Use the "\loglogsys" command to typeset double-logarithmic
+% coordinate systems.
+% \begin{quote}
+% \begin{picture}(230,125)(-70,-65)
+% \loglogsys(-50,-50)(160,60)
+% \put(55,25){\texttt{\textbackslash loglogsys(-50,-50)(150,60)}}
+% \end{picture}
+% \end{quote}
+% \DescribeMacro{\loglogsys*}
+% Thus,
+% \begin{quote}
+% "\loglogsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\loglogsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}
+% \end{quote}
+% typeset coordinate systems with two logarithmic axes,
+% where \parg{ll} is the lower-left corner
+% and \parg{ur} is the upper-right corner.
+% The optional argument \meta{h-spacing} gives the spacing between the
+% thick tick marks (powers of $10$) on the horizontal axis;
+% the default is 50 units.
+% The optional argument \meta{v-spacing} gives the spacing between the
+% thick tick marks (powers of $10$) on the vertical axis;
+% the default is 50 units.
+% The starred version omits the labels.
+% All the arguments must be integers.
+%
+% \DescribeMacro{\loggrid}
+% \DescribeMacro{\loggrid*}
+% \DescribeMacro{\semiloggrid}
+% \DescribeMacro{\semiloggrid*}
+% \DescribeMacro{\logloggrid}
+% \DescribeMacro{\logloggrid*}
+% The "\loggrid", "\loggrid*", "\semiloggrid",
+% "\semiloggrid*", "\logloggrid", and "\logloggrid*" commands
+% typeset logarithmic grids.
+% \begin{quote}
+% \begin{verbatim}
+% \logloggrid*(0,0)(300,100)
+% \end{verbatim}
+% \begin{picture}(300, 100)
+% \logloggrid*(0,0)(300,100)
+% \end{picture}
+% \end{quote}
+% Thus,
+% \begin{quote}
+% "\loggrid"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\loggrid*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\semiloggrid"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\semiloggrid*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\logloggrid"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\
+% "\logloggrid*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}
+% \end{quote}
+% typeset logarithmic, semi-logarithmic, and double-logarithmic
+% coordinate grids where \parg{ll} is the lower-left corner
+% and \parg{ur} is the upper-right corner.
+% The optional argument \meta{h-spacing} gives the spacing between the
+% vertical grid lines and
+% the optional argument \meta{v-spacing} gives the spacing between the
+% horizontal grid lines;
+% The default spacing is 10 units on linear axes and 50 units between the
+% thick tick marks (the powers of $10$) on logarithmic axes.
+% The starred versions use solid lines;
+% the un-starred versions use dotted lines.
+% All the arguments must be integers.
+%
+%
+% \section{Filling the Coordinate Systems}
+% The purpose of the \textsf{coordsys} and \textsf{logsys} packages
+% is to typeset coordinate systems, so maybe the package should end here.
+% However, I have had to write a bit of code to help me fill my
+% coordinate systems, so I'll share that.
+%
+% \subsection{Intervals}
+% \DescribeMacro{\interval}
+% The "\interval" command takes as argument an interval in standard notation
+% and draws it on the horizontal coordinate axis or number line.
+% \begin{quote}
+% \begin{verbatim}
+% \numbline{-15}{65}
+% \interval[-7.5,30)
+% \end{verbatim}
+% \begin{picture}(80,15)(-15,-12)
+% \numbline{-15}{65}
+% \interval[-7.5,30)
+% \end{picture}
+% \end{quote}
+% The interval can be open, half-open, or closed as in
+% $(a,b)$, $(a,b]$, $[a,b)$, and $[a,b]$\footnote{The notation
+% $\left]a,b\right[$ for open (or half-open) intervals is also
+% supported.} You can specify infinite intervals with "<" or ">".
+% \begin{quote}
+% \begin{verbatim}
+% \numbline{-15}{65}
+% \interval<-14,30[
+% \end{verbatim}
+% \begin{picture}(80,15)(-15,-12)
+% \numbline{-15}{65}
+% \interval<-14,30[
+% \end{picture}
+% \end{quote}
+% \DescribeMacro{\intervalthickness}
+% The "\intervalthickness" command sets the thickness of the fat line
+% that marks the interval.
+% An optional argument allows you to draw the fat line off centre.
+% \begin{quote}
+% \begin{verbatim}
+% \numbline{-15}{65}
+% \intervalthickness[0.5pt]{1pt}
+% \interval[-7.5,30]
+% \color{red}
+% \intervalthickness[-0.5pt]{1pt}
+% \interval(10,55>
+% \end{verbatim}
+% \begin{picture}(80,15)(-15,-12)
+% \numbline{-15}{65}
+% \intervalthickness[0.5pt]{1pt}
+% \interval[-7.5,30]
+% \color{red}
+% \intervalthickness[-0.5pt]{1pt}
+% \interval(10,55>
+% \end{picture}
+% \end{quote}
+% \DescribeMacro{\vinterval}
+% The "\vinterval" command similarly draws intervals on the vertical axis.
+% \begin{quote}
+% \begin{verbatim}
+% \fcoordsys[5](150,50)(350,160)
+% \interval[200,300]
+% \vinterval(75,150>
+% \end{verbatim}
+% \begin{picture}(220,125)(130,35)
+% \fcoordsys[5](150,50)(350,160)
+% \interval[200,300]
+% \vinterval(75,150>
+% \end{picture}
+% \end{quote}
+%
+% To sum up:
+% \begin{quote}
+% "\interval"\meta{L-delim}\meta{from}","\meta{to}\meta{R-delim}\\
+% "\vinterval"\meta{L-delim}\meta{from}","\meta{to}\meta{R-delim}\\
+% "\intervalthickness"\oarg{offset}\marg{width}
+% \end{quote}
+% Here \meta{L-delim} must be one of "[", "(", "<", or "]", and
+% \meta{R-delim} must be one of "]", ")", ">", or "[".
+% Both \meta{from} and \meta{to} are numbers, integers or
+% decimals\footnote{Due to implementation details, a decimal
+% must have at least one digit on either side of the decimal point.
+% Thus \texttt{0.5} is ok but \texttt{.5} is not.}
+% Both \meta{offset} and \meta{width} must be lengths.
+% The centre of the fat interval line will drawn \meta{offset} above the
+% horizontal axis or \meta{offset} to the right of the vertical axis.
+%
+%
+% \subsection{Curves}
+% For plotting curves I recommend the \textsf{epic} and
+% \textsf{eepic} packages.\footnote{Both are old \LaTeX209 packages that work
+% fine in \LaTeXe. The \textsf{eepic} package re-implements the \textsf{epic}
+% package making use of \textsc{PostScript}. The \textsf{eepic} package
+% works well with dvips and dvipdfm but not with pdf\LaTeX.}
+% I especially like \textsf{(e)epic}'s "\putfile" command which allows
+% you to calculate your plot with some external program, export the points to
+% plot to a text file, and import that file to have \LaTeX\ draw the plot.
+% For external program I use Maple.
+% The \textsf{coordsys} package includes a piece of
+% Maple code that exports a Maple plot in the form "\putfile" expects.
+% You can therefore take advantage of Maple adaptive plotting
+% algorithm\footnote{Maple cleverly calculates more points where the curve
+% wiggles.} in your \LaTeX\ plots.
+%
+% Here is how it works:
+% In Maple, read in the file \url{putfile} which is part of the
+% \textsf{coordsys} package.
+% \begin{verbatim}
+% > read "/where/you/placed/putfile";
+% \end{verbatim}
+% Make your plot, here $y=\frac{x^2}{10}$.
+% \begin{verbatim}
+% > plot( x^2/10, x=-10..10, title="x^2/10");
+% \end{verbatim}
+% When you are happy with your plot, assign it to a variable.
+% \begin{verbatim}
+% > P := %:
+% \end{verbatim}
+% Then use the "putfile" command to export the curve to the file
+% \url{parabola.put}.
+% \begin{verbatim}
+% > putfile( "parabola.put", P );
+% \end{verbatim}
+%
+% In \LaTeX, use the "\putfile" command to put "\picsquare"s at each
+% point listed in \url{parabola.put}.
+% \begin{quote}
+% \begin{verbatim}
+% \coordsys[1](-10,0)(11,11)
+% \putfile{parabola.put}{\picsquare}
+% \end{verbatim}
+% \ifx\putfile\undefined
+% You do not have the \textsf{epic} and \textsf{eepic} packages,
+% so \LaTeX\ cannot generate the result of the above commands.
+% \else
+% \setlength{\unitlength}{7pt}
+% \begin{picture}(21,13)(-10,-2)
+% \coordsys[1](-10,0)(11,11)
+% \putfile{parabola.put}{\picsquare}
+% \end{picture}
+% \fi
+% \end{quote}
+%
+% The \textsf{(e)epic} package provides an environment,
+% \textsf{drawjoin}, that joins all points set with the
+% special "\put" command "\jput".
+% Thus, to draw a curve with the "\putfile" command you enter a
+% \textsf{drawjoin} environment, let "\put" be a synonym for
+% "\jput", and call "\putfile".
+% \begin{quote}
+% \begin{verbatim}
+% \coordsys[1](-10,0)(11,11)
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{parabola.put}{\picsquare}
+% \end{drawjoin}
+% \end{verbatim}
+% \ifx\putfile\undefined
+% You do not have the \textsf{epic} and \textsf{eepic} packages,
+% so \LaTeX\ cannot generate the result of the above commands.
+% \else
+% \setlength{\unitlength}{7pt}
+% \begin{picture}(21,13)(-10,-2)
+% \coordsys[1](-10,0)(11,11)
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{parabola.put}{\picsquare}
+% \end{drawjoin}
+% \end{picture}
+% \fi
+% \end{quote}
+%
+% To draw a curve that requires (or looks best with) different scales on
+% the two axes, you can use the "scale" option to
+% "putfile" in Maple:
+% \begin{verbatim}
+% > plot( (x+2)*(x-1)*(x-2), x=-3..4 );
+% > putfile( "cubic.put", %, scale=[10, 1] );
+% \end{verbatim}
+% Now all the $x$-coordinates in "cubic.put" are $10$ times larger
+% than they should be. Thus re-scale the horizontal labels
+% by~$\frac{1}{10}$.
+% \begin{quote}
+% \begin{verbatim}
+% \rescaleby{1}{10}{\hlabel}
+% \coordsys[2](-30,-20)(40,36)
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{cubic.put}{\picsquare}
+% \end{drawjoin}
+% \end{verbatim}
+% \ifx\putfile\undefined
+% You do not have the \textsf{epic} and \textsf{eepic} packages,
+% so \LaTeX\ cannot generate the result of the above commands.
+% \else
+% \setlength{\unitlength}{2.3pt}
+% \begin{picture}(70,56)(-30,-20)
+% \rescaleby{1}{10}{\hlabel}
+% \coordsys[2](-30,-20)(40,36)
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{cubic.put}{\picsquare}
+% \end{drawjoin}
+% \end{picture}
+% \fi
+% \end{quote}
+%
+% Scaling can be necessary even when the two axes do use the same
+% scale. Consider the graph of $r=1+\sin\theta$ in polar coordinates. The
+% graph is $2.6$ units wide and $2.25$ units tall. All the arguments to the
+% "\coordsys" command must be integers, so the smallest distance between
+% tick marks is $1$ unit; the coordinate system will have very few tick marks.
+% Instead scale up by, say, a factor $100$.
+% In Maple:
+% \begin{verbatim}
+% > polarplot( 1+sin(theta), theta=0..2*Pi );
+% > putfile( "cardioid.put", %, scale=[100,100] );
+% \end{verbatim}
+% In \LaTeX:
+% \begin{quote}
+% \begin{verbatim}
+% \rescaleby{1}{100}{\hlabel}
+% \rescaleby{1}{100}{\vlabel}
+% \coordsys(-130,-25)(130,215)
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{cardioid.put}{\picsquare}
+% \end{drawjoin}
+% \end{verbatim}
+% \ifx\putfile\undefined
+% You do not have the \textsf{epic} and \textsf{eepic} packages,
+% so \LaTeX\ cannot generate the result of the above commands.
+% \else
+% \setlength{\unitlength}{0.5pt}
+% \begin{picture}(260,240)(-130,-25)
+% \rescaleby{1}{100}{\hlabel}
+% \rescaleby{1}{100}{\vlabel}
+% \coordsys(-130,-25)(130,215)
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{cardioid.put}{\picsquare}
+% \end{drawjoin}
+% \end{picture}
+% \fi
+% \end{quote}
+%
+% If the plot contains more than one curve, "putfile" generates
+% one file for each. You can of course specify multiple curves
+% directly, but they can also be the result of the "discont"
+% option to "plot".
+% \begin{verbatim}
+% > plot( csc(x), x=0..2*Pi, y=-10..10, discont=true );
+% > putfile( "csc.put", %, scale=[180/Pi, 10] );
+% \end{verbatim}
+% Here "putfile" wrote two files calling them "csc1.put"
+% and "csc2.put". These two curves must be drawn by different
+% \textsf{drawjoin} environments.
+% \begin{quote}
+% \begin{verbatim}
+% \renewcommand{\hthickratio}{3}
+% \rescaleby[\pi]{1}{180}{\hlabel}
+% \rescaleby{1}{10}{\vlabel}
+% \coordsys(0,-100)(360,115)
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{csc1.put}{\picsquare}
+% \end{drawjoin}
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{csc2.put}{\picsquare}
+% \end{drawjoin}
+% \end{verbatim}
+% \ifx\putfile\undefined
+% You do not have the \textsf{epic} and \textsf{eepic} packages,
+% so \LaTeX\ cannot generate the result of the above commands.
+% \else
+% \setlength{\unitlength}{0.5pt}
+% \begin{picture}(400,215)(-40,-100)
+% \renewcommand{\hthickratio}{3}
+% \rescaleby[\pi]{1}{180}{\hlabel}
+% \rescaleby{1}{10}{\vlabel}
+% \coordsys(0,-100)(360,115)
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{csc1.put}{\picsquare}
+% \end{drawjoin}
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{csc2.put}{\picsquare}
+% \end{drawjoin}
+% \end{picture}
+% \fi
+% \end{quote}
+%
+% For logarithmic plots scaling is almost always necessary. Consider the
+% graph of $y=\frac{1}{1+e^{-x}}$ for $x$ running from $-10$ to $10$.
+% The $y$-coordinates extend over five powers of $10$, so scale by $4$
+% to make it comparable to the range of $x$-coordinates.
+% \begin{verbatim}
+% > logplot(1/(1+exp(-x)), x=-10..10);
+% > putfile("logistic.put", %, scale=[1,4]);
+% \end{verbatim}
+% The "\rescaleby" command is not suitable for logarithmic axes.
+% Instead set the optional \meta{spacing} argument to the correct
+% distance between the powers of~$10$, in this case~$4$.
+% \begin{quote}
+% \begin{verbatim}
+% \logsys[1][4](-10,-20)(11,1)
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{logistic.put}{\picsquare}
+% \end{drawjoin}
+% \end{verbatim}
+% \ifx\putfile\undefined
+% You do not have the \textsf{epic} and \textsf{eepic} packages,
+% so \LaTeX\ cannot generate the result of the above commands.
+% \else
+% \setlength{\unitlength}{7pt}
+% \begin{picture}(25,23)(-14,-22)
+% \definecolor{gray}{gray}{0.5}
+% \definecolor{lightgray}{gray}{0.75}
+% \gridstyle{\linethickness{0.12pt}\color{lightgray}}%
+% {\linethickness{0.12pt}\color{gray}}
+% \loggrid*[1][4](-10,-20)(11,1)
+% \logsys[1][4](-10,-20)(11,1)
+% \color{red}
+% \begin{drawjoin}
+% \let\put=\jput
+% \putfile{logistic.put}{\picsquare}
+% \end{drawjoin}
+% \end{picture}
+% \fi
+% \end{quote}
+%
+% Use the "putfile" command as follows:
+% \begin{quote}
+% "putfile(" \meta{filename}"," \meta{PLOT structure} [","
+% \meta{options} ] ");"
+% \end{quote}
+% If \meta{filename} is a string and the \meta{PLOT structure} contains
+% more than one curve, "putfile" will append $1, 2, 3, \dots$ as needed;
+% "putfile" also appends an extension of ".tex" if the \meta{filename}
+% has no extension.
+% If the \meta{filename} is a list or set of filenames, they are used
+% as is. (So if you do not want "putfile" to meddle with your filename,
+% give it in a set.)
+%
+% The only possible option is
+% \begin{quote}
+% "scale" "=" "[" \meta{number}"," \meta{number} "]"
+% \end{quote}
+% The "putfile" command will multiply all $x$-coordinates by the first
+% number and all $y$-coordinates by the second number.
+% Both numbers must be "evalf"able.
+%
+% If you scale the coordinates of a curve, you must
+% of course compensate for that to get an honest
+% representation of your data in \LaTeX.
+% \begin{itemize}
+% \item If you scale a regular (linear) axis by, say,
+% "scale=[3/5,1]", you should use "\rescaleby{5}{3}{\hlabels}"
+% to re-scale the labels.
+%
+% \item If you scale a logarithmic axis by, say, "scale=[1,30]"
+% you should use the optional \meta{spacing} argument to
+% the command that draws the coordinate system, say
+% "\logsys[30]("\dots
+% \end{itemize}
+%
+%
+% \section{Installation}
+% Extract the \url{.sty} files from
+% the \url{.dtx} file by running \url:coordsys.ins: through \LaTeX.
+% Then generate the documentation for the \textsf{coordsys} and
+% \textsf{logsys} packages
+% by running the file \url:coordsys.dtx: through
+% \LaTeX---thrice to resolve cross references.\footnote{If you want an index,
+% you must run MakeIndex
+% (\texttt{makeindex -s gind.ist coordsys}) between the second and third
+% \LaTeX{} run.}
+%
+% You now have to decide what to do with several files.
+% \begin{itemize}
+% \item Move the files \url:coordsys.sty: and \url:logsys.sty: to some
+% directory where \LaTeX\ can find it;
+% \url:(local)texmf/tex/latex/misc: would be
+% the natural choice.
+% \item Move the documentation, \url:coordsys.dvi: or \url:coordsys.pdf:, to
+% \url:(local)texmf/doc/latex/misc:.
+% \item You may discard the source files, \url:coordsys.dtx: and
+% \url:coordsys.ins:, or store them in
+% \url:(local)texmf/source/latex/misc:.
+% \item If you ran \url{coordsys.dtx} through \LaTeX, several \url{.put}
+% were created. You can discard those.
+% \end{itemize}
+%
+%
+%
+% \section{License}\label{sec:license}
+% This program may be distributed and/or modified under the
+% conditions of the \LaTeX\ Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% \url;http://www.latex-project.org/lppl.txt;
+% and version 1.2 or later is part of all distributions of \LaTeX \
+% version 2003/12/01 or later.
+%
+% This program consists of the files \url:coordsys.dtx: and
+% \url:coordsys.ins:.
+%
+%
+% \section{Acknowledgements}
+% Thank you to Scott Pakin
+% (\url{pakin@uiuc.edu}) for his input on the implementation of Euclid's
+% algorithm.
+%
+% Thank you to Svend Daugaard Pedersen
+% (\url{Svend@DaugaardPedersen.dk})
+% for catching an error in the logarithmic systems
+% and for suggestions that led to "\gridstyle".
+%
+% Thank you to Staffan Lundberg who found an error in my understanding
+% of Maple's structured types and thus prompted me to polish the
+% Maple code for "pufile".
+%
+%
+% \StopEventually{
+% \PrintIndex
+% }
+%
+% \section{Implementation}
+%
+% \subsection{The \textsf{coordsys} Package}
+% \subsubsection{Identification}
+% First we must declare ourselves.
+% \begin{macrocode}
+%<*coordsys>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{coordsys}[2004/11/15 version 1.3]
+% \end{macrocode}
+%
+% \subsubsection{Declaration of Options}
+% \begin{macro}{\ticklength}
+% \begin{macro}{\vtickmark}
+% \begin{macro}{\htickmark}
+% The options define "\ticklength", "vtickmark", and
+% "\htickmark". First check that these three commands are not defined
+% elsewhere.
+% \begin{macrocode}
+\newcommand{\ticklength}{\relax}
+\newcommand{\vtickmark}{\relax}
+\newcommand{\htickmark}{\relax}
+% \end{macrocode}
+% The "\vtickmark" and "\htickmark" commands set the individual
+% ticks; "\vtickmark" sets vertical ticks on a horizontal axis,
+% and "\htickmark" sets horizontal ticks on a vertical axis.
+% "\@wholewidth" is the current line width,
+% that is, the width of "\thinlines" or "\thicklines".
+% \begin{macrocode}
+\DeclareOption{centred}{%
+ \def\vtickmark{\makebox(0,0){\rule{\@wholewidth}{\ticklength}}}%
+ \def\htickmark{\makebox(0,0){\rule{\ticklength}{\@wholewidth}}}%
+ \def\ticklength{6\p@}%
+}
+\DeclareOption{outside}{%
+ \def\vtickmark{\makebox(0,0)[t]{\rule{\@wholewidth}{\ticklength}}}%
+ \def\htickmark{\makebox(0,0)[r]{\rule{\ticklength}{\@wholewidth}}}%
+ \def\ticklength{3\p@}%
+}
+\DeclareOption{inside}{%
+ \def\vtickmark{\makebox(0,0)[b]{\rule{\@wholewidth}{\ticklength}}}%
+ \def\htickmark{\makebox(0,0)[l]{\rule{\ticklength}{\@wholewidth}}}%
+ \def\ticklength{3\p@}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+%
+% \subsubsection{Execution of Options}
+% The default option is \textsf{centred}.
+% \begin{macrocode}
+\ExecuteOptions{centred}
+\ProcessOptions
+% \end{macrocode}
+%
+% \subsubsection{Main Code}
+% \begin{macro}{\vgridfromto}
+% \begin{macro}{\hgridfromto}
+% The "\vgridfromto" and "\hgridfromto" commands typeset vertical
+% and horizontal dotted lines for the dotted coordinate grids.
+% \begin{quote}
+% "\vgridfromto"\marg{from}\marg{to}\\
+% "\hgridfromto"\marg{from}\marg{to}
+% \end{quote}
+% The dotted line is to run from ($y$- or $x$-coordinate) \meta{from} to ($y$-
+% or $x$-coordinate) \meta{to}. The two commands set the lines by means of
+% leaders in a box. The box is set at $y$- or $x$-coordinate zero and the
+% leaders extend to the right length by skipping back and forth. This way the
+% dots line up nicely in a predictable manner. When "\vgridfromto" or
+% "\hgridfromto" is called, "\coordsys@w" should contain the size
+% (height or width) of the box containing each dot.
+% \begin{macrocode}
+\newcommand{\vgridfromto}[2]{%
+ \vbox to \z@{\vskip -#2\unitlength
+ \leaders\vbox to \coordsys@w{\vss\hbox{\picsquare}\vss}
+ \vfill
+ \vskip #1\unitlength}}
+\newcommand{\hgridfromto}[2]{%
+ \hbox to \z@{\hskip #1\unitlength
+ \leaders\hbox to \coordsys@w{\hss\picsquare\hss}\hfill
+ \hskip-#2\unitlength}}
+% \end{macrocode}
+% \end{macro}\end{macro}
+% \begin{macro}{\vgridlength}
+% \begin{macro}{\hgridlength}
+% The "\vgriglength" and "\hgridlength" command typesets
+% solid vertical and horizontal lines.
+% \begin{quote}
+% "\vgridlength"\marg{length}\\
+% "\hgridlength"\marg{length}
+% \end{quote}
+% The line is to have length \meta{length} and is set at the left-hand or
+% bottom edge of the coordinate system.
+% \begin{macrocode}
+\newcommand{\vgridlength}[1]{\line(0,1){#1}}
+\newcommand{\hgridlength}[1]{\line(1,0){#1}}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\setvlabel}
+% \begin{macro}{\sethlabel}
+% The "\setvlabel" and "\sethlabel" commands typeset the labels on
+% the vertical and horizontal axes, respectively.
+% The "\setvlabel" command sets 5\,pt of space between the label and the
+% axis, which is about right, considering that the tick marks extend 3\,pt on
+% either side of the axis.
+% The "\sethlabel" command places the labels on a baseline 3\,pt plus
+% the current "\baselineskip" below the axis by means of a strut (a
+% zero-width rule).\nextlinelabel{cl:setlabels}
+% \begin{macrocode}
+\@ifpackageloaded{color}{%
+ \newcommand{\setvlabel}[2][r]{%
+ \makebox(0,0)[#1]{\colorbox{white}{$#2$}\hspace{5pt}}}
+ \newcommand{\sethlabel}[2][t]{%
+ \makebox(0,0)[#1]{%
+ \setlength{\@tempdimc}{3pt}%
+ \addtolength{\@tempdimc}{\baselineskip}%
+ \rule{0pt}{\@tempdimc}\colorbox{white}{$#2$}}}%
+}{% no colour
+ \newcommand{\setvlabel}[2][r]{%
+ \makebox(0,0)[#1]{$#2$\hspace{5\p@}}}
+ \newcommand{\sethlabel}[2][t]{%
+ \makebox(0,0)[#1]{%
+ \setlength{\@tempdimc}{3\p@}%
+ \addtolength{\@tempdimc}{\baselineskip}%
+ \rule{\z@}{\@tempdimc}$#2$}}%
+}% end if color package
+% \end{macrocode}
+% You may want to redefine "\setvlabel" and "\sethlabel" to present
+% the labels in a different way---use a smaller font, increase the distance to
+% the axes,\dots. Your redefined commands must take one optional and one
+% mandatory argument---the "\window" command uses the optional argument.
+% Do not assume that the mandatory argument is always a number---the
+% "\window" command uses "\setvlabel" and "\sethlabel" to
+% typeset the min\slash max labels.
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\hlabel}
+% \begin{macro}{\vlabel}
+% The "\hlabel" and "\vlabel" commands calculate the labels that
+% "\setvlabel" and "\sethlabel" typeset. The default definitions
+% of "\hlabel" and "\vlabel" do nothing, but you can redefine them
+% with the "\rescaleby" command.
+% \begin{macrocode}
+\newcommand{\hlabel}[1]{#1}%
+\newcommand{\vlabel}[1]{#1}%
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\rescaleby}
+% The "\rescaleby" command redefines it's fourth argument
+% (the third mandatory argument)
+% which should be either "\hlabel" or "\vlabel".
+% After
+% \begin{quote}
+% "\rescaleby"\oarg{opt}\marg{num}\marg{den}"{\hlabel}"
+% \end{quote}
+% the result of "\hlabel"\marg{x} should be
+% $\frac{\meta{num}\times \meta{x}}{\meta{den}} \meta{opt}$.
+% \begin{macrocode}
+\newcommand{\rescaleby}[4][]{\renewcommand{#4}[1]{{%
+ \count@=##1\relax
+ \ifnum\count@<0\count@=-\count@\fi
+ \ifnum\count@=0\relax
+ \@tempcntb=1\relax
+ \else
+ \multiply\count@ #2\relax
+ \@EuclidGCD{\count@}{#3}%
+ \count@=##1\relax
+ \multiply\count@ #2\relax
+ \divide\count@\@tempcnta
+ \@tempcntb=#3\relax
+ \divide\@tempcntb\@tempcnta
+ \fi
+% \end{macrocode}
+% We have reduced the fraction. Now print it nicely.
+% \begin{macrocode}
+ \ifnum\count@<0\relax
+ -%
+ \count@=-\count@
+ \fi
+ \def\coordsys@a{#1}%
+ \ifx\coordsys@a\@empty\relax
+ \ifnum\@tempcntb=1\relax
+ \the\count@
+ \else
+ \frac{\the\count@}{\the\@tempcntb}%
+ \fi
+ \else
+ \ifnum\@tempcntb=1\relax
+ \ifnum\count@=1\relax
+ \coordsys@a
+ \else
+ \the\count@\coordsys@a
+ \fi
+ \else
+ \ifnum\count@=1\relax
+ \frac{\coordsys@a}{\the\@tempcntb}%
+ \else
+ \frac{\the\count@}{\the\@tempcntb}\coordsys@a
+ \fi
+ \fi
+ \fi
+}}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\hthickratio}
+% \begin{macro}{\vthickratio}
+% By default every fifth tick mark is thick.
+% \begin{macrocode}
+\newcommand{\hthickratio}{5}
+\newcommand{\vthickratio}{5}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\text}
+% Hopefully the \textsf{amstext} package will override this very simple
+% "\text" command intended for subscripts only.
+% \begin{macrocode}
+\providecommand{\text}[1]{\mbox{\scriptsize #1}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\picsquare}
+% The "\picsquare" command typesets a square of size the current line
+% width---as in the \textsf{epic} package.
+% \begin{macrocode}
+\providecommand{\picsquare}{%
+ \makebox(0,0){\rule{\@wholewidth}{\@wholewidth}}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\count@}
+% \begin{macro}{\c@@coord}
+% \begin{macro}{\@tenpcnta}
+% \begin{macro}{\@tenpcntb}
+% \begin{macro}{\if@numbline}
+% We need three counters. \LaTeX\ inherits one, "\count@", from plain
+% \TeX\ and defines two more, "\@tempcnta" and "\@tempcntb".
+% We create a \LaTeX\ counter, "@coord",\nextlinelabel{cl:@coord} without
+% allocating a new counter
+% by making "\c@@coord" a synonym for "\count@"\footnote{I don't
+% quite understand why I bother do that; I copied the idea from Lamport's
+% \textsf{graphpap} package, which is where the \textsf{coordsys} package
+% began.}
+% The "\if" controls whether to set labels.
+% \begin{macrocode}
+\let\c@@coord\count@
+\newif\if@numbline
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro}
+%
+% \begin{macro}{\tickstyle}
+% \begin{macro}{\thin@ticks}
+% \begin{macro}{\thick@ticks}
+% The commands "\thin@ticks" and "\thick@ticks" store the style of
+% the tick marks. The "\tickstyle" command defines those two. The
+% default is "\thinlines" for the thin tick marks and "\thicklines"
+% for the thick tick marks.
+% \begin{macrocode}
+\newcommand{\tickstyle}[2]{%
+ \def\thin@ticks{#1}%
+ \def\thick@ticks{#2}}
+\tickstyle{\thinlines}{\thicklines}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+%
+% \begin{macro}{\@set@ticks}
+% The "\@set@ticks" command calculates the positions of the
+% tick marks.
+% \begin{quote}
+% "\@set@ticks"\marg{thickratio}\marg{spacing}^^A
+% \marg{from}\marg{to}\marg{tickfree}\marg{cmd}
+% \end{quote}
+% \begin{macro}{\coordsys@a}
+% \begin{macro}{\coordsys@b}
+% \begin{macro}{\coordsys@c}
+% The "\@set@ticks" command calculates three parameters:
+% "\coordsys@a" is the position of the first tick;
+% "\coordsys@b" is the number of ticks to set; and
+% "\coordsys@c" is the spacing between the ticks (that is,
+% \meta{spacing} for the thin ticks and $\meta{thickratio}\meta{spacing}$
+% for the thick ticks).
+% \end{macro}\end{macro}\end{macro}
+% Then "\@set@ticks" calls \meta{cmd} to actually set the ticks using
+% these parameters.\nextlinelabel{cl:BeginTickCalc}
+% \begin{macrocode}
+\newcommand{\@set@ticks}[6]{%
+ \thin@ticks
+ \edef\coordsys@c{#2}%
+% \end{macrocode}
+% First we must round \meta{from} up to a multiple of \meta{spacing}.
+% Knuth's implementation of integer division
+% always rounds toward zero,
+% so for negative \meta{from} we can simply divide and multiply
+% by \meta{spacing}. If \meta{from} is positive, we must play around a
+% little to round up instead of down.
+% \begin{macrocode}
+ \@tempcnta=#3\relax
+ \ifnum\@tempcnta>0\advance\@tempcnta -1\relax\fi
+ \divide\@tempcnta \coordsys@c\relax
+ \ifnum #3>0\advance\@tempcnta 1\relax\fi
+ \multiply\@tempcnta \coordsys@c\relax
+ \edef\coordsys@a{\the\@tempcnta}%
+% \end{macrocode}
+% Then we must calculate how many ticks to set.
+% To avoid collision between ticks and arrowheads,
+% there is to be no ticks in the last \meta{tickfree} length.
+% \begin{macrocode}
+ \@tempcntb=#4\relax
+ \advance\@tempcntb -\@tempcnta\relax
+ \setlength{\@tempdima}{\@tempcntb\unitlength}%
+ \addtolength{\@tempdima}{-#5}%
+ \ifdim\@tempdima<\z@\relax
+ \def\coordsys@b{0}%
+ \else
+ \divide\@tempdima\unitlength\relax
+ \divide\@tempdima\coordsys@c\relax
+ \@tempcntb=\@tempdima%
+ \advance\@tempcntb 1\relax%
+ \edef\coordsys@b{\the\@tempcntb}%
+ \fi
+ #6%
+% \end{macrocode}
+% \nextlinelabel[0]{cl:EndTickCalc}
+% Then the thick ticks.
+% This time the spacing is $\meta{thickratio}\meta{spacing}$, so calculate
+% that number
+% and store it in "\coordsys@c".
+% \begin{macrocode}
+ \thick@ticks
+ \@tempcntb=#1\relax
+ \multiply\@tempcntb \coordsys@c\relax
+ \edef\coordsys@c{\the\@tempcntb}%
+% \end{macrocode}
+% Calculate the position of the first (thick) tick as above.
+% \begin{macrocode}
+ \@tempcnta=#3\relax
+ \ifnum\@tempcnta>0\advance\@tempcnta -1\relax\fi
+ \divide\@tempcnta \coordsys@c\relax
+ \ifnum #3>0\advance\@tempcnta 1\relax\fi
+ \multiply\@tempcnta \coordsys@c\relax
+ \edef\coordsys@a{\the\@tempcnta}%
+% \end{macrocode}
+% Then calculate the number of \emph{thin} ticks
+% between the first thick tick ("\@tempcnta") and
+% \meta{to} less \meta{tickfree}, namely
+% $\left\lfloor\frac{\meta{to}-\meta{first}-\meta{tickless}}{\meta{spacing}}\right\rfloor+1$.
+% \begin{macrocode}
+ \@tempcntb=#4\relax
+ \advance\@tempcntb -\@tempcnta\relax
+ \setlength{\@tempdima}{\@tempcntb\unitlength}%
+ \addtolength{\@tempdima}{-#5}%
+ \ifdim\@tempdima<\z@\relax
+ \def\coordsys@b{0}%
+ \else
+ \divide\@tempdima\unitlength\relax
+ \divide\@tempdima#2\relax
+ \@tempcntb=\@tempdima%
+% \advance\@tempcntb 1\relax
+% \end{macrocode}
+% The number of thick ticks is then
+% $\left\lceil\frac{\meta{number of thin ticks}}{\meta{thickratio}}\right\rceil$.
+% \begin{macrocode}
+% \advance\@tempcntb -1\relax
+ \divide\@tempcntb #1\relax
+ \advance\@tempcntb 1\relax
+ \edef\coordsys@b{\the\@tempcntb}%
+ \fi
+ #6%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\numbline}
+% The "\numbline" command checks for a star,
+% \begin{macrocode}
+\newcommand{\numbline}{%
+ \@ifstar{\@numblinefalse\hnumbline@i}
+ {\@numblinetrue \hnumbline@i}}
+% \end{macrocode}
+% \begin{macro}{\hnumbline@i}
+% then "\hnumbline@i" picks up the optional argument,
+% \begin{macrocode}
+\newcommand{\hnumbline@i}[1][10]{\leavevmode\hnumbline@ii{#1}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\hnumbline@ii}
+% and "\hnumbline@ii" does the work:
+% Calculate the length of the arrow and set it, then call "\@set@ticks"
+% to set the tick marks. The extra set of braces localizes the
+% "\tickstyle" declarations.
+% \begin{macrocode}
+\newcommand{\hnumbline@ii}[3]{{\color@begingroup
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \put(#2,0){\vector(1,0){\coordsys@w}}%
+ \@set@ticks{\hthickratio}{#1}{#2}{#3}{6\p@}{
+ \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b\vtickmark}%
+% \end{macrocode}
+% Set the labels if we have to.
+% The parameters "\coordsys@a", "\coordsys@b", and
+% "\coordsys@c" that "\@set@ticks" calculated for the thick tick
+% marks are still available. In particular, "\coordsys@a" is the
+% position and, hence, the value of the first label.
+% \begin{macrocode}
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b{%
+ \edef\coordsys@a{\arabic{@coord}}%
+ \sethlabel{\hlabel{\coordsys@a}}%
+ \addtocounter{@coord}{\coordsys@c}}
+ \fi
+ \color@endgroup}%
+% \end{macrocode}
+% Finally store the vertical coordinate of the number line in
+% "\coordsys@w" for the sake of the "\interval" command.
+% \begin{macrocode}
+ \def\coordsys@w{0}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\vnumbline}
+% \begin{macro}{\vnumbline@i}
+% \begin{macro}{\vnumbline@ii}
+% The "\vnumbline" command and friends work in much the same way.
+% \begin{macrocode}
+\newcommand{\vnumbline}{%
+ \@ifstar{\@numblinefalse\vnumbline@i}
+ {\@numblinetrue \vnumbline@i}}
+\newcommand{\vnumbline@i}[1][10]{\leavevmode\vnumbline@ii{#1}}
+\newcommand{\vnumbline@ii}[3]{{\color@begingroup
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \put(0,#2){\vector(0,1){\coordsys@h}}%
+ \@set@ticks{\vthickratio}{#1}{#2}{#3}{6\p@}{%
+ \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b\htickmark}%
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b{%
+ \edef\coordsys@a{\arabic{@coord}}%
+ \setvlabel{\vlabel{\coordsys@a}}%
+ \addtocounter{@coord}{\coordsys@c}}
+ \fi
+ \color@endgroup}%
+ \def\coordsys@h{0}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+%
+% \begin{macro}{\coordsys}
+% All the coordinate-system drawing command use similar syntax, so we use a
+% unified approach for picking up the arguments.
+% The "\coordsys" command defines the temporary variable
+% "\coordsys@c" to be the name of the command that does the real work.
+% Then "\coordsys" checks for the presence of a star.
+% \begin{macrocode}
+\newcommand{\coordsys}{%
+ \def\coordsys@c{\coordsys@i}%
+ \@ifstar{\@numblinefalse\coordsys@args@i}
+ {\@numblinetrue \coordsys@args@i}}
+% \end{macrocode}
+% \begin{macro}{\coordsys@args@i}
+% \begin{macro}{\@hticksep}
+% The "\coordsys@args@i" command picks up the first optional argument
+% storing it
+% in "\@hticksep" so that we can use that variable as the default for the
+% second optional argument.
+% \begin{macrocode}
+\newcommand{\coordsys@args@i}[1][10]{\leavevmode
+ \def\@hticksep{#1}%
+ \coordsys@args@ii}
+% \end{macrocode}
+% \end{macro}\end{macro}
+% \begin{macro}{\coordsys@args@ii}
+% \begin{macro}{\@vticksep}
+% Then "\coordsys@args@ii" picks up the second optional argument,
+% \begin{macrocode}
+\newcommand{\coordsys@args@ii}[1][\@hticksep]{%
+ \def\@vticksep{#1}%
+ \coordsys@args@iii}
+% \end{macrocode}
+% \end{macro}\end{macro}
+% \begin{macro}{\coordsys@args@iii}
+% and the "\coordsys@args@iii" command picks up the first point and
+% brutally
+% replaces whatever the following may be with a "(". Since \TeX\ ignores
+% spaces when looking for an argument, this allows the user to leave a space
+% between the first and the second point.
+% \begin{macrocode}
+\def\coordsys@args@iii(#1,#2)#3{\coordsys@c{#1}{#2}(}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\coordsys@i}
+% Finally the real command, "\coordsys@c", that is "\coordsys@i",
+% picks up the second point (as well as the first), and gets to work:
+% First calculate the length of each axis and set it.
+% \begin{macrocode}
+\def\coordsys@i#1#2(#3,#4){{\color@begingroup
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \put(#1,0){\vector(1,0){\coordsys@w}}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \put(0,#2){\vector(0,1){\coordsys@h}}%
+% \end{macrocode}
+% Then set the tick marks on the horizontal axis.
+% \begin{macrocode}
+ \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{6\p@}{%
+ \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b\vtickmark}%
+% \end{macrocode}
+% This style of coordinate system has intersecting axes, so we must suppress
+% the label ``0''.
+% \begin{macrocode}
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b{%
+ \ifnum\value{@coord}=0\relax\else
+ \edef\coordsys@a{\arabic{@coord}}%
+ \sethlabel{\hlabel{\coordsys@a}}%
+ \fi
+ \addtocounter{@coord}{\coordsys@c}}%
+ \fi
+% \end{macrocode}
+% Then do the tick marks and labels on the vertical axis.
+% \begin{macrocode}
+ \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{6\p@}{%
+ \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b\htickmark}%
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b{%
+ \ifnum\value{@coord}=0\relax\else
+ \edef\coordsys@a{\arabic{@coord}}%
+ \setvlabel{\vlabel{\coordsys@a}}%
+ \fi
+ \addtocounter{@coord}{\coordsys@c}}%
+ \fi
+ \color@endgroup}%
+% \end{macrocode}
+% Finally store the location of the axis in "\coordsys@w" and "\coordsys@h"
+% for the sake of the "\interval" command.
+% \begin{macrocode}
+ \def\coordsys@w{0}%
+ \def\coordsys@h{0}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\fcoordsys}
+% \begin{macro}{\fcoordsys@i}
+% The "\fcoordsys" and "\fcoordsys@i" commands work much like
+% "\coordsys" and "\coordsys@i" above.
+% \begin{macrocode}
+\newcommand{\fcoordsys}{%
+ \def\coordsys@c{\fcoordsys@i}%
+ \@ifstar{\@numblinefalse\coordsys@args@i}
+ {\@numblinetrue \coordsys@args@i}}
+\def\fcoordsys@i#1#2(#3,#4){{\color@begingroup
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \put(#1,#2){\vector(1,0){\coordsys@w}}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \put(#1,#2){\vector(0,1){\coordsys@h}}%
+ \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{6\p@}{%
+ \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b\vtickmark}%
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b{%
+ \edef\coordsys@a{\arabic{@coord}}%
+ \sethlabel{\hlabel{\coordsys@a}}%
+ \addtocounter{@coord}{\coordsys@c}}%
+ \fi
+ \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{6\p@}{%
+ \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b\htickmark}%
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b{%
+ \edef\coordsys@a{\arabic{@coord}}%
+ \setvlabel{\vlabel{\coordsys@a}}%
+ \addtocounter{@coord}{\coordsys@c}}%
+ \fi
+ \color@endgroup}%
+ \def\coordsys@h{#1}%
+ \def\coordsys@w{#2}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\bcoordsys}
+% \begin{macro}{\bcoordsys@i}
+% The "\bcoordsys" and "\bcoordsys@i" commands work much like
+% "\coordsys" and "\coordsys@i" above.
+% \begin{macrocode}
+\newcommand{\bcoordsys}{%
+ \def\coordsys@c{\bcoordsys@i}%
+ \@ifstar{\@numblinefalse\coordsys@args@i}
+ {\@numblinetrue \coordsys@args@i}}
+\def\bcoordsys@i#1#2(#3,#4){{\color@begingroup
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \put(#1,#2){\line(1,0){\coordsys@w}}%
+ \put(#1,#4){\line(1,0){\coordsys@w}}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \put(#1,#2){\line(0,1){\coordsys@h}}%
+ \put(#3,#2){\line(0,1){\coordsys@h}}%
+ \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{\z@}{%
+ \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b\vtickmark}%
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b{%
+ \edef\coordsys@a{\arabic{@coord}}%
+ \sethlabel{\hlabel{\coordsys@a}}%
+ \addtocounter{@coord}{\coordsys@c}}%
+ \fi
+ \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{\z@}{%
+ \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b\htickmark}%
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b{%
+ \edef\coordsys@a{\arabic{@coord}}%
+ \setvlabel{\vlabel{\coordsys@a}}%
+ \addtocounter{@coord}{\coordsys@c}}%
+ \fi
+ \color@endgroup}%
+ \def\coordsys@h{#1}%
+ \def\coordsys@w{#2}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\window}
+% \begin{macro}{\window@i}
+% And yet another modification of the same old thing.
+% \begin{macrocode}
+\newcommand{\window}{%
+ \def\coordsys@c{\window@i}%
+ \@ifstar{\let\coordsys@a\phantom\coordsys@args@i}
+ {\let\coordsys@a\relax \coordsys@args@i}}
+\def\window@i#1#2(#3,#4){{%
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta-#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta-#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \put(#1,#2){\line(1,0){\coordsys@w}}%
+ \put(#1,#2){\line(0,1){\coordsys@h}}%
+ \put(#3,#4){\line(-1,0){\coordsys@w}}%
+ \put(#3,#4){\line(0,-1){\coordsys@h}}%
+% \end{macrocode}
+% Set the labels; "\ensuremath" for the sake of the
+% subscripts.
+% \begin{macrocode}
+ \put(#1,#2){\sethlabel[tl]%
+ {\ensuremath{x_{\text{min}}=\coordsys@a{#1}}}}%
+ \put(#3,#2){\sethlabel[tr]%
+ {\ensuremath{x_{\text{max}}=\coordsys@a{#3}}}}%
+ \put(#1,#2){\setvlabel[rb]%
+ {\ensuremath{y_{\text{min}}=\coordsys@a{#2}}}}%
+ \put(#1,#4){\setvlabel[rt]%
+ {\ensuremath{y_{\text{max}}=\coordsys@a{#4}}}}%
+% \end{macrocode}
+% If the axes are in the window, typeset them (without labels).
+% \begin{macrocode}
+ \ifnum #1<0\relax\ifnum #3>0\relax
+ \vnumbline*[\@vticksep]{#2}{#4}%
+ \fi\fi
+ \ifnum #2<0\relax\ifnum #4>0\relax
+ \numbline*[\@hticksep]{#1}{#3}%
+ \fi\fi
+ }%
+ \def\coordsys@h{#1}%
+ \def\coordsys@w{#2}%
+}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\gridstyle}
+% \begin{macro}{\grid@style}
+% The "\gridstyle" command defines "\grid@style" to issue a suitable
+% "\tickstyle" command at the proper time. The default
+% "\grid@style" is to do nothing---that is, use the current
+% "\tickstyle" unchanged.
+% \begin{macrocode}
+\newcommand{\gridstyle}[2]{\def\grid@style{\tickstyle{#1}{#2}}}
+\newcommand{\grid@style}{\relax}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\coordgrid}
+% The "\coordgrid" command chooses between the starred version,
+% "\coordgrid@ii", with solid lines and the un-starred version,
+% "\coordgrid@i", with dotted lines.
+% \begin{macrocode}
+\newcommand{\coordgrid}{%
+ \@ifstar{\def\coordsys@c{\coordgrid@ii}\coordsys@args@i}
+ {\def\coordsys@c{\coordgrid@i}\coordsys@args@i}}
+% \end{macrocode}
+% \begin{macro}{\coordgrid@i}
+% The "\coordgrid@i" command calls "\coordgrid@calc" to calculate
+% the size, "\coordsys@w", of the box containing each dot of the dotted
+% lines based on the values of "\@hticksep" and "\@vticksep". Then
+% set the dotted lines with "\@set@ticks".
+% \begin{macrocode}
+\def\coordgrid@i#1#2(#3,#4){{\color@begingroup
+ \coordgrid@calc
+ \grid@style
+ \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{\z@}{%
+ \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b
+ {\vgridfromto{#2}{#4}}}%
+ \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{\z@}{%
+ \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b
+ {\hgridfromto{#1}{#3}}}%
+ \color@endgroup}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\coordgrid@ii}
+% The "\coordgrid@ii" command is similar to "\fcoordsys@i" above.
+% \begin{macrocode}
+\def\coordgrid@ii#1#2(#3,#4){{\color@begingroup
+ \grid@style
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{\z@}{%
+ \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b
+ {\vgridlength{\coordsys@h}}}%
+ \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{\z@}{%
+ \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b
+ {\hgridlength{\coordsys@w}}}%
+ \color@endgroup}}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\coordgrid@calc}
+% To typeset pretty grids of dots the number of dots between lines must be an
+% integer. Thus, the number of dots must be a factor of the greatest common
+% divisor of "\@vticksep" and "\@hticksep". The "\@EuclidGCD"
+% command returns the $\gcd$ in the counter "\@tempcnta"
+% \begin{macrocode}
+\newcommand{\coordgrid@calc}{%
+ \@EuclidGCD{\@vticksep}{\@hticksep}%
+ \@tempdima=\unitlength
+ \multiply\@tempdima\@tempcnta
+% \end{macrocode}
+% Now "\@tempdima" is the longest length that fits an integer number of
+% times between lines. The dots should not be closer than 2\,pt.
+% \begin{macrocode}
+ \@tempdimb=2\p@\relax
+ \ifdim\@tempdima<\@tempdimb
+ \PackageWarning{coordsys}{The tick marks are too
+ close\MessageBreak for a pretty grid}%
+ \else
+% \end{macrocode}
+% However, "\@tempdima" may be able to contain multiple dots.
+% \begin{macrocode}
+ \divide\@tempdima \@tempdimb\relax
+ \@tempdimb=\unitlength
+ \multiply\@tempdimb\@tempcnta
+ \divide\@tempdimb\@tempdima
+ \fi
+% \end{macrocode}
+% In either case store the box size in "\coordsys@w".
+% \begin{macrocode}
+ \edef\coordsys@w{\the\@tempdimb}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\interval}
+% We use "\newcommand" to check that "\interval" is not already defined;
+% then we need plain \TeX's "\def" because "\interval" picks up its
+% arguments in a non-standard way.
+% \begin{macrocode}
+\newcommand{\interval}{}
+\def\interval#1#2,{%
+ \def\coordsys@a{#1}%
+ \def\coordsys@b{#2}%
+ \def\coordsys@c{}%
+% \end{macrocode}
+% Now "\coordsys@a" is the \meta{L-delim} and "\coordsys@b" is whatever follows
+% up to the first comma, that is \meta{from}.
+% Then define "\coordsys@a" to be the correct symbol suitably aligned
+% in a box. Note that the characters in \LaTeX's circle font are placed
+% rather peculiarly inside their bounding box.
+% \begin{macrocode}
+ \if\coordsys@a]\def\coordsys@a{(}\fi
+ \if\coordsys@a[%
+ \def\coordsys@a{%
+ \makebox[0.5\width][l]{\@circlefnt\char'163}}%
+ \else\if\coordsys@a(%
+ \def\coordsys@a{%
+ \makebox[0.5\width][l]{\@circlefnt\char'143}}%
+ \else\if\coordsys@a<%
+ \def\coordsys@a{%
+ \raisebox{-\fontdimen22\textfont2}{%
+ \makebox[\z@]{$<$}}}%
+ \else
+ \PackageError{coordsys}
+ {Bad delimiter}
+ {\string\interval\space expects [, (, <, or ] %
+ but got \coordsys@a}%
+ \def\coordsys@a{}%
+ \fi\fi\fi
+% \end{macrocode}
+% Picking up the \meta{from} was easy because we know the
+% number ends at the comma. But we do not know where the \meta{to} number ends.
+% \TeX\ knows how to read an integer, so do that and proceed with "\interv@l"
+% which picks up either the right-hand delimiter or a decimal point as its
+% first argument.
+% \begin{macrocode}
+ \afterassignment\interv@l\count@=}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\interv@l}
+% If we got a decimal point, store the integer part of the number in
+% "\coordsys@c" and try again.
+% \begin{macrocode}
+\newcommand{\interv@l}[1]{%
+ \if#1.%
+ \edef\coordsys@c{\the\count@.}%
+ \def\next{\afterassignment\interv@l\count@=}%
+% \end{macrocode}
+% Otherwise, append the number we just read to "\coordsys@c".
+% Now "\coordsys@c" contains \meta{to}. So calculate the
+% length (in~pt) of the interval.
+% \begin{macrocode}
+ \else
+ \edef\coordsys@c{\coordsys@c\the\count@}%
+ \setlength{\@tempdima}{\coordsys@b\unitlength}%
+ \setlength{\@tempdima}{-\@tempdima}%
+ \addtolength{\@tempdima}{\coordsys@c\unitlength}%
+% \end{macrocode}
+% Define "\coordsys@c" to be the correct symbol for the \meta{R-delim}.
+% \begin{macrocode}
+ \def\coordsys@c{#1}%
+ \if\coordsys@c[\def\coordsys@c{)}\fi
+ \if\coordsys@c]%
+ \def\coordsys@c{\mbox{%
+ \@circlefnt
+ \settowidth{\@tempdima}{\char'163}%
+ \hskip 0.5\@tempdima
+ \char'163%
+ \hskip -\@tempdima}%
+ }%
+ \else\if\coordsys@c)%
+ \def\coordsys@c{\mbox{%
+ \@circlefnt
+ \settowidth{\@tempdima}{\char'143}%
+ \hskip 0.5\@tempdima
+ \char'143%
+ \hskip -\@tempdima}%
+ }%
+ \else\if\coordsys@c>%
+ \def\coordsys@c{%
+ \raisebox{-\fontdimen22\textfont2}{%
+ \makebox[\z@]{$>$}}}%
+ \else
+ \PackageError{coordsys}
+ {Bad delimiter}
+ {\string\interval\space expects ], ), <, or [ %
+ but got \coordsys@c}%
+ \def\coordsys@c{}%
+ \fi\fi\fi
+% \end{macrocode}
+% Finally, "\put" the pieces down. Here "\coordsys@w" is the vertical
+% coordinate of the last typeset horizontal axis (usually~$0$),
+% and "\interval@line" is defined by "\intervalthickness" below.
+% \begin{macrocode}
+ \put(\coordsys@b,\coordsys@w){\makebox[\@tempdima][s]{%
+ \coordsys@a
+ \interval@line
+ \coordsys@c
+ }}%
+ \let\next=\ignorespaces
+ \fi
+ \next}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\vinterval}
+% \begin{macro}{\vinterv@l}
+% The "\vinterval" and "\vinterv@l" commands work as their horizontal cousins.
+% \begin{macrocode}
+\newcommand{\vinterval}{}
+\def\vinterval#1#2,{%
+ \def\coordsys@a{#1}%
+ \def\coordsys@b{#2}%
+ \def\coordsys@c{}%
+ \if\coordsys@a]\def\coordsys@a{(}\fi
+ \if\coordsys@a[%
+ \def\coordsys@a{\hbox to\z@{%
+ \@circlefnt
+ \settowidth{\@tempdima}{\char'163}%
+ \hskip 0.5\@tempdima minus 1fil
+ \char'163%
+ \hskip -0.5\@tempdima minus 1fil
+ \vrule width \z@ depth \z@ height 0.5\@tempdima
+ }}%
+ \else\if\coordsys@a(%
+ \def\coordsys@a{\hbox to\z@{%
+ \@circlefnt
+ \settowidth{\@tempdima}{\char'143}%
+ \hskip 0.5\@tempdima minus 1fil
+ \char'143%
+ \hskip -0.5\@tempdima minus 1fil
+ \vrule width \z@ depth \z@ height 0.5\@tempdima
+ }}%
+ \else\if\coordsys@a<%
+ \def\coordsys@a{\hbox to\z@{\hss
+ \raisebox{-\fontdimen22\textfont2}[\z@][\z@]{%
+ $\vee$}\hss}}%
+ \else
+ \PackageError{coordsys}
+ {Bad delimiter}
+ {\string\vinterval\space expects [, (, <, or ] %
+ but got \coordsys@a}%
+ \def\coordsys@a{}%
+ \fi\fi\fi
+ \afterassignment\vinterv@l\count@=}
+\newcommand{\vinterv@l}[1]{%
+ \if#1.%
+ \edef\coordsys@c{\the\count@.}%
+ \def\next{\afterassignment\interv@l\count@=}%
+ \else
+ \edef\coordsys@c{\coordsys@c\the\count@}%
+ \setlength{\@tempdima}{\coordsys@b\unitlength}%
+ \setlength{\@tempdima}{-\@tempdima}%
+ \addtolength{\@tempdima}{\coordsys@c\unitlength}%
+ \def\coordsys@c{#1}%
+ \if\coordsys@c[\def\coordsys@c{)}\fi
+ \if\coordsys@c]%
+ \def\coordsys@c{\hbox to\z@{%
+ \@circlefnt
+ \settowidth{\@tempdima}{\char'163}%
+ \hskip 0.5\@tempdima minus 1fil
+ \char'163%
+ \hskip -0.5\@tempdima minus 1fil
+ \vrule width \z@ depth 0.5\@tempdima height \z@
+ }}%
+ \else\if\coordsys@c)%
+ \def\coordsys@c{\hbox to\z@{%
+ \@circlefnt
+ \settowidth{\@tempdima}{\char'143}%
+ \hskip 0.5\@tempdima minus 1fil
+ \char'143%
+ \hskip -0.5\@tempdima minus 1fil
+ \vrule width \z@ depth 0.5\@tempdima height \z@
+ }}%
+ \else\if\coordsys@c>%
+ \def\coordsys@c{\hbox to\z@{\hss%
+ \raisebox{-\fontdimen22\textfont2}[\z@][\z@]{%
+ $\wedge$}\hss}}%
+ \else
+ \PackageError{coordsys}
+ {Bad delimiter}
+ {\string\vinterval\space expects ], ), <, or [ %
+ but got \coordsys@c}%
+ \def\coordsys@c{}%
+ \fi\fi\fi
+ \put(\coordsys@h,\coordsys@b){\vbox{%
+ \setlength{\baselineskip}{\z@}%
+ \setlength{\lineskip}{\z@}%
+ \settoheight{\@tempdimb}{\coordsys@a}%
+ \addtolength{\@tempdima}{-\@tempdimb}%
+ \settodepth {\@tempdimb}{\coordsys@c}%
+ \addtolength{\@tempdima}{-\@tempdimb}%
+ \coordsys@c
+ \vinterval@line
+ \coordsys@a
+ }}%
+ \let\next=\ignorespaces
+ \fi
+ \next}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\intervalthickness}
+% The "\intervalthickness" command defines the two commands "\interval@line"
+% and "\vinterval@line" that draw the thick line indicating the interval.
+% \begin{macrocode}
+\newcommand{\intervalthickness}[2][\z@]{%
+ \setlength{\@tempdima}{#2}%
+ \setlength{\@tempdima}{0.5\@tempdima}%
+ \setlength{\@tempdimb}{-\@tempdima}%
+ \addtolength{\@tempdima}{#1}%
+ \addtolength{\@tempdimb}{#1}%
+ \edef\coordsys@a{\the\@tempdima}%
+ \edef\coordsys@b{-\the\@tempdimb}%
+ \edef\interval@line{%
+ \leaders\hrule depth \coordsys@b height \coordsys@a\hss}%
+ \setlength{\@tempdima}{#2}%
+ \setlength{\@tempdima}{-0.5\@tempdima}%
+ \addtolength{\@tempdima}{#1}%
+ \edef\coordsys@a{\the\@tempdima}%
+ \edef\vinterval@line{%
+ \hbox to\z@{%
+ \hskip \coordsys@a
+ \vrule height\@tempdima width #2%
+ \hss
+ }%
+ }%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% Then a few defaults for "\interval" and "\vinterval".
+% \begin{macrocode}
+\intervalthickness{1.6\p@}
+\def\coordsys@w{0}
+\def\coordsys@h{0}
+%</coordsys>
+% \end{macrocode}
+%
+% \iffalse Don't document this fragment of code.
+% \begin{macrocode}
+%<*euclid>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{euclidgcd}[2004/11/15 version 1.3]
+\newcommand{\EuclidGCD}[2]{%
+ \@EuclidGCD{#1}{#2}%
+ \the\@tempcnta}
+%</euclid>
+% \end{macrocode}
+% \fi
+%
+% \begin{macro}{\@EuclidGCD}
+% The "\@EuclidGCD" command calculates the greatest common divisor
+% of two positive integers using Euclid's algorithm.\footnote{Euclid's
+% algorithm uses the fact that $\gcd(n, d) = \gcd(d, r)$, where $r$ is
+% the remainder after dividing $n$ by $d$. Since $r<d$, the second
+% $\gcd$ is easier to find. Repeat.}
+% After calling "\@EuclidGCD", the counter "\@tempcnta" contains the
+% $\gcd$.
+% \begin{macrocode}
+%<*coordsys|euclid>
+\newcommand{\@EuclidGCD}[2]{%
+ \@tempcnta=#1\relax
+ \@tempcntb=#2\relax
+ \loop
+ \count@=\@tempcntb
+ \divide\count@\@tempcnta
+ \multiply\count@\@tempcnta
+ \advance\count@ -\@tempcntb
+% \end{macrocode}
+% Now "\count@" is $-r$, where $r$ is the remainder after dividing
+% "\@tempcntb" by "\@tempcnta".
+% \begin{macrocode}
+ \ifnum\count@<0\relax
+ \@tempcntb=\@tempcnta
+ \@tempcnta=-\count@
+ \repeat
+}
+%</coordsys|euclid>
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{The \textsf{logsys} Package}
+% \subsubsection{Identification}
+% First we must declare ourselves.
+% \begin{macrocode}
+%<*logsys>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{logsys}[2004/11/15 version 1.3]
+% \end{macrocode}
+%
+% \subsubsection{Options}
+% Pass all options to \textsf{coordsys}.
+% \begin{macrocode}
+\DeclareOption{centred}{\PassOptionsToPackage{centred}{coordsys}}
+\DeclareOption{outside}{\PassOptionsToPackage{outside}{coordsys}}
+\DeclareOption{inside}{\PassOptionsToPackage{inside}{coordsys}}
+\ProcessOptions
+% \end{macrocode}
+%
+% \subsubsection{Package Loading}
+% The \textsf{logsys} package extends the \textsf{coordsys} package.
+% \begin{macrocode}
+\RequirePackage{coordsys}[2004/11/15]
+% \end{macrocode}
+%
+% \subsubsection{Main Code}
+% \begin{macro}{\loglabel}
+% The "\loglabel" command typesets logarithmic labels.
+% \begin{macrocode}
+\newcommand{\loglabel}[1]{%
+ \ifnum #1=-2\relax \frac{1}{100}%
+ \else\ifnum #1=-1\relax \frac{1}{10}%
+ \else\ifnum #1= 0\relax 1%
+ \else\ifnum #1= 1\relax 10%
+ \else\ifnum #1= 2\relax 100%
+ \else 10^{#1}%
+ \fi\fi\fi\fi\fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\v@logbox}
+% \begin{macro}{\h@logbox}
+% The "\v@logbox" and "\h@logbox" commands each typeset one block
+% of logarithmic tick marks. Each take two arguments: the size of a block and
+% the tick mark to typeset.
+% The glue in the boxes is (10000 times) $\log10-\log9$, $\log9-\log8$,
+% $\log8-\log7$, \dots, and $\log2-\log1$.
+% \begin{macrocode}
+\newcommand{\v@logbox}[2]{%
+ \vbox to #1\unitlength{%
+ \offinterlineskip
+ \vskip \z@ plus 458fil\relax
+ \vbox to \z@{\vss\hbox{#2}\vss}% 9
+ \vskip \z@ plus 512fil\relax
+ \vbox to \z@{\vss\hbox{#2}\vss}% 8
+ \vskip \z@ plus 580fil\relax
+ \vbox to \z@{\vss\hbox{#2}\vss}% 7
+ \vskip \z@ plus 669fil\relax
+ \vbox to \z@{\vss\hbox{#2}\vss}% 6
+ \vskip \z@ plus 792fil\relax
+ \vbox to \z@{\vss\hbox{#2}\vss}% 5
+ \vskip \z@ plus 969fil\relax
+ \vbox to \z@{\vss\hbox{#2}\vss}% 4
+ \vskip \z@ plus 1249fil\relax
+ \vbox to \z@{\vss\hbox{#2}\vss}% 3
+ \vskip \z@ plus 1761fil\relax
+ \vbox to \z@{\vss\hbox{#2}\vss}% 2
+ \vskip \z@ plus 3010fil\relax
+ }}
+\newcommand{\h@logbox}[2]{%
+ \hbox to #1\unitlength{%
+ \hskip \z@ plus 3010fill\relax
+ \hbox to \z@{\hss #2\hss}% 2
+ \hskip \z@ plus 1761fill\relax
+ \hbox to \z@{\hss #2\hss}% 3
+ \hskip \z@ plus 1249fill\relax
+ \hbox to \z@{\hss #2\hss}% 4
+ \hskip \z@ plus 969fill\relax
+ \hbox to \z@{\hss #2\hss}% 5
+ \hskip \z@ plus 792fill\relax
+ \hbox to \z@{\hss #2\hss}% 6
+ \hskip \z@ plus 669fill\relax
+ \hbox to \z@{\hss #2\hss}% 7
+ \hskip \z@ plus 580fill\relax
+ \hbox to \z@{\hss #2\hss}% 8
+ \hskip \z@ plus 512fill\relax
+ \hbox to \z@{\hss #2\hss}% 9
+ \hskip \z@ plus 458fill\relax
+ }}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\@sethlogticks}
+% In the linear case we got away with using one command, "\@set@ticks",
+% to calculate the positions of the tick marks on both horizontal and vertical
+% axes. The logarithmic case is more complicated, so we create separate
+% command for the horizontal and vertical case. This split then allows the
+% logarithmic commands to do more than just calculate the positions of the
+% ticks:
+% \begin{quote}
+% "\@sethlogticks"\marg{spacing}\marg{from}\marg{to}^^A
+% \marg{y0}\marg{tick}
+% \end{quote}
+% \emph{typesets} the logarithmic tick marks on a horizontal axis at
+% $y$-coordinate \meta{y0}. Moreover, it typesets the labels.
+%
+% The calculation is much like the calculation for thin tick marks in the
+% linear case; compare with code
+% lines~\ref{cl:BeginTickCalc}--\ref{cl:EndTickCalc}.
+% \begin{macrocode}
+\newcommand{\@sethlogticks}[5]{%
+ \thin@ticks
+ \@tempcnta=#2\relax
+ \ifnum\@tempcnta>0\advance\@tempcnta -1\relax\fi
+ \divide\@tempcnta #1\relax
+ \ifnum #2>0\advance\@tempcnta 1\relax\fi
+ \multiply\@tempcnta #1\relax
+ \edef\coordsys@a{\the\@tempcnta}%
+ \@tempcntb=#3\relax
+ \ifnum\@tempcnta<\@tempcntb\relax
+ \advance\@tempcntb -\@tempcnta\relax
+ \divide\@tempcntb #1\relax
+ \edef\coordsys@b{\the\@tempcntb}%
+ \multiput(\coordsys@a,#4)(#1,0)\coordsys@b
+ {\h@logbox{#1}{#5}}%
+% \end{macrocode}
+% In the linear case we took some measure against colliding tick marks and
+% arrow heads; in
+% the logarithmic case we leave that worry to the user\footnote{Because
+% calculating the position of individual logarithmic tick mark is difficult;
+% this code works by setting blocks of tick marks.}. Therefore we can (and
+% should) set one more thick tick mark than we have blocks.
+% \begin{macrocode}
+ \thick@ticks
+ \@tempcntb=\coordsys@b\relax
+ \advance\@tempcntb 1\relax
+ \edef\coordsys@b{\the\@tempcntb}%
+ \multiput(\coordsys@a,#4)(#1,0)\coordsys@b
+ {#5}%
+% \end{macrocode}
+% Then set the labels: First set the counter "@coord" to\footnote{The
+% calculation uses a horrible mixture of \LaTeX\ syntax and plain \TeX\ since
+% \LaTeX\ does not provide a division command. Maybe I should avoid the
+% \LaTeX\ style counter and just use plain \TeX. See the note to code
+% line~\ref{cl:@coord}.}
+% $\frac{\meta{from}}{\meta{spacing}}$, then step that counter by one.
+% \begin{macrocode}
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \divide\c@@coord #1\relax
+ \multiput(\coordsys@a,#4)(#1,0)\coordsys@b{%
+ \sethlabel{\loglabel{\arabic{@coord}}}%
+ \stepcounter{@coord}}%
+ \fi
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@setvlogticks}
+% The vertical version works in much the same way.
+% \begin{macrocode}
+\newcommand{\@setvlogticks}[5]{%
+ \thin@ticks
+ \@tempcnta=#2\relax
+ \ifnum\@tempcnta>0\advance\@tempcnta -1\relax\fi
+ \divide\@tempcnta #1\relax
+ \ifnum #2>0\advance\@tempcnta 1\relax\fi
+ \multiply\@tempcnta #1\relax
+ \edef\coordsys@a{\the\@tempcnta}%
+ \@tempcntb=#3\relax
+ \ifnum\@tempcnta<\@tempcntb\relax
+ \advance\@tempcntb -\@tempcnta\relax
+ \divide\@tempcntb #1\relax
+ \edef\coordsys@b{\the\@tempcntb}%
+ \multiput(#4,\coordsys@a)(0,#1)\coordsys@b
+ {\v@logbox{#1}{#5}}%
+ \thick@ticks
+ \@tempcntb=\coordsys@b\relax
+ \advance\@tempcntb 1\relax
+ \edef\coordsys@b{\the\@tempcntb}%
+ \multiput(#4,\coordsys@a)(0,#1)\coordsys@b
+ {#5}%
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \divide\c@@coord #1\relax
+ \multiput(#4,\coordsys@a)(0,#1)\coordsys@b{%
+ \setvlabel{\loglabel{\arabic{@coord}}}%
+ \stepcounter{@coord}}%
+ \fi
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\logline}
+% The "\logline" command checks for a star,
+% \begin{macrocode}
+\newcommand{\logline}{%
+ \@ifstar{\@numblinefalse\hlogline@i}
+ {\@numblinetrue \hlogline@i}}
+% \end{macrocode}
+% \begin{macro}{\hlogline@i}
+% then "\hlogline@i" picks up the optional argument,
+% \begin{macrocode}
+\newcommand{\hlogline@i}[1][50]{\leavevmode\hlogline@ii{#1}}
+% \end{macrocode}
+% \begin{macro}{\hlogline@ii}
+% and "\hlogline@ii" does the work---which isn't much since
+% "\@sethlogticks" does almost everything.
+% \begin{macrocode}
+\newcommand{\hlogline@ii}[3]{{\color@begingroup
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \put(#2,0){\vector(1,0){\coordsys@w}}%
+ \@sethlogticks{#1}{#2}{#3}{0}{\vtickmark}
+ \color@endgroup}%
+ \def\coordsys@w{0}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+%
+% \begin{macro}{\vlogline}
+% \begin{macro}{\vlogline@i}
+% \begin{macro}{\vlogline@ii}
+% The "\vlogline" command and friends work in much the same way.
+% \begin{macrocode}
+\newcommand{\vlogline}{%
+ \@ifstar{\@numblinefalse\vlogline@i}
+ {\@numblinetrue \vlogline@i}}
+\newcommand{\vlogline@i}[1][50]{\leavevmode\vlogline@ii{#1}}
+\newcommand{\vlogline@ii}[3]{{\color@begingroup
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \put(0,#2){\vector(0,1){\coordsys@h}}%
+ \@setvlogticks{#1}{#2}{#3}{0}{\htickmark}
+ \color@endgroup}%
+ \def\coordsys@h{0}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+%
+% \begin{macro}{\logsys}
+% The logarithmic coordinate system commands have different default values for
+% the optional arguments than their linear cousins. We therefore need a new
+% approach for picking up optional arguments.
+%
+% The "\logsys" command defines "\coordsys@c" to be the command that
+% eventually sets the coordinate system. Then "\logsys" define
+% "\@hticksep" and "\@vticksep" to be the default values for the
+% optional arguments. (Each logarithmic coordinate system type has a different
+% set of default values.) Then "\logsys" checks for a star and calls
+% "\logsys@args@i".
+% \begin{macrocode}
+\newcommand{\logsys}{%
+ \def\coordsys@c{\logsys@i}%
+ \def\@hticksep{10}%
+ \def\@vticksep{50}%
+ \@ifstar{\@numblinefalse\logsys@args@i}
+ {\@numblinetrue \logsys@args@i}}
+% \end{macrocode}
+% \begin{macro}{\logsys@args@i}
+% The "\logsys@args@i" command picks up the first optional argument
+% storing it in "\@hticksep" for later processing.
+% \begin{macrocode}
+\newcommand{\logsys@args@i}[1][\@hticksep]{\leavevmode
+ \edef\@hticksep{#1}%
+ \logsys@args@ii}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\logsys@args@ii}
+% Then "\logsys@args@ii" picks up the second optional argument and calls
+% the good old "\coordsys@args@iii" command to pick up (some of) the
+% remaining arguments.
+% \begin{macrocode}
+\newcommand{\logsys@args@ii}[1][\@vticksep]{%
+ \edef\@vticksep{#1}%
+ \coordsys@args@iii}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\logsys@i}
+% Finally "\logsys@i" sets the coordinate system:
+% First calculate the width and height of the system, then set the axes
+% and the tick marks and labels on the linear (horizontal) axis---all of it
+% much like "\fcoordsys@i" above.
+% \begin{macrocode}
+\def\logsys@i#1#2(#3,#4){{\color@begingroup
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \put(#1,#2){\vector(1,0){\coordsys@w}}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \put(#1,#2){\vector(0,1){\coordsys@h}}%
+ \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{6\p@}{%
+ \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b\vtickmark}%
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b{%
+ \edef\coordsys@a{\arabic{@coord}}%
+ \sethlabel{\hlabel{\coordsys@a}}%
+ \addtocounter{@coord}{\coordsys@c}}%
+ \fi
+% \end{macrocode}
+% Finally call "\@setvlogticks" to set the tick marks and labels on the
+% logarithmic (vertical) axis.
+% \begin{macrocode}
+ \@setvlogticks{\@vticksep}{#2}{#4}{#1}{\htickmark}%
+ \color@endgroup}%
+ \def\coordsys@h{#1}%
+ \def\coordsys@w{#2}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\semilogsys}
+% \begin{macro}{\semilogsys@i}
+% The "\semilogsys" and "\semilogsys@i" commands work in much the
+% same manner.
+% \begin{macrocode}
+\newcommand{\semilogsys}{%
+ \def\coordsys@c{\semilogsys@i}%
+ \def\@hticksep{50}%
+ \def\@vticksep{10}%
+ \@ifstar{\@numblinefalse\logsys@args@i}
+ {\@numblinetrue \logsys@args@i}}
+\def\semilogsys@i#1#2(#3,#4){{\color@begingroup
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \put(#1,#2){\vector(1,0){\coordsys@w}}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \put(#1,#2){\vector(0,1){\coordsys@h}}%
+ \@sethlogticks{\@hticksep}{#1}{#3}{#2}{\vtickmark}%
+ \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{6\p@}{%
+ \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b\htickmark}%
+ \if@numbline
+ \setcounter{@coord}{\coordsys@a}%
+ \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b{%
+ \edef\coordsys@a{\arabic{@coord}}%
+ \setvlabel{\vlabel{\coordsys@a}}%
+ \addtocounter{@coord}{\coordsys@c}}%
+ \fi
+ \color@endgroup}%
+ \def\coordsys@h{#1}%
+ \def\coordsys@w{#2}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\loglogsys}
+% \begin{macro}{\loglogsys@i}
+% The "\loglogsys" and "\loglogsys@i" commands work in much the
+% same manner.
+% \begin{macrocode}
+\newcommand{\loglogsys}{%
+ \def\coordsys@c{\loglogsys@i}%
+ \def\@hticksep{50}%
+ \def\@vticksep{50}%
+ \@ifstar{\@numblinefalse\logsys@args@i}
+ {\@numblinetrue \logsys@args@i}}
+\def\loglogsys@i#1#2(#3,#4){{\color@begingroup
+ \thinlines
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \put(#1,#2){\vector(1,0){\coordsys@w}}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \put(#1,#2){\vector(0,1){\coordsys@h}}%
+ \@sethlogticks{\@hticksep}{#1}{#3}{#2}{\vtickmark}%
+ \@setvlogticks{\@vticksep}{#2}{#4}{#1}{\htickmark}%
+ \color@endgroup}%
+ \def\coordsys@h{#1}%
+ \def\coordsys@w{#2}%
+}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\loggrid}
+% The "\loggrid" command is the obvious cross between "\logsys" and
+% "\coordgrid".
+% \begin{macrocode}
+\newcommand{\loggrid}{%
+ \def\@hticksep{10}%
+ \def\@vticksep{50}%
+ \@numblinefalse
+ \@ifstar{\def\coordsys@c{\loggrid@ii}\logsys@args@i}
+ {\def\coordsys@c{\loggrid@i}\logsys@args@i}}
+% \end{macrocode}
+% \begin{macro}{\loggrid@i}
+% Similarly, "\loggrid@i" is a cross between "\logsys@i" and
+% "\coordgrid@i",
+% \begin{macrocode}
+\def\loggrid@i#1#2(#3,#4){{\color@begingroup
+ \coordgrid@calc
+ \grid@style
+ \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{\z@}{%
+ \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b
+ {\vgridfromto{#2}{#4}}}%
+ \@setvlogticks{\@vticksep}{#2}{#4}{0}{\hgridfromto{#1}{#3}}%
+ \color@endgroup}}
+% \end{macrocode}
+% \end{macro}
+% \begin{macro}{\loggrid@ii}
+% and "\loggrid@ii" is a cross between "\logsys@i" and
+% "\coordgrid@ii".
+% \begin{macrocode}
+\def\loggrid@ii#1#2(#3,#4){{\color@begingroup
+ \grid@style
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{\z@}{%
+ \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b
+ {\vgridlength{\coordsys@h}}}%
+ \@setvlogticks{\@vticksep}{#2}{#4}{#1}{\hgridlength{\coordsys@w}}%
+ \color@endgroup}}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\semiloggrid}
+% \begin{macro}{\semiloggrid@i}
+% \begin{macro}{\semiloggrid@ii}
+% Semi-logarithmic grids provide no surprises,
+% \begin{macrocode}
+\newcommand{\semiloggrid}{%
+ \def\@hticksep{50}%
+ \def\@vticksep{10}%
+ \@numblinefalse
+ \@ifstar{\def\coordsys@c{\semiloggrid@ii}\logsys@args@i}
+ {\def\coordsys@c{\semiloggrid@i}\logsys@args@i}}
+\def\semiloggrid@i#1#2(#3,#4){{\color@begingroup
+ \coordgrid@calc
+ \grid@style
+ \@sethlogticks{\@hticksep}{#1}{#3}{0}{\vgridfromto{#2}{#4}}%
+ \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{\z@}{%
+ \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b
+ {\hgridfromto{#1}{#3}}}%
+ \color@endgroup}}
+\def\semiloggrid@ii#1#2(#3,#4){{\color@begingroup
+ \grid@style
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \@sethlogticks{\@hticksep}{#1}{#3}{#2}{\vgridlength{\coordsys@h}}%
+ \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{\z@}{%
+ \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b
+ {\hgridlength{\coordsys@w}}}%
+ \color@endgroup}}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% \begin{macro}{\logloggrid}
+% \begin{macro}{\logloggrid@i}
+% \begin{macro}{\logloggrid@ii}
+% and nor do double-logarithmic grids.
+% \begin{macrocode}
+\newcommand{\logloggrid}{%
+ \def\@hticksep{50}%
+ \def\@vticksep{50}%
+ \@numblinefalse
+ \@ifstar{\def\coordsys@c{\logloggrid@ii}\logsys@args@i}
+ {\def\coordsys@c{\logloggrid@i}\logsys@args@i}}
+\def\logloggrid@i#1#2(#3,#4){{\color@begingroup
+ \coordgrid@calc
+ \grid@style
+ \@sethlogticks{\@hticksep}{#1}{#3}{0}{\vgridfromto{#2}{#4}}%
+ \@setvlogticks{\@vticksep}{#2}{#4}{0}{\hgridfromto{#1}{#3}}%
+ \color@endgroup}}
+\def\logloggrid@ii#1#2(#3,#4){{\color@begingroup
+ \grid@style
+ \@tempcnta=#3\relax
+ \advance\@tempcnta -#1\relax
+ \edef\coordsys@w{\the\@tempcnta}%
+ \@tempcnta=#4\relax
+ \advance\@tempcnta -#2\relax
+ \edef\coordsys@h{\the\@tempcnta}%
+ \@sethlogticks{\@hticksep}{#1}{#3}{#2}{\vgridlength{\coordsys@h}}%
+ \@setvlogticks{\@vticksep}{#2}{#4}{#1}{\hgridlength{\coordsys@w}}%
+ \color@endgroup}}
+%</logsys>
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+%
+%
+% \subsection{The \texttt{putfile} Maple Code}
+% \begin{macrocode}
+%<*putfile>
+putfile := proc(fn::{string, list(string), set(string)},
+ P::specfunc(anything, PLOT) )
+ option `Copyright 2000-04 by Mogens Lemvig Hansen`;
+ description "version 1.0";
+ local L, fns, i, V, scl, FH, ttl, pt, path, ext;
+ global StringTools;
+% \end{macrocode}
+% Process the options.
+% \begin{macrocode}
+ L := [args[3..-1]];
+ if hasoption(L, 'scale', scl, 'L') then
+ scl := evalf(scl);
+ if not type(scl, ['numeric', 'numeric']) then
+ error "the scale option must be [numeric, numeric] but got %1",
+ scl;
+ fi;
+ else
+ scl := [1,1];
+ fi;
+ if L <> [] then
+ error "unknown options: %1", L;
+ fi;
+% \end{macrocode}
+% Pull the "CURVES" from the "PLOT" structure.
+% \begin{macrocode}
+ L := map( `putfile/grabcurves`, [op(P)] );
+% \end{macrocode}
+% If a single filename is given, we can construct a suitable list of filenames:
+% The path ends with the last backslash, slash, or colon in "fn";
+% the extension begins with the last period after that.
+% \begin{macrocode}
+ if type(fn, 'string') then
+ path := map(StringTools:-FirstFromRight, ["\\", "/", ":"], fn);
+ path := max(op(path));
+ ext := StringTools:-FirstFromRight(".", fn[path+1..-1]);
+% \end{macrocode}
+% If there is not extension, prepare to append
+% ".tex";\footnote{The extension \texttt{.tex} for these data files
+% may not be logical, but it is what \TeX\ assumes in the
+% \texttt{\bslash putfile} command, so at least we have consistent
+% assumptions.}
+% otherwise save and strip the extension.
+% \begin{macrocode}
+ if ext = 0 then
+ ext := ".tex";
+ fns := fn;
+ else
+ ext := fn[path+ext..-1];
+ fns := fn[1..-length(ext)-1]
+ fi;
+% \end{macrocode}
+% Multiply the filename if necessary, and append the extension.
+% \begin{macrocode}
+ if nops(L) = 1 then
+ fns := [fns];
+ else
+ fns := [ seq(cat(fns, i), i=1..nops(L)) ];
+ fi;
+ fns := map(cat, fns, ext);
+% \end{macrocode}
+% If we have a set or list or filenames, their number must match the number of
+% "CURVES".
+% \begin{macrocode}
+ else
+ fns := fn;
+ if nops(fns) <> nops(L) then
+ error "the number of filenames must match "
+ "the number of curves, "
+ "received %1 names but %2 curves.",
+ nops(fns), nops(L);
+ fi;
+ fi;
+% \end{macrocode}
+% Extract the view-port from the "PLOT" structure.
+% \begin{macrocode}
+ V := select(type, [op(P)], 'specfunc'('anything', 'VIEW'));
+ if nops(V) <> 1 then
+ V := ['DEFAULT', 'DEFAULT'];
+ else
+ V := [ op([1,1], V), op([1,2], V) ];
+ fi;
+ V := subs('DEFAULT'=Float(-infinity)..Float(infinity), V);
+% \end{macrocode}
+% Finally, extract the title, if any.
+% The title will be included as a comment.
+% Since the title could be a multi-line string, we must insert "%" characters
+% before any new-lines.
+% \begin{macrocode}
+ ttl := select(type, [op(P)], 'specfunc'('anything', 'TITLE'));
+ if nops(ttl) = 1 then
+ ttl := op([1,1], ttl);
+ ttl := StringTools:-SubstituteAll(ttl, "\n", "\n%% ");
+ fi;
+% \end{macrocode}
+% Fit the curves to the view-port, and scale as requested.
+% \begin{macrocode}
+ L := map( `putfile/cleancurve`, L, V);
+ L := map2( map, u->[scl[1]*u[1], scl[2]*u[2]], L );
+% \end{macrocode}
+% For each curve, write the title (if any), the view-port, and all the points to
+% the file.
+% \begin{macrocode}
+ for i from 1 to nops(L) do try
+ FH := fopen(fns[i], 'WRITE', 'TEXT');
+ if type(ttl, 'string') then fprintf(FH, "%%%% %s\n", ttl) fi;
+ if scl <> [1,1] then fprintf(FH, "%% scaled %a\n", scl) fi;
+ V := [ map2(op, 1, L[i]), map2(op, 2, L[i]) ];
+ V := map( u-> min(op(u))..max(op(u)), V );
+ fprintf(FH, "%% horizontal range: %f..%f\n", op(V[1]));
+ fprintf(FH, "%% vertical range: %f..%f\n", op(V[2]));
+ for pt in L[i] do
+ fprintf(FH, "%f \t%f\n", op(pt));
+ od;
+ finally fclose(FH);
+ end try end do;
+end;
+% \end{macrocode}
+%
+% The sub-routines that follow use Maple's naming convention for such.
+%
+% We are interested in "CURVES" objects in a "PLOT" structure.
+% A "CURVES" object contains options (which we ignore) and lists of
+% \meta{curve}s, where a \meta{curve} is a list of \meta{point}s and a
+% \meta{point} is a list of length two usually containing two numeric values.
+% If "x" is not a "CURVES", return nothing. If "x" is a
+% "CURVES", extract the list of \meta{curve}s and return the
+% corresponding sequence of \meta{curve}s. If the "PLOT" structure
+% contains more than one "CURVES" object, the sequences returned by
+% "putfile/grabcurves" will flatten to one sequence of \meta{curve}s
+% \begin{macrocode}
+`putfile/grabcurves` := proc(x)
+ option `Copyright 2000-04 by Mogens Lemvig Hansen`;
+ description "version 1.0";
+ local L;
+ if op(0, x) = 'CURVES' then
+ L := [ op(x) ];
+ L := select(type, L, 'list');
+ RETURN(op(L));
+ else
+ RETURN(NULL);
+ fi;
+end;
+% \end{macrocode}
+% Each curve has to be fitted inside the view-port.
+% The curve, "CC", is a list of points.
+% The view-port, "V", is a list of the form
+% \texttt{[numeric..numeric, numeric..numeric]}.
+% \begin{macrocode}
+`putfile/cleancurve` := proc(CC::list, V::list)
+ local C, B, pts, pt, m, i;
+ option `Copyright 2004 by Mogens Lemvig Hansen`;
+ description "version 1.0";
+% \end{macrocode}
+% Remove any non-numeric points.
+% \begin{macrocode}
+ C := select(type, CC, ['numeric', 'numeric']);
+ if nops(C) < 1 then error "no numeric points in %1", C fi;
+% \end{macrocode}
+% Then build a new list of point: each time a consecutive pair of points in
+% "C" straddles a boundary of the view-port, add the point of intersection
+% between the line through the two points and the view-port.
+% \begin{macrocode}
+ B := C[1];
+ for i from 2 to nops(C) do
+ if C[i] = C[i-1] then next fi;
+ pts := NULL;
+ if ( C[i-1][1] < lhs(V[1]) and C[i][1] > lhs(V[1]) )
+ or ( C[i-1][1] > lhs(V[1]) and C[i][1] < lhs(V[1]) ) then
+ m := ( C[i-1][2] - C[i][2] ) / ( C[i-1][1] - C[i][1] );
+ pt := lhs(V[1]);
+ pt := [ pt, m*(pt-C[i][1]) + C[i][2] ];
+ pts := pts, pt;
+ fi;
+ if ( C[i-1][1] < rhs(V[1]) and C[i][1] > rhs(V[1]) )
+ or ( C[i-1][1] > rhs(V[1]) and C[i][1] < rhs(V[1]) ) then
+ m := ( C[i-1][2] - C[i][2] ) / ( C[i-1][1] - C[i][1] );
+ pt := rhs(V[1]);
+ pt := [ pt, m*(pt-C[i][1]) + C[i][2] ];
+ pts := pts, pt;
+ fi;
+ if ( C[i-1][2] < lhs(V[2]) and C[i][2] > lhs(V[2]) )
+ or ( C[i-1][2] > lhs(V[2]) and C[i][2] < lhs(V[2]) ) then
+ m := ( C[i-1][1] - C[i][1] ) / ( C[i-1][2] - C[i][2] );
+ pt := lhs(V[2]);
+ pt := [ m*(pt-C[i][2]) + C[i][1], pt ];
+ pts := pts, pt;
+ fi;
+ if ( C[i-1][2] < rhs(V[2]) and C[i][2] > rhs(V[2]) )
+ or ( C[i-1][2] > rhs(V[2]) and C[i][2] < rhs(V[2]) ) then
+ m := ( C[i-1][1] - C[i][1] ) / ( C[i-1][2] - C[i][2] );
+ pt := rhs(V[2]);
+ pt := [ m*(pt-C[i][2]) + C[i][1], pt ];
+ pts := pts, pt;
+ fi;
+% \end{macrocode}
+% If the two points straddle more than one view-port boundary, we add one point
+% for each boundary. The order of the added points must be in the direction
+% of the curve.
+% \begin{macrocode}
+ pts := [pts];
+ if C[i-1][1] < C[i][1] then
+ pts := sort(pts, (u,v)->evab(u[1]<v[1]));
+ elif C[i-1][1] > C[i][1] then
+ pts := sort(pts, (u,v)->evab(u[1]>v[1]));
+ elif C[i-1][2] < C[i][2] then
+ pts := sort(pts, (u,v)->evab(u[2]<v[2]));
+ elif C[i-1][2] > C[i][2] then
+ pts := sort(pts, (u,v)->evab(u[2]>v[2]));
+ else
+ error "cannot happen";
+ fi;
+ B := B, op(pts), C[i];
+ od;
+ C := [B];
+% \end{macrocode}
+% Finally remove the point outside the view-port.
+% \begin{macrocode}
+ C := select( u->evalb(lhs(V[1])<=u[1] and u[1] <= rhs(V[1])), C);
+ C := select( u->evalb(lhs(V[2])<=u[2] and u[2] <= rhs(V[2])), C);
+ C;
+end;
+%</putfile>
+% \end{macrocode}
+%
+% \Finale
+%
diff --git a/Master/texmf-dist/source/latex/coordsys/coordsys.ins b/Master/texmf-dist/source/latex/coordsys/coordsys.ins
new file mode 100644
index 00000000000..439f205d738
--- /dev/null
+++ b/Master/texmf-dist/source/latex/coordsys/coordsys.ins
@@ -0,0 +1,51 @@
+% The coordsys and logsys packages, version 1.3.
+% Run first this file, coordsys.ins, then coordsys.dtx
+% through LaTeX and read the documentation in coordsys.dvi
+%
+\input docstrip.tex
+\preamble
+
+
+ This is the coordsys and logsys packages
+ Copyright 2000-04 by Mogens Lemvig Hansen,
+ mlhansen@uniserve.com
+
+This program may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3
+of this license or (at your option) any later version. The latest
+version of this license is in
+ http://www.latex-project.org/lppl.txt
+and version 1.2 or later is part of all distributions of LaTeX
+version 2003/12/01 or later.
+
+This program consists of the files coordsys.dtx and coordsys.ins
+
+\endpreamble
+\generate{\file{coordsys.sty} {\from{coordsys.dtx}{coordsys}}
+ \file{logsys.sty} {\from{coordsys.dtx}{logsys}}
+% \file{euclidgcd.sty}{\from{coordsys.dtx}{euclid}}
+ }
+
+{\catcode`\#=12\gdef\MetaPrefix{##}}
+\preamble
+
+
+ This is the coordsys and logsys packages
+ Copyright 2000-04 by Mogens Lemvig Hansen,
+ mlhansen@uniserve.com
+
+This program may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3
+of this license or (at your option) any later version. The latest
+version of this license is in
+ http://www.latex-project.org/lppl.txt
+and version 1.2 or later is part of all distributions of LaTeX
+version 2003/12/01 or later.
+
+This program consists of the files coordsys.dtx and coordsys.ins
+
+\endpreamble
+\nopostamble
+\generate{\file{putfile.} {\from{coordsys.dtx}{putfile}}
+ }
+\endbatchfile
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-25 21:42:04 +0000