\makeatletter %% PAGE PARAMETERS: \setlength{\parindent{0pt % paragraph indent \setlength{\parskip{4pt plus 1pt minus 1pt \setlength{\topmargin{-2.5pc \setlength{\headheight{12pt % height of running head \setlength{\headsep{30pt % distance between header and text \setlength{\textheight{54pc % height of text on page %% DATES, VERSIONS AND TITLES: \def\expanddate#1/#2/#3/{\year=19#1 \month=#2 \day=#3 \begingroup \expandafter\expanddate\filedate/ \xdef\thefiledate{\today \endgroup \date{Version \fileversion\\ \thefiledate \def\@maketitle{% \begin{center} {\Large\bf \ \vskip 1.2em {\lineskip .5em \begin{tabular[t]{c\ \vskip .8em {\@date% \end{center \par \vskip .5em %% PAGE STYLE: \pagestyle{myheadings \markright{Documentation for multido.tex \hfill v.\fileversion\hskip 1em \thefiledate\hfill% %% VERBATIM: \begingroup \catcode‘\{=12 \catcode‘\=12 \catcode‘\(=1 \catcode‘\)=2 \catcode‘\+=0 \catcode‘\\=12 +gdef+|(\) % \| = character \ +gdef+{({) % \{ = character { +gdef+() % \ = character +endgroup \def\Backslash{\protect\| %% Define some functional font commands: \def\MainFont{\tt % For macro definitions. \def\UsageFont{\tt % For in-line macro names. \def\InlineFont{\tt % For other in-line snipets of code. \def\MetaFont{\rm\it % For meta arguments. %% Short-cuts for font commands: \def\s#1{\string#1 \def\t#1{{\InlineFont\string#1 % For other in-line code. \def\m#1{{\MetaFont #1\/ % For just putting things in italics \def\M#1{{\InlineFont\{\m{#1\ % Arg is in italic, enclosed in tt braces. \let\N\t % For in-line macro names. \catcode‘\<=13 \def<#1>{\m{#1 % <meta> %% This is for listing macro definitions in a quote-like environment. \begingroup \catcode‘\[=1 \catcode‘\]=2 \catcode‘\{=13 \catcode‘\=12 \gdef\@MD[% \catcode‘\{=13 \catcode‘\=12 \def{##1[\{[\MetaFont ##1]\]] \endgroup \def\MD{% \quote \begingroup \@MD \def\end{\endgroup\end% \def\\{\@centercr\s% \MainFont \s \def\endMD{\endquote %% END PREAMBLE: \catcode‘\"=13 \def"{\verb" \catcode‘\1=2 \begin{document %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \title{Documentation for multido.tex:\\[2pt] A loop macro for Generic \protect\TeX \author{Timothy Van Zandt% \thanks{Author’s address: Department of Economics, Princeton University, Princeton, NJ 08544-1021, USA. Internet: {\tt tvz@Princeton.EDU \maketitle "multido.tex"/"multido.sty" contains the \N\multido\ macro, which is a loop facility for Generic TeX. This macro happens to be useful for drawing pictures, and was originally developed for the PSTricks package,\footnote{PSTricks is an extensive collection of PostScript-based macros for Generic TeX. It is available from the /pub directory at Princeton.EDU, and \TeX\ archives. but you can use it for other purposes as well. A special feature is support of fixed-point addition. For example, PSTricks uses the \N\multido\ to put numbers on axes, much like in the following \LaTeX\ example: \begin{verbatim \setlength{\unitlength{1cm \small \begin{picture(8,1)(0,-.5) \put(0,0){\vector(1,0){8 \multido{\i=0+1,\n=0+0.25{8{% \put(\i,-.1){\line(0,1){.2 \put(\i,-.2){\makebox(0,0)[t]{\n \end{picture \end{verbatim \begin{center \setlength{\unitlength{1cm \small \begin{picture(8,1)(0,-.5) \put(0,0){\vector(1,0){8 \multido{\i=0+1,\n=0+0.25{8{% \put(\i,-.1){\line(0,1){.2 \put(\i,-.2){\makebox(0,0)[t]{\n \end{picture \end{center The general syntax for \N\multido\ is: \begin{MD \multido{variables{repetitions{stuff \end{MD <stuff> is whatever you want repeated; it can be any balanced \TeX\ input. <repetitions> is the number times <stuff> is repeated. The first argument is the interesting one. <variables> is a comma-separated list of variable declarations.\footnote{Don’t use commas to mark the decimal point within the \protect<variables> argument, as they will be confused for delimiters. Each variable declaration is of the form: \begin{center\tt <variable> = <initial value> + <increment> \end{center <variable> is a command sequence that can be used in <stuff>. It is initially set to <initial value>, and is then incremented by <increment> with each repetition. The first letter of the variable name determines the variable type. There are four variable types: \begin{description \item[Dimension (d or D)] The initial value and the increment should be dimensions (lengths, in \LaTeX\ parlance). The substitution text is a dimension, with "sp" units. E.g., "\dx=4cm+5pt".\footnote{For PSTricks users, the unit is optional. \item[Number (n or N)] The initial value and increment should be integers or numbers with the same number of digits to the right of the decimal. The one exception is that it is always OK for the initial value to be an integer. There can be at most 8 digits on each side of the decimal. The substitution text is a number, with fixed-point addition. E.g., "\n=3+7.05", "\Nx=5.30+-1.25". \item[Integer (i or I)] The initial value and increment should be integers. This gives the same result as using a number variable, but it is faster. E.g., "\I=2+-1". \item[Real (r or R)] The initial value and increment should be integers or numbers with at most 4 digits on each side of the decimal. The substitution text is a number, but with floating point addition and occasional small errors. This gives a less satisfactory result than using a number variable, but it is faster. E.g., "\ry=4.2+1.05". \end{description Here are some examples that illustrate how the substitution text is determined: \begin{quote "\multido{{10{\TeX\ "\\[3pt] \hbox to 2em{\multido{{10{\TeX\ {\\[8pt] "\multido{\d=2pt+3pt{5{\d, "\\[3pt] \hbox to 2em{\multido{\d=2pt+3pt{5{\d, {\\[8pt] "\multido{\n=2+3{10{\n, "\\[3pt] \hbox to 2em{\multido{\n=2+3{10{\n, {\\[8pt] "\multido{\i=2+-3{10{\i, "\\[3pt] \hbox to 2em{\multido{\i=2+-3{10{\i, {\\[8pt] "\multido{\r=2+3.05{6{\r, "\\[3pt] \hbox to 2em{\multido{\r=2+3.05{6{\r, {\\[8pt] "\multido{\n=2.00+-3.05{8{\n, "\\[3pt] \hbox to 2em{\multido{\n=2.00+-3.05{8{\n, { \end{quote Here are some details about the choice of names: \begin{itemize \item Your computer won’t explode if you use names that conflict with \TeX\ internal commands, but you might want to check name conflicts if you get inexplicable errors. The command \N\MultidoCheckNames\ can be useful in this case. It causes \N\multido\ to report an error whenever you use a variable name that is already defined. But see the next item. \item The whole \N\multido\ loop is grouped. This means, e.g., that although "\i" is a Plain \TeX\ command sequence (giving a dotless “\i”), you can use the variable "\i" if you do not use any dotless i’s in <stuff> (and if you do not use \N\MultidoCheckNames). \end{itemize Here are a few more details: \begin{itemize \item \N\Multido\ commands can be nested. \item Spaces after a \N\multido\ command are ignored. This makes \N\multido\ more hospitable for pictures. \item Spaces between the various parts of the <variables> argument are ignored. \end{itemize And finally here a few special features, some of which are of interest mainly macro writers and other \TeX nicians: \begin{itemize \item The material that is repeated is not grouped, so that you can insert your own recursive routines. \item There is a variant, "\mmultido", which works just like "\multido" except that the variables are all incremented once before starting. \item If you use "\Multido" or "\MMultido" instead of "\multido" or "\mmultido", resp., then the whole loop is not grouped. This can be useful, e.g., for making entries in an alignment environment. However, these cannot be nested within any "\multido" macro. \item If the number of repetitions is a negative number, the variables are incremented backwards. \item The count register "\multidocount" keeps track of the number of current iteration. \item The command "\multidostop" causes the "\multido" loop to quit at the end of the current iteration. \item Fixed point addition is performed by \N\FPadd\ and \N\FPsub: \begin{MD \FPadd{num1{num2{command\\ \FPsub{num1{num2{command \end{MD <num2> is added to or subtracted from <num1>, and the answers is stored in the command sequence given as the third argument. The rules about decimals and so on that apply to number variables apply here as well. E.g., after \begin{verbatim \FPsub{1.75{-0.15{\answer \end{verbatim the definition of "\answer" is 1.90. \end{itemize \subsection*{Changes: \begin{description \item[V1.1] Fixed bug in \N\FPadd\ that gave wrong answer for, e.g., $3.4 + -0.2.$ \item[V1.2] Made unit optional for dimension variables when using PSTricks. \item[V1.3] Now 0 repetitions really gets 0 repetitions. "\def\multido" changed to "\long\def\multido." \end{description \end{document %% END multido.doc

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