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+% \iffalse
+%
+% permute.dtx and permute.ins and all files generated from these files are
+% referred to as `the permute package'. It is distributed under the terms
+% of the \LaTeX\ Project Public License from CTAN archives in directory
+% macros/latex/base/lppl.txt. Either version 1.0 or, at your option, any
+% later version. The use of the package is completely free.
+%
+% Permission is granted to modify the permute package. You are not allowed to
+% distribute any changed version of the package, neither under the same name
+% nor under a different one.
+%
+% Send comments, ideas and bug reports via electronic mail to
+%
+% cheinz@gmx.de
+%
+% (w)(c) 1997--1999 by Carsten Heinz
+%
+%<*driver>
+\documentclass{ltxdoc}
+
+\usepackage{permute}[1999/11/10]
+
+\EnableCrossrefs
+\CodelineIndex
+\OnlyDescription
+
+\begin{document}
+ \DocInput{permute.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \newbox\abstractbox
+% \setbox\abstractbox=\vbox{
+% \begin{abstract}
+% The \textsf{permute} package inputs, outputs and composes permutations.
+% For example, |$\pmt{(123)}\circ\pmt{(321)} = \pmt{(123)(321)}$| produces
+% $\pmt{(123)}\circ\pmt{(321)}=\pmt{(123)(321)}$. A misleading example is
+% $(a\ldots z)\circ(z\ldots a)=\pmt{(a\ldots z)(z\ldots a)}$ printed via
+% |$(a\ldots z)\circ(z\ldots a)=\pmt{(a\ldots z)(z\ldots a)}$|
+% --- misleading since the package doesn't care about the human
+% interpretation of ``\ldots''.
+% \end{abstract}}
+%
+% \title{The \textsf{Permute} Package}
+% \author{Copyright 1997--1999 by Carsten Heinz}
+% \date{Version 0.12\\ \box\abstractbox}
+% \maketitle
+%
+%^^A
+%^^A private adjustments
+%^^A
+% \makeatletter
+% \renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}^^A
+% {1.25ex \@plus1ex \@minus.2ex}^^A
+% {-1em}^^A
+% {\normalfont\normalsize\bfseries}}
+% \makeatother
+% \newenvironment{syntax}{\list{}{\itemindent-\leftmargin}}{\endlist}
+%
+%
+% \section{User's guide}
+%
+%
+% \subsection{Software license}
+%
+% \texttt{permute.dtx} and \texttt{permute.ins} and all files generated from
+% these files are referred to as `the \textsf{permute} package'.
+% It is distributed under the terms of the \LaTeX\ Project Public License
+% from CTAN archives in directory \texttt{macros/latex/base/lppl.txt}.
+% Either version 1.0 or, at your option, any later version.
+% The use of the package is completely free.
+%
+% Permission is granted to modify the \textsf{permute} package.
+% You are not allowed to distribute any changed version of the package,
+% neither under the same name nor under a different one.
+%
+% Send comments, ideas and bug reports via electronic mail to
+% \texttt{cheinz@gmx.de}.
+%
+%
+% \subsection{Installation}
+%
+% \begin{enumerate}
+% \item Following the \TeX\ directory structure (TDS) you should put the files
+% of the package into directories as follows:
+% \begin{center}
+% \begin{tabular}{l@{\quad$\to$\quad}l}
+% \texttt{permute.dvi}
+% & \texttt{texmf/doc/latex/permute}\\
+% \texttt{permute.dtx}, \texttt{permute.ins}
+% & \texttt{texmf/source/latex/permute}\\
+% \end{tabular}
+% \end{center}
+% Of course, you need not to use the TDS.
+% Simply adjust the directories below.
+% \item Create the directory \texttt{texmf/tex/latex/permute}.
+% \item Change the working directory to \texttt{texmf/source/latex/permute}
+% and run \texttt{permute.ins} through \TeX.
+% \item Move the generated file to \texttt{texmf/tex/latex/permute} if this
+% is not already done.
+% \item If your \TeX\ implementation uses a filename database, update it.
+% \end{enumerate}
+%
+%
+% \subsection{Input and output formats}
+%
+% \paragraph{General notation.}
+% First we restrict ourselves to $S_1,\ldots,S_9$:
+% $$S_n:=\{f:\{1,\ldots,n\}\to\{1,\ldots,n\}\,\vert\,
+% f\textrm{ is one-to-one and onto}\}.$$
+% A permutation $f\in S_n$ can be written \textbf{verbose} as an explicit
+% sequence of pre-image/image pairs like this:
+% $$f=\pmtv[12\ldots n]{1{f(1)} 2{f(2)} \ldots\ldots n{f(n)}}.$$
+% A permutation $\sigma$ is a \textbf{cycle} and written
+% $\sigma=(x_1x_2\ldots x_k)$
+% if and only if there are distinct numbers
+% $x_1,x_2,\ldots,x_k\in\{1,\ldots,n\}$
+% satisfying
+% \begin{eqnarray*}
+% \sigma(x_i)&=&x_{i+1}\qquad\textrm{ for all }1\leq i<k\\
+% \sigma(x_k)&=&x_1\\
+% \sigma(x)&=&x\hphantom{\mbox{$_{i+1}$}}\qquad%
+% \textrm{ for all }x\in\{1,\ldots,n\}\setminus\{x_1,\ldots,x_k\}.
+% \end{eqnarray*}
+% This means that a cycle $(x_1x_2\ldots x_k)$ maps
+% $x_1$ to $x_2$, $x_2$ to $x_3$, \ldots, $x_k$ back to $x_1$,
+% and fixes all other elements.
+% Each permutation in $S_n$ can be written as a composition of cycles, for
+% example $\pmtv[12345]{12 21 35 43 54}=(12)\circ(354)=(12)(354)$---we leave
+% out the ``$\circ$''.
+% Note that $S_n$ is not commutative in general and that we compose from the
+% right to the left.
+% In the example 3 is mapped to 5 and then 5 stays 5 since unchanged by (12).
+%
+% \paragraph{Input formats.}
+% If you want to enter a permutation cycle based, just write the cycles after
+% each other.
+% |(12)(354)| would be legal; there must not be a |\circ| in between.
+% The verbose input format lists all pre-image/image pairs without any
+% separators, but a space is allowed in between.
+% The permutation above could also be entered as |12 21 35 43 54|.
+% The package distinguishes the two formats by looking at the first token:
+% If and only if it's a left parenthesis, the package accepts cycles.
+%
+% Now we drop the restriction $n\leq 9$ and the limitation of permuting
+% numbers; we can do it with nearly arbitrary (token) strings.
+% To enter a string as pre-image, image or inside a cycle, enclose
+% the string in braces. That's all!
+% For example, I typed
+% \begin{verbatim}
+% 1{f(1)} 2{f(2)} \ldots\ldots n{f(n)}\end{verbatim}
+% for $\pmtv[12\ldots n]{1{f(1)} 2{f(2)}\ldots\ldots n{f(n)}}$, which actually
+% isn't a permutation at all.
+%
+% In the sequel \meta{pmt} means either a verbose sequence or a sequence of
+% cycles.
+% \emph{Do not use} |\empty| \emph{or} |\relax| \emph{or equivalent
+% definitions inside} \meta{pmt}.
+%
+% \paragraph{Output formats.}
+% The package provides a cycle based and two verbose output formats.
+% Some of the commands described below have an optional \meta{print order}
+% argument.
+% Now let \meta{print order} equal $n_1n_2\ldots n_k$ where each $n_i$ is a
+% single token or a braced string.
+% If $n_i$ and $n_{i+1}$ both appear in a permutation and appear in different
+% cycles, then the cycle containing $n_i$ is printed first.
+% Moreover the cycle starts with the element $n_i$.
+% Cycles not covered by \meta{print order} are printed as they appear in the
+% internal data format.
+% Some examples on printing (12)(34)(56):
+% \begin{center}
+% \begin{tabular}{ll@{\qquad\qquad}ll}
+% \meta{print order} & results in & \meta{print order} & results in\\
+% no order & \pmt{(12)(34)(56)} & empty & \pmt[]{(12)(34)(56)}\\
+% |2| & \pmt[2]{(12)(34)(56)} & |23| & \pmt[23]{(12)(34)(56)}\\
+% |6| & \pmt[6]{(12)(34)(56)}\\
+% \end{tabular}
+% \end{center}
+% All results represent the same permutation.
+% Note the difference between `no order' and `empty':
+% The package uses a standard order if you don't request a special one.
+%
+% There is some danger if you want to use a \emph{single token string} as
+% \meta{print order}. In this case you must enclose the string in
+% \emph{two level} of braces. Use \meta{print order}$=$|{{one}}| to control
+% |({one}{two})({two}{three})({three}{four})|, for example. Since \TeX\
+% discards one group level, |{one}| would lead to the order |o|, |n|, |e|.
+% However, \meta{print order}$=$|{one}{two}| needs no extra braces.
+%
+% \medbreak
+% For the verbose output formats, \meta{print order} plays the role of domain.
+% The package uses exactly the elements and order, i.e.\ all pre-images not
+% appearing in \meta{print order} are not printed, and we assume image=pre-image
+% if pre-image appears in \meta{print order} but not in the permutation.
+% Some examples on printing |1{f(1)} 2{f(2)} \ldots\ldots n{f(n)}|:
+% \begin{center}
+% \begin{tabular}{ll}
+% \meta{print order}&results in\\
+% no order & \pmtv{1{f(1)} 2{f(2)} \ldots\ldots n{f(n)}}\\ \noalign{\smallskip}
+% |n\ldots 21| & \pmtv[n\ldots21]{1{f(1)} 2{f(2)} \ldots\ldots n{f(n)}}\\ \noalign{\smallskip}
+% |2\ldots n{n+1}|& \pmtv[2\ldots n{n+1}]{1{f(1)} 2{f(2)} \ldots\ldots n{f(n)}}\\ \noalign{\smallskip}
+% empty & \pmtv[]{1{f(1)} 2{f(2)} \ldots\ldots n{f(n)}}
+% \end{tabular}
+% \end{center}
+% The first example doesn't print `$\ldots$' and `$f(n)$' since the pre-images
+% `$\ldots$' and `$n$' don't appear in the standard printing order (which is
+% the domain here).
+% But it shows image=pre-image pairs not in the permutation since the standard
+% domain defines the elements as pre-images.
+%
+% Note:
+% (a) The (full) verbose format uses math mode and the \TeX-primitive |\atop|.
+% The latter causes a warning if used together with \texttt{amsmath.sty}.
+% (b) The package defines a short verbose output format, too.
+% It prints the row of images only.
+% Don't take it for the cycle based format!
+%
+% \medbreak
+% Finally, some commands also have a star-form which separate the output like
+% this: \pmt*{(12)(23)(34)}.
+% It is useful if you use strings instead of numbers, for example the
+% permutation \pmt*[{{one}}]{({one}{two})({two}{three})({three}{four})} is
+% printed with a |*|-command.
+%
+%
+% \subsection{User commands}
+%
+% \begin{syntax}
+% \item |\pmt|[|*|][\oarg{print order}]\marg{pmt}
+%
+% calculates the composition of the cycles (if any) and prints the
+% permutation:
+% |\pmt{(12)(23)(34)}| prints \pmt{(12)(23)(34)} and
+% |\pmt{12 23 34 41}| gives \pmt{12 23 34 41}.
+% Note that this command outputs cycles only.
+% Some examples:
+% \begin{center}
+% \begin{tabular}{l@{\ prints\ }p{0.4\linewidth}}
+% |\pmt{(12)(34)(56)}|&\pmt{(12)(34)(56)}\\
+% |\pmt*[2]{(12)(34)(56)}|&\pmt*[2]{(12)(34)(56)}\\
+% |\pmt[23]{(12)(34)(56)}|&\pmt[23]{(12)(34)(56)}\\
+% |\pmt*[6]{(12)(34)(56)}|&\pmt*[6]{(12)(34)(56)}\\
+% \end{tabular}
+% \end{center}
+% The macro |\pmtprintorder| contains the standard printing order,
+% see \ref{uParameters}.
+%
+% \item |\pmtv|[|*|][\oarg{print order}]\marg{pmt}
+%
+% prints a verbose form of the permutation.
+% The commands |\pmtvshorttrue| and |\pmtvshortfalse| controls whether
+% the package prints only the row of images or the full pre-image/image
+% format.
+%
+% \item |\pmttable|[|*|][\oarg{print order}]\marg{list of pmts}\marg{list of pmts}
+% \item |\pmtvtable|[|*|][\oarg{print order}]\marg{list of pmts}\marg{list of pmts}
+%
+% The commands compose each $\sigma_1$ of the first list with each
+% $\sigma_2$ of the second list and write the result
+% $\sigma_1\circ\sigma_2$ in row $\sigma_1$ and column $\sigma_2$.
+% For example,
+% \begin{verbatim}
+% $$\pmttable{(),(12),(13),(23),(123),(132)}
+% {(),(12),(13),(23),(123),(132)}$$\end{verbatim}
+% creates
+% $$\pmttable{(),(12),(13),(23),(123),(132)}
+% {(),(12),(13),(23),(123),(132)}$$
+% '()' stands for the identity map here.
+% \emph{Do not write} |\pmttable{,(12),...|. You may write
+% |\pmttable{(12),(123)}{(),(23),(123),(132)}|
+% to typeset a piece of the table or use |\pmtvtable| to print all
+% permutations verbose. The optional arguments effect all printed
+% permutations.
+%
+% If you create really big tables like the one of $S_5$, you surely want
+% to cut the whole table in pieces and produce subtables on different
+% pages. This leads to alignment problems since the first column on the
+% first page need not to have the width of the first column on the second
+% page. Bad luck!
+% \end{syntax}
+% \medbreak
+% Now we discuss how to calculate with the \textsf{permute} package.
+% Let \meta{current pmt} denote the (internal) current permutation and
+% \meta{name} another internal (stored) permutation.
+% \begin{syntax}
+% \item |\pmtload|\marg{name}\hphantom{mmmmmm}\qquad
+% \meta{current pmt} $\gets$ \meta{name}
+%
+% \item |\pmtsave|\marg{name}\hphantom{mmmmmm}\qquad
+% \meta{name} $\gets$ \meta{current pmt}
+%
+% \item |\pmtid|[\oarg{name}]\hphantom{\meta{pmt}\ttfamily mmmmmm}$\!$\qquad
+% \meta{current pmt} $\gets$ identity map
+%
+% \item |\pmtdo|[\oarg{name}]\marg{pmt}\hphantom{\ttfamily mmmm}$\!$\qquad
+% \meta{current pmt} $\gets$ \meta{pmt} $\circ$ \meta{current pmt}
+%
+% \item |\pmtcirc|[\oarg{name}]\marg{pmt}\hphantom{\ttfamily mm}$\!$\qquad
+% \meta{current pmt} $\gets$ \meta{current pmt} $\circ$ \meta{pmt}
+%
+% \item |\pmtprint|[|*|][\oarg{print order}]\hphantom{\ttfamily m}\qquad
+% prints \meta{current pmt}.
+%
+% \item |\pmtvprint|[|*|][\oarg{print order}]\qquad
+% prints \meta{current pmt}.
+%
+% \item |\pmtimageof|[\oarg{name}]\marg{pre-image}
+%
+% prints image of \meta{pre-image} under \meta{current pmt}.
+%
+% \item |\pmtpreimageof|[\oarg{name}]\marg{image}
+%
+% prints pre-image of \meta{image} under \meta{current pmt}.
+% \end{syntax}
+% If you use any optional \oarg{name}, this permutation replaces
+% \meta{current pmt}.
+% For example, |\pmtid[a]| makes the permutation $a$ to be the identity map
+% or |\pmtdo[a]|\marg{pmt} performs $a$ $\gets$ \meta{pmt} $\circ$ $a$.
+%
+% \medbreak
+% Finally examples which all print the result of
+% $\pmtv[1\ldots kl\ldots n]{1{f(1)} \ldots\ldots k{f(k)} l{f(l)}^^A
+% \ldots\ldots n{f(n)}}\circ \pmt{(kl)}$,
+% namely
+% \pmtid\pmtdo{(kl)}\pmtdo{1{f(1)} k{f(k)} l{f(l)} n{f(n)}}
+% \pmtvprint[1\ldots kl\ldots n].
+% \begin{verbatim}
+% \pmtid
+% \pmtdo{1{f(1)} \ldots\ldots k{f(k)} l{f(l)} \ldots\ldots n{f(n)}}
+% \pmtcirc{(kl)}
+% \pmtvprint[1\ldots kl\ldots n]
+%
+% \pmtid
+% \pmtdo{(kl)}
+% \pmtdo{1{f(1)} k{f(k)} l{f(l)} n{f(n)}}
+% \pmtvprint[1\ldots kl\ldots n]\end{verbatim}
+% We can drop the two |\ldots| pairs (also in the first example) since image
+% and pre-image are equal.
+%
+%
+% \subsection{Parameters}\label{uParameters}
+%
+% \begin{syntax}
+% \item |\pmtprintorder|
+%
+% contains the standard printing order which is used whenever you leave
+% out or forget the optional \meta{print order} argument. By default it
+% contains the sequence |123456789abcdefghi|. You may adjust it to your
+% needs, for example, |\renewcommand*\pmtprintorder{123456}| if you work
+% with $S_6$. This is especially good if you use the verbose printing
+% format. You can forget the optional \meta{print order} in this case:
+% \begin{center}
+% \renewcommand*\pmtprintorder{123456}
+% \begin{tabular}{@{}ll@{}}
+% |\renewcommand*\pmtprintorder{123456}|\\
+% |\pmtv{()}|&prints \pmtv{()}\\ \noalign{\medskip}
+% |\pmtv{(123)}|&prints \pmtv{(123)}\\ \noalign{\medskip}
+% |\pmtv{(12)(23)(16)(34)(45)}|&prints \pmtv{(12)(23)(16)(34)(45)}
+% \end{tabular}
+% \end{center}
+%
+% \item |\pmtseparator|
+%
+% contains the separator used for the optional star. By default it is a
+% space: |\newcommand*\pmtseparator{ }|. Since it's not a backslashed
+% space |\|\textvisiblespace, it is ignored in math mode, in particular
+% in the verbose output format. But you may write
+% |\renewcommand*\pmtseparator{\ }|.
+%
+% \item |\pmtidname|
+%
+% contains the string which is printed in the cycle based format
+% if a permutation is the identity map. It is predefined via
+% |\newcommand*\pmtidname{id}|.
+%
+% \item |\pmtldelim|
+% \item |\pmtrdelim|
+%
+% contain the left respectively right delimiter for the verbose format.
+% |\left(| and |\right)| are used by default.
+%
+% \item |\pmttableborders|
+%
+% contains |lt| which makes a left border column and a top border line.
+% You may redefine it to be empty or to contain |l|, |t|, |lt| or |tl|.
+%
+% \item |\pmtarraystretch|
+%
+% contains |2| and is used as |\arraystretch| for the table. You may
+% write |\renewcommand*\pmtarraystretch{1.3}| and get more compact
+% tables:
+% $$\def\pmtarraystretch{1.3}
+% \pmttable{(),(12),(23)}{(),(12),(23)}$$
+% \end{syntax}
+%
+%
+% \StopEventually{}
+%
+%
+% \CheckSum{717}
+%
+%
+% \section{Implementation}
+%
+%
+% \subsection{General concept}
+%
+% Permutations, pre-images, and images are stored in macros. In the sequel we
+% use, for example, \meta{image} for an argument which must be a macro and
+% \marg{image} if the image is required explicitly. We define the following
+% internal commands, which make the definition of the user commands easier.
+%
+% \begin{syntax}
+% \item |\pmt@GetImageOf|\marg{pre-image}\meta{pmt}
+%
+% Defines |\pmt@preimage|, its image |\pmt@image|, and \emph{removes} the
+% pre-image/image pair from \meta{pmt}. |\pmt@iffound| equals |\iffalse|
+% if and only if the pair couldn't be removed (since never existent).
+%
+% \item |\pmt@GetPreimageOf|\marg{image}\meta{pmt}
+%
+% Defines |\pmt@image|, its pre-image |\pmt@preimage|, and leaves
+% \meta{pmt} \emph{unchanged}. |\pmt@iffound| equals |\iffalse|
+% if and only if such pair is not found.
+%
+% \item |\pmt@Whirl|\meta{a}\meta{b}\meta{c}
+%
+% \meta{a} $\gets$ \meta{b} $\circ$ \meta{c}.
+% Note that \meta{c} must not equal |\pmt@b|.
+%
+% \item |\pmt@GetPmt|\meta{macro}\marg{pmt}
+%
+% The cycle/verbose input format is converted to the internal data
+% format and assigned to \meta{macro}.
+%
+% \item |\pmt@PrintPmt|\meta{pmt}\qquad and\qquad |\pmt@PrintVPmt|\meta{pmt}
+%
+% print the permutation (verbose) with respect to |\pmt@order|.
+% \emph{Both destroy} |\pmt@a|,\ldots,|\pmt@c|, |\pmt@image|,
+% \emph{and so on.}
+% \end{syntax}
+%
+%
+% \subsection{Preliminaries}
+%
+% \begingroup
+% \begin{macrocode}
+%<*package>
+\ProvidesPackage{permute}[1999/11/10 v0.12 (aeio)(cdt)(knm)]
+% \end{macrocode}
+% I still wonder whether someone finds out what |(aeio)(cdt)(knm)| means.
+% \vskip\lineskip
+% \endgroup
+%
+% \begin{macro}{\pmt@iffirst}
+% \begin{macro}{\pmt@iffound}
+% \begin{macro}{\pmt@ifsep}
+% are each controlled by two simple definitions.
+% \begin{macrocode}
+\def\pmt@firsttrue{\let\pmt@iffirst\iftrue}
+\def\pmt@firstfalse{\let\pmt@iffirst\iffalse}
+% \end{macrocode}
+% \begin{macrocode}
+\def\pmt@foundtrue{\let\pmt@iffound\iftrue}
+\def\pmt@foundfalse{\let\pmt@iffound\iffalse}
+% \end{macrocode}
+% \begin{macrocode}
+\def\pmt@septrue{\let\pmt@ifsep\iftrue}
+\def\pmt@sepfalse{\let\pmt@ifsep\iffalse}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+%
+%
+% \subsection{The data format}
+%
+% We store a permutation as a list of pre-image/image pairs, but we drop all
+% with pre-image=image, e.g.\ |{1}{2}{2}{3}{3}{1}| represents (123) no matter
+% whether considered as element of $S_3$, $S_4$ or $S_6$.
+% The identity map is represented by an empty macro.
+%
+% \begin{macro}{\pmt@GetPreimageOf}
+% We define the image and get its pre-image from a submacro. |\pmt@firsttrue|
+% indicates that we are looking for the first of pre-image/image.
+% \begin{macrocode}
+\def\pmt@GetPreimageOf#1#2{%
+ \def\pmt@image{#1}\pmt@firsttrue
+ \expandafter\pmt@GIO@#2\relax\relax}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@GetImageOf}
+% We assign the pre-image, empty |\pmt@gio| (which holds the rest of |#2|), get
+% the image, and assign the rest of the permutation to |#2|. |\pmt@firstfalse|
+% indicates that we are looking for the second of pre-image/image.
+% \begin{macrocode}
+\def\pmt@GetImageOf#1#2{%
+ \def\pmt@preimage{#1}\let\pmt@gio\@empty \pmt@firstfalse
+ \expandafter\pmt@GIO@#2\relax\relax
+ \let#2\pmt@gio}
+% \end{macrocode}
+% Now we iterate down the list. |\pmt@image| or |\pmt@preimage| is used as
+% temporary macro. If we have found the correct (pre-)image, we can define it
+% and get the rest of the permutation (up to |\relax\relax|).
+% \begin{macrocode}
+\def\pmt@GIO@#1#2{%
+ \pmt@iffirst \def\pmt@preimage{#2}\else
+ \def\pmt@image{#1}\fi
+ \ifx\pmt@image\pmt@preimage
+ \def\pmt@preimage{#1}\def\pmt@image{#2}\pmt@foundtrue
+ \expandafter\pmt@GIO@@
+ \else
+% \end{macrocode}
+% If we haven't found the correct (pre-)image: Image and pre-image must be
+% equal if we have reached the end of list; otherwise we probably extend
+% |\pmt@gio| and continue the loop.
+% \begin{macrocode}
+ \ifx\relax#2%
+ \pmt@foundfalse
+ \pmt@iffirst \let\pmt@preimage\pmt@image
+ \else \let\pmt@image\pmt@preimage \fi
+ \expandafter\@gobbletwo
+ \else
+ \pmt@iffirst\else \pmt@AddTo\pmt@gio{{#1}{#2}}\fi
+ \fi
+ \expandafter\pmt@GIO@
+ \fi}
+% \end{macrocode}
+% The following macro gets the rest of permutation.
+% \begin{macrocode}
+\def\pmt@GIO@@#1\relax\relax{%
+ \pmt@iffirst\else \pmt@AddTo\pmt@gio{#1}\fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@AddTo}
+% \begin{macro}{\pmt@Extend}
+% |\pmt@AddTo| adds |#2| to the contents of the macro |#1|.
+% |\pmt@Extend| expands the first token of |#2| before doing the same.
+% \begin{macrocode}
+\def\pmt@AddTo#1#2{\expandafter\def\expandafter#1\expandafter{#1#2}}
+\def\pmt@Extend#1#2{%
+ \expandafter\pmt@AddTo\expandafter#1\expandafter{#2}}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+%
+% \subsection{Whirling things round}\label{iWhirlingThingsRound}
+%
+% \begin{macro}{\pmt@Whirl}
+% Init, whirl, assign.
+% \begin{macrocode}
+\def\pmt@Whirl#1#2#3{%
+ \let\pmt@b#2\let\pmt@c#3\let\pmt@a\@empty
+ \pmt@Whirl@
+ \let#1\pmt@a}
+% \end{macrocode}
+% If |\pmt@c| is empty, we only need to append the contents of |\pmt@b| to
+% |\pmt@a| since |\pmt@c| represents the identity map.
+% \begin{macrocode}
+\def\pmt@Whirl@{%
+ \ifx\pmt@c\@empty
+ \pmt@Extend\pmt@a\pmt@b
+ \else
+% \end{macrocode}
+% Otherwise we append the first pre-image and its image under the composition,
+% and continue to check whether |\pmt@c| is empty.
+% \begin{macrocode}
+ \expandafter\pmt@Whirl@@\pmt@c\relax
+ \expandafter\pmt@Whirl@
+ \fi}
+% \end{macrocode}
+% |\pmt@c| becomes shorter, we get the `composed' image, \ldots
+% \begin{macrocode}
+\def\pmt@Whirl@@#1#2#3\relax{%
+ \def\pmt@first{#1}\def\pmt@c{#3}%
+ \pmt@GetImageOf{#2}\pmt@b
+% \end{macrocode}
+% and append the new pre-image/image pair if first$\neq$image.
+% There is only some trouble in making braces around the (pre-)image.
+% \begin{macrocode}
+ \ifx\pmt@first\pmt@image\else
+ \def\pmt@first{{#1}}%
+ \pmt@Extend\pmt@first{\expandafter{\pmt@image}}%
+ \pmt@Extend\pmt@a\pmt@first
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Getting input}
+%
+% \begin{macro}{\pmt@InputError}
+% gives an error message.
+% \begin{macrocode}
+\def\pmt@InputError#1{\PackageError{Permute}{#1}\@ehd}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@GetPmt}
+% We initialize |\pmt@a|, do the conversion and assign the result to |#1|.
+% \begin{macrocode}
+\def\pmt@GetPmt#1#2{%
+ \def\pmt@a{#2}%
+ \pmt@foundtrue \pmt@firstfalse
+ \@ifnextchar({\let\pmt@a\@empty \pmt@GetCPmt}%
+ \pmt@GetVPmt
+ #2\relax\relax
+ \let#1\pmt@a}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@GetVPmt}
+% For the verbose format we only test for an even number of arguments.
+% \begin{macrocode}
+\def\pmt@GetVPmt#1#2{%
+ \ifx\relax#2%
+ \ifx\relax#1\else
+ \pmt@InputError{Odd number of tokens}%
+ \let\pmt@a\@empty
+ \fi
+ \else
+ \expandafter\pmt@GetVPmt
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@GetCPmt}
+% is called |\pmt@GetCPmt|\meta{cycles}|\relax| and |\pmt@a| becomes |\pmt@a|
+% $\circ$ \meta{cycles}. If we haven't found a right parenthesis and reach the
+% end of the cycles, we give an error message. Reaching |\relax| we terminate
+% the loop by gobbling a far away |\pmt@GetCPmt|.
+% \begin{macrocode}
+\def\pmt@GetCPmt#1{%
+ \ifx#1\relax
+ \pmt@iffound\else \pmt@InputError{Missing `)'}\fi
+ \expandafter\@gobble
+ \else
+% \end{macrocode}
+% If we find a right parenthesis, we either give an error message or use the
+% first element of the current cycle as image of the last element. In this case
+% we compose |\pmt@a| and |\pmt@c| via |\pmt@Whirl| defined in section
+% \ref{iWhirlingThingsRound}.
+% \begin{macrocode}
+ \ifx#1)%
+ \pmt@iffound
+ \pmt@InputError{Extra `)'}%
+ \else
+ \pmt@iffirst\else
+ \pmt@Extend\pmt@c\pmt@first
+ \pmt@Whirl\pmt@a\pmt@a\pmt@c
+ \fi
+ \pmt@foundtrue
+ \fi
+ \else
+% \end{macrocode}
+% A left parenthesis might lead to an error, but in any case initializes two
+% \texttt{if}s.
+% \begin{macrocode}
+ \ifx#1(%
+ \pmt@iffound\else
+ \pmt@InputError{Extra `(' or missing `)'}%
+ \fi
+ \pmt@firsttrue \pmt@foundfalse
+ \else
+% \end{macrocode}
+% Now we handle all other tokens. If we are outside a cycle (i.e.\ a closing
+% parenthesis has been found), we give an error message.
+% \begin{macrocode}
+ \pmt@iffound
+ \pmt@InputError{Missing `('}%
+ \else
+% \end{macrocode}
+% Otherwise we initialize or extend |\pmt@c|.
+% \begin{macrocode}
+ \pmt@iffirst
+ \pmt@firstfalse \def\pmt@first{{#1}}\def\pmt@c{{#1}}%
+ \else
+ \pmt@AddTo\pmt@c{{#1}{#1}}%
+ \fi
+ \fi\fi\fi
+ \fi
+% \end{macrocode}
+% Continue the loop (if not gobbled).
+% \begin{macrocode}
+ \pmt@GetCPmt}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Doing output}
+%
+% \begin{macro}{\pmt@PrintVPmt}
+% Is easy.
+% \begin{macrocode}
+\def\pmt@PrintVPmt#1{%
+ \let\pmt@a#1\pmt@sepfalse
+ \ensuremath{\pmtldelim
+ \expandafter\pmt@PrintVPmt@\pmt@order\relax
+ \pmtrdelim}}
+% \end{macrocode}
+% While |\relax| is not reached, we define pre-image, get the image, and use
+% |\atop| to typeset the pre-image/image pair.
+% \begin{macrocode}
+\def\pmt@PrintVPmt@#1{%
+ \ifx\relax#1\@empty \else
+ \pmt@GetImageOf{#1}\pmt@a
+ \pmt@ifsep \pmt@separator \else \pmt@septrue \fi
+ \mkern1mu%
+ \pmt@ifshort \pmt@image
+ \else{\pmt@preimage\atop\pmt@image}\fi
+ \mkern1mu%
+ \expandafter\pmt@PrintVPmt@
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmtshorttrue}
+% \begin{macro}{\pmtshortfalse}
+% The user accessible \texttt{if} used above.
+% \begin{macrocode}
+\def\pmtshorttrue{\let\pmt@ifshort\iftrue}
+\def\pmtshortfalse{\let\pmt@ifshort\iffalse}
+\pmtshortfalse
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\pmt@GetFirst}
+% defines |\pmt@first| and gobbles all tokens up to the next |\relax|.
+% \begin{macrocode}
+\def\pmt@GetFirst#1#2\relax{\def\pmt@first{#1}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@PrintPmt}
+% We print |\pmtidname| if necessary.
+% \begin{macrocode}
+\def\pmt@PrintPmt#1{%
+ \let\pmt@a#1%
+ \ifx\pmt@a\@empty \pmtidname \else
+ \expandafter\pmt@PrintPmt@\pmt@order\relax
+ \fi}
+% \end{macrocode}
+% While having an order, we define the first pre-image and print the cycle.
+% \begin{macrocode}
+\def\pmt@PrintPmt@#1{%
+ \ifx\relax#1\@empty
+ \expandafter\pmt@PrintPmt@@
+ \else
+ \def\pmt@first{#1}\pmt@PrintCycle
+ \expandafter\pmt@PrintPmt@
+ \fi}
+% \end{macrocode}
+% Having no order, we print the rest.
+% \begin{macrocode}
+\def\pmt@PrintPmt@@{%
+ \ifx\pmt@a\@empty\else
+ \expandafter\pmt@GetFirst\pmt@a\relax
+ \pmt@PrintCycle
+ \expandafter\pmt@PrintPmt@@
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@PrintCycle}
+% We print the cycle containing (and beginning with) the contents of
+% |\pmt@first| if it appears as pre-image.
+% \begin{macrocode}
+\def\pmt@PrintCycle{%
+ \expandafter\pmt@GetImageOf\expandafter{\pmt@first}\pmt@a
+ \pmt@iffound
+ (\pmt@preimage\pmt@separator\pmt@image
+ \ifx\pmt@a\@empty\else \pmt@PrintCycle@\pmt@image \fi
+ )%
+ \fi}
+% \end{macrocode}
+% While we haven't found the end of the cycle, \ldots
+% \begin{macrocode}
+\def\pmt@PrintCycle@#1{%
+ \expandafter\pmt@GetImageOf\expandafter{#1}\pmt@a
+ \ifx\pmt@image\pmt@first\else
+% \end{macrocode}
+% we print the image and use the image as new pre-image if permutation is
+% not empty yet.
+% \begin{macrocode}
+ \pmt@separator\pmt@image
+ \ifx\pmt@a\@empty \expandafter\@gobblefour \fi
+ \expandafter\pmt@PrintCycle@\expandafter\pmt@image
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{User commands and parameters}
+%
+% \begin{macro}{\pmtidname}
+% \begin{macro}{\pmtprintorder}
+% \begin{macro}{\pmtseparator}
+% \begin{macro}{\pmtldelim}
+% \begin{macro}{\pmtrdelim}
+% \begin{macro}{\pmttableborders}
+% \begin{macro}{\pmtarraystretch}
+% Some predefined values.
+% \begin{macrocode}
+\newcommand*\pmtidname{id}
+\newcommand*\pmtprintorder{123456789abcdefghi}
+\newcommand*\pmtseparator{ }
+\newcommand*\pmtldelim{\left(}
+\newcommand*\pmtrdelim{\right)}
+\newcommand*\pmttableborders{lt}
+\newcommand*\pmtarraystretch{2}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+% \end{macro}\end{macro}\end{macro}
+%
+% \begin{macro}{\pmt@GetPrintArgs}
+% This helper executes |#1| after getting the optional printing arguments.
+% \begin{macrocode}
+\def\pmt@GetPrintArgs#1{%
+ \let\pmt@order\pmtprintorder \def\pmt@next{#1}%
+ \@ifstar{\let\pmt@separator\pmtseparator \pmt@GPA@}%
+ {\let\pmt@separator\@empty \pmt@GPA@}}
+% \end{macrocode}
+% If there is no optional argument, we use |\pmtprintorder|, i.e.\ we don't
+% redefine |\pmt@order|.
+% \begin{macrocode}
+\def\pmt@GPA@{\@ifnextchar[\pmt@GPA@@\pmt@next}
+\def\pmt@GPA@@[#1]{\def\pmt@order{#1}\pmt@next}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt}
+% \begin{macro}{\pmtv}
+% \begin{macro}{\pmtprint}
+% \begin{macro}{\pmtvprint}
+% The first user commands in terms of known definitions.
+% \begin{macrocode}
+\newcommand*\pmt {\pmt@GetPrintArgs{\pmt@\pmt@PrintPmt}}
+\newcommand*\pmtv{\pmt@GetPrintArgs{\pmt@\pmt@PrintVPmt}}
+\def\pmt@#1#2{\pmt@GetPmt\pmt@a{#2}#1\pmt@a}
+% \end{macrocode}
+% \begin{macrocode}
+\newcommand*\pmtprint {\pmt@GetPrintArgs{\pmt@PrintPmt\pmt@curr}}
+\newcommand*\pmtvprint{\pmt@GetPrintArgs{\pmt@PrintVPmt\pmt@curr}}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+%
+% \begin{macro}{\pmt@OptName}
+% `executes' |#1| with argument |\pmt@curr| \ldots
+% \begin{macrocode}
+\def\pmt@OptName#1{\def\pmt@next##1{#1}%
+ \@ifnextchar[\pmt@OptName@{\pmt@next\pmt@curr}}
+% \end{macrocode}
+% or |\pmt@s@|\meta{name} if an optional argument is given. |\pmt@LoadPmt|
+% ensures that the permuation |#1|$=$\meta{name} is defined.
+% \begin{macrocode}
+\def\pmt@OptName@[#1]{%
+ \pmt@LoadPmt{#1}\pmt@a
+ \expandafter\pmt@next\csname pmt@s@#1\endcsname}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@LoadPmt}
+% loads the permutation with name |#1| to |#2|.
+% \begin{macrocode}
+\def\pmt@LoadPmt#1#2{%
+ \@ifundefined{pmt@s@#1}%
+ {\expandafter\let\csname pmt@s@#1\endcsname\@empty}
+ \expandafter\let\expandafter#2\csname pmt@s@#1\endcsname}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmtsave}
+% \begin{macro}{\pmtload}
+% \begin{macro}{\pmtid}
+% Some more user commands.
+% \begin{macrocode}
+\def\pmtsave#1{\expandafter\let\csname pmt@s@#1\endcsname\pmt@curr}
+\def\pmtload#1{\pmt@LoadPmt{#1}\pmt@curr}
+% \end{macrocode}
+% |##1| $\in$ \{|\pmt@curr|,|\pmt@s@|\meta{name}\} becomes empty.
+% \begin{macrocode}
+\newcommand*\pmtid{\pmt@OptName{\let##1\@empty \ignorespaces}}
+\pmtid
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+%
+% \begin{macro}{\pmtdo}
+% \begin{macro}{\pmtcirc}
+% The only difference here is the order of |\pmt@a| and |##1|.
+% \begin{macrocode}
+\newcommand*\pmtdo{\pmt@OptName{\pmtdo@##1\pmt@a##1}}
+\newcommand*\pmtcirc{\pmt@OptName{\pmtdo@##1##1\pmt@a}}
+\def\pmtdo@#1#2#3#4{\pmt@GetPmt\pmt@a{#4}\pmt@Whirl#1#2#3\ignorespaces}
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\pmtimageof}
+% \begin{macro}{\pmtpreimageof}
+% We use different arguments to the submacro to get and print the (pre-)image.
+% \begin{macrocode}
+\newcommand*\pmtimageof{\pmtimageof@\pmt@GetImageOf\pmt@image}
+\newcommand*\pmtpreimageof{\pmtimageof@\pmt@GetPreimageOf\pmt@preimage}
+% \end{macrocode}
+% \begin{macrocode}
+\def\pmtimageof@#1#2{%
+ \@ifnextchar[{\pmtimageof@@#1#2}{\pmtimageof@@#1#2[]}}
+\def\pmtimageof@#1#2[#3]#4{%
+ \ifx\@empty#3\@empty
+ \let\pmt@a\pmt@curr
+ \else
+ \pmt@LoadPmt{#3}\pmt@a
+ \fi
+ #1{#4}\pmt@a
+ #2}
+% \end{macrocode}
+% TODO: These two user macros don't behave like |\pmtid|, |\pmtdo|, and so on.
+% An empty named permutation \meta{name} leads here to \meta{current pmt} and not
+% to |\pmt@s@|\meta{name}.
+% \end{macro}\end{macro}
+%
+%
+% \subsection{Making tables}
+%
+% \begin{macro}{\pmtvtable}
+% We use appropriate local redefinitions of |\pmtprint|.
+% \begin{macrocode}
+\newcommand*\pmttable
+ {\begingroup
+ \def\pmtprint{\let\pmt@order\pmt@porder\pmt@PrintPmt\pmt@curr}%
+ \pmt@GetPrintArgs\pmt@PrintTable}
+% \end{macrocode}
+% \begin{macrocode}
+\newcommand*\pmtvtable
+ {\begingroup
+ \def\pmtprint{\let\pmt@order\pmt@porder\pmt@PrintVPmt\pmt@curr}%
+ \pmt@GetPrintArgs\pmt@PrintTable}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@PrintTable}
+% We use macros defined below to indicate the desired borders.
+% \begin{macrocode}
+\def\pmt@PrintTable#1#2{%
+ \let\pmt@ifleft\iffalse
+ \pmt@topfalse
+ \expandafter\pmt@SetBorders\pmttableborders\relax
+% \end{macrocode}
+% \begin{macrocode}
+ \let\pmt@porder\pmt@order
+ \let\arraystretch\pmtarraystretch
+% \end{macrocode}
+% Determine how many columns the table will have, and choose the right
+% tabular call (according to the desired left border)
+% \begin{macrocode}
+ \@tempcnta\z@ \pmt@for{\advance\@tempcnta\@ne}{#2}%
+% \end{macrocode}
+% Note: It's possible to write |\begin{tabular}{\pmt@ifleft c|\ldots, but the
+% construction here is independent of that.
+% \begin{macrocode}
+ \edef\pmt@next{%
+ \noexpand\begin{tabular}{\pmt@ifleft c|\else p{\z@}@{}\fi
+ *{\the\@tempcnta}{@{\ }c@{\ }}}}%
+ \pmt@next
+% \end{macrocode}
+% Print the top border if desired.
+% \begin{macrocode}
+ \pmt@iftop
+ \pmt@ifleft \ensuremath{\circ}\fi
+ \pmt@for{&\pmtid\pmtdo{##1}\pmtprint}{#1}%
+ \\ \hline
+ \fi
+% \end{macrocode}
+% And process the rest of the table: we end the previous tabular line (if there
+% is any), print the left border (if desired) and print one line of the table.
+% \begin{macrocode}
+ \gdef\pmt@topperms{#2}\pmt@toptrue
+ \pmt@for{%
+ \pmt@iftop \pmt@topfalse \else \expandafter\\\fi
+ \pmt@ifleft \pmtid\pmtdo{##1}\pmtprint \fi
+ \pmt@PrintTableLine{##1}}%
+ {#1}%
+ \end{tabular}\endgroup}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@PrintTableLine}
+% is |\pmt@PrintTableLine@{#1}|$\langle$\textit{expansion of}
+% |\pmt@topperms|$\rangle$|,\relax,|
+% \begin{macrocode}
+\def\pmt@PrintTableLine#1{%
+ \def\pmt@next{\pmt@PrintTableLine@{#1}}%
+ \expandafter\pmt@next\pmt@topperms,\relax,}
+% \end{macrocode}
+% Now we get |#1| and (step by step) each permutation of |\pmt@topperms|,
+% and print the composition.
+% \begin{macrocode}
+\def\pmt@PrintTableLine@#1#2,{%
+ \ifx\relax#2\else
+ \def\pmt@next{&\pmtid\pmtdo{#2}\pmtdo{#1}\pmtprint
+ \pmt@PrintTableLine@{#1}}%
+ \expandafter\pmt@next
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@for}
+% performs |#1| for each element of the comma separated list |#2|.
+% \begin{macrocode}
+\def\pmt@for#1#2{%
+ \gdef\pmt@for@##1,{%
+ \ifx\relax##1\else
+ \def\pmt@next{#1\expandafter\pmt@for@}%
+ \expandafter\pmt@next
+ \fi}%
+ \pmt@for@#2,\relax,}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmt@SetBorders}
+% \begin{macro}{\pmt@topfalse}
+% \begin{macro}{\pmt@toptrue}
+% \begin{macro}{\pmt@lefttrue}
+% Get characters up to |\relax| and set \texttt{if}s.
+% \begin{macrocode}
+\def\pmt@SetBorders#1{%
+ \ifx\relax#1\else
+ \if l#1\pmt@lefttrue \fi
+ \if t#1\pmt@toptrue \fi
+ \expandafter\pmt@SetBorders
+ \fi}
+% \end{macrocode}
+% \begin{macrocode}
+\def\pmt@topfalse{\global\let\pmt@iftop\iffalse}
+\def\pmt@toptrue{\global\let\pmt@iftop\iftrue}
+\def\pmt@lefttrue{\let\pmt@ifleft\iftrue}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}\end{macro}
+%
+% \begingroup
+% \begin{macrocode}
+%</package>
+% \end{macrocode}
+% \endgroup
+%
+%
+% \subsection{To do}
+%
+% It would be nice to have commands |\pmtpartialtable| and |\pmtvpartialtable|
+% which print a specified part of a whole table. If requested, these commands
+% should determine the width of the columns such that the columns are aligned
+% correctly if all parts are printed and put together. For this procedure it
+% would be convenient either to store the lists of permutations so that the
+% commands can access them, or to let the package take control and print the
+% table on different pages (if necessary).
+%
+% Cycle substitution: After |\pmtsubstitute{(123)(45)}{a}| the permutation
+% (123)(45) is replaced by $a$ in the output. Difficult to implement (due to
+% \meta{print order} and |\pmtprintorder|) and even more difficult if this
+% substitution should take place `inside' permutations.
+% In general, the latter is not possible or not reasonable.
+% But it is interesting in context with the next ``to do'' paragraph.
+%
+% Implement possibility to print (and store) permutations as they have been
+% entered.
+% This does not mean just to store the character sequence since composition
+% with other permutations must be possible, of course.
+% The internal data format (or an additional list) must represent the input.
+% Storing an additional \meta{print order} is not sufficient.
+% For example, (123)(321) is represented by an empty string, but we cannot
+% recreate it from the empty string and \meta{print order}.
+% Thus we might need two additional data: \meta{print order} and something
+% like the original string.
+%
+% New command |\pmtinverse|[\oarg{name}] (easy) and its applications.
+%
+%
+% \subsection{History}
+%
+% \renewcommand\labelitemi{--}
+% \begin{itemize}
+% \item[0.1] from 1997/11/08 (unpublished)
+% \item commands |\pmt|, |\pmtloadid| (became |\pmtid|), |\pmtdo| (became
+% |\pmtcirc|), |\pmtprint| and |\pmttable| support $S_1,\ldots,S_9$
+% \item[0.11] from 1998/12/17
+% \item restriction to $S_1,\ldots,S_9$ dropped
+% \item new commands |\pmtv|, |\pmtvprint|, |\pmtvtable| provide verbose
+% printing format and the old commands |\pmt|, |\pmtv|, |\pmtdo|,
+% |\pmtcirc|, |\pmttable| and |\pmtvtable| now accept verbose input
+% \item |\pmtprintorder|, |\pmtseparator|, |\pmtidname|, |\pmtldelim|,
+% |\pmtrdelim|, |\pmttableborders| (prior optional argument),
+% |\pmtarraystretch| are new parameters
+% \item[0.12] from 1999/11/10
+% \item new commands |\pmtvshorttrue|, |\pmtvshortfalse|, |\pmtsave|,
+% |\pmtload|, |\pmtimageof| and |\pmtpreimageof|
+% \item enhanced commands |\pmtid|, |\pmtdo| and |\pmtcirc|
+% \end{itemize}
+%
+%
+% \Finale
+%
+\endinput
diff --git a/Master/texmf-dist/source/latex/permute/permute.ins b/Master/texmf-dist/source/latex/permute/permute.ins
new file mode 100644
index 00000000000..42b83dcab28
--- /dev/null
+++ b/Master/texmf-dist/source/latex/permute/permute.ins
@@ -0,0 +1,35 @@
+%%
+%% Installation file: Permute package for LaTeX
+%% (w)(c) 1997,1998,1999 by Carsten Heinz
+%%
+\def\batchfile{permute.ins}
+\input docstrip
+\keepsilent
+
+\preamble
+
+(w)(c) 1997,1998,1999 by Carsten Heinz
+
+All files of the permute package are distributed freely.
+You are not allowed to take money for the distribution or use of these
+files, except for a nominal charge for copying etc..
+
+The files are distributed without any warranty, express or implied, as to
+merchantability or fitness for any particular purpose.
+
+You are not allowed to distribute any changed version of the package,
+neither under the same name nor under a different one.
+You are not allowed to change one of the files, except using a clearly
+different file name.
+
+\endpreamble
+
+\askforoverwritefalse
+
+\generate{\file{permute.sty}{\from{permute.dtx}{package}}}
+
+\Msg{*}
+\Msg{* Move `permute.sty' into a directory searched by TeX.}
+\Msg{*}
+\Msg{* Run the `.dtx' file through LaTeX2e to get the documentation.}
+\Msg{*}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-15 13:06:04 +0000