path: root/Master/texmf-dist/source/latex/youngtab/youngtab.dtx

% \iffalse
%% File: youngtab.dtx
%% Copyright (C) 1996,98,99 Volker B"orchers and Stefan Gieseke,
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN
%% archives in directory macros/latex/base/lppl.txt; either
%% version 1 of the License, or any later version.
%
%<package>\NeedsTeXFormat{LaTeX2e}
%<package>\ProvidesPackage{youngtab}
%<package>[1999/05/19 v1.1; Macros for Young-Tableaux]
%
%<*driver>
\documentclass{ltxdoc}
\usepackage[enableskew]{youngtab}
\GetFileInfo{youngtab.sty}
\begin{document}
\title{The \textsf{youngtab} package\thanks{This file has version number
    \fileversion, dated \filedate.}}
\author{Volker B\"orchers\thanks{email: boercher@physik.uni-bremen.de}
  \\Stefan Gieseke\\
  Universit\"at Bremen}
\date{\filedate}
 \maketitle
 \DocInput{youngtab.dtx}
\end{document}
%</driver>
% \fi
%\iffalse
%
%% Package `youngtab' to use with TeX, LaTeX209 or LaTeX2e
%% (You will need LaTeX2e to extract the documentation and a STY-file
%% without comments from the .dtx file)
%
% Version:     Date:     Changes:
%
%  1.0       1996/03/25  First working version. (After much
%                        frustrating tries to teach TeX accept
%                        indefinite count of arguments - lerning TeX
%                        in the meanwhile)
%  1.1       1998/05/05  Added possibility to typeset ``skew''
%                        tableaux (package option `enableskew')
%                        suggested by Andrew Mathas
%                        <mathas@maths.usyd.edu.au>. Added AUC-TeX
%                        support for the youngtab macros (youngtab.el).
%            1999/05/19  Only change: added licence informations
%\fi
%
%
% \DoNotIndex{\advance,\box,\CurrentOption,\DeclareOption,\def}
% \DoNotIndex{\else,\fi,\hbox,\hfil,\hrule,\hspace,\ht,\ifcat}
% \DoNotIndex{\ifmmode,\ifnum,\ifvoid,\loop,\MessageBreak,\newcount}
% \DoNotIndex{\newdimen,\newif,\newskip,\offinterlineskip}
% \DoNotIndex{\PackageWarning,\ProcessOptions,\relax,\repeat,\setbox}
% \DoNotIndex{\space,\typeout,\unskip,\vbox,\vcenter,\vrule,\vspace}
%
% \CheckSum{322}
%
% \newcommand{\yt}{Young-Tableau}
% \newcommand{\yts}{Young-Tableaux}
% \newcommand{\newfeature}[1]{\leavevmode%
%    \marginpar{\small\sffamily\begin{center}
%     New feature\\#1\end{center}}}
% 
% \begin{abstract}
%   This package provides two macros for typesetting
%   \yts\ with \TeX\ or \LaTeX. We use 2 macros, the first for empty
%   boxes (|\yng|), and the second for labelled boxes (|\young|). The
%   syntax of the macros is simple to avoid spelling-mistakes.
% \end{abstract}
%
% \tableofcontents
%
% \section{Introduction}
% The \yt-formalism is a strong algrebraic tool in group theory. Of course
% we will deal here only with the problems of \emph{typesetting} \yts.
% They are mathematical objects, so they usually occur in mathematical
% environments. On the surface \yts\ consist of boxes like this:
% \yng(1) --- or optionally labelled (usually with letters): \young(a).
%
% There is already one \LaTeX-package for typesetting \yts, the
% \texttt{young.sty} by J\"org Knappen (based on |young.tex| by P. E. S.
% Wormer). It provides a \texttt{Young}-environment with a syntax
% similar to the \texttt{tabular}-environment.
%
% An Example for the usage of \texttt{Young}:
%
% \begin{minipage}[t]{5cm}
% \begin{verbatim}
% \begin{Young}
%   $a$&&\cr
%   &\cr
%   \cr
% \end{Young}
% \end{verbatim}
% \end{minipage}
% \parbox[t]{4cm}{ \young(a\hfil\hfil,\hfil\hfil,\hfil) }
%
% \iffalse
% COMMENT: Maybe that's not the correct way to pretend the use of the
% |Young|-environment, but otherwise we had to use |young.sty| only
% for this tableau!
% \fi
%
% This way of implementing \yts\ has one big advantage: It can deal with
% an indefinite number of rows and columns (of course this is needed!).
% A second argument for using a \texttt{tabular}-like environment might
% be it's simple encoding.
%
% Nevertheless we wanted a simpler user-interface, for the use of |&| and
% |\cr| is usually a very good source of typing mistakes (e.g. you
% have to type \emph{three} |&|'s to get \emph{four} boxes in one
% row). In addition the \TeX-code for mathematical relations with more
% than two or three \yts\ becomes unreadable.
%
% The cure would be of course a \emph{macro} with a compact, intuitive
% syntax. But there is the above mentioned problem: \TeX\ is not made to
% handle an indefinite number of arguments. For \yts\ composed of empty
% boxes we would like to have a macro with one argument for each row
% (counting the number of boxes per row) for example this way:
% |\thisdoesnotwork{5}{3}{1}|\dots.  For \yts\ composed of labelled
% boxes the problem is even worse since we have one letter
% \emph{per box}!
%
% So we had to hide the fact of having an indefinite number of arguments
% from \TeX. The macros in this package have --- as \TeX\ sees it ---
% only one argument; this is parsed for the necessary information
% by the macros themselves. Whereas, for the user, the number of rows and
% number of boxes per row are plain to see.
%
% \section{Using the youngtab package}
% Invoke the |youngtab| package by
% requesting it in the preamble:\footnote{Of course this does not work
% if you use the |youngtab|-package with \TeX\ instead of \LaTeX. For
%   compatibility-questions see section \ref{compat}}
%
% |\usepackage[...]{youngtab}|
%
% The package has four options (increasing)\DescribeMacro{Options}.
% The \emph{first option}, |vcentermath|\DescribeMacro{vcentermath},
% \emph{turns on} the vertical centering of the tableaux in math mode. The
% \emph{second option}, |noautoscale|\DescribeMacro{noautoscale}, \emph{turns
% off} the automatic scaling of the boxes according to the actual font.
% The \emph{third one}, |stdtext|\DescribeMacro{stdtext}, switches
% to text mode in the inside of labelled boxes. Choosing one of this
% options does not mean that you have, for example, to stick to
% |noautoscale| till the end of your days.  You may change this
% settings as often as you like.\\
% The \emph{fourth option},
% |enableskew|\DescribeMacro{enableskew}\newfeature{1998/05/05}
% enables typesetting of skew \yts\ (tableaux that are not
% left-aligned). This option is different from the other in the way
% that there is no command to enable this feature after the package is
% loaded.
%
% \yts\ usually have more than one row, so the vertical alignment is a
% problem\DescribeMacro{vcentermath}. You can turn on vertical centering
% (only) in mathmode either by choosing the option |vcentermath| with
% |\usepackage| or later with the command
% |\Yvcentermath|\meta{num}. Say |\Yvcentermath1| if you want
% vertical centering and |\Yvcentermath0| to switch it off. Without
% vcentering the tableaux are standing on the baseline.
%
% Since the boxes are quadratic (if you do not want want this,
% complain!), there is only one dimension to determine: the length and
% height of the boxes. Usually the macros determine this for
% themselves,\footnote{So that a \yt\ e.g.\ \texttt{\bslash young(ab)}
%   \young(ab) appears smaller in a footnote than in normal text!} but
% you can change this behavior by calling the macro
% |\Yautoscale|\meta{num}\DescribeMacro{\Yautoscale}. Call it with
% an argument of |1| if you want autoscaling after this, or with
% the argument |0| if you want to adjust the box dimensions
% yourself.
%
% \DescribeMacro{\Yboxdim}If you switch off autoscaling and
% want to change the box dimensions, you have to call the macro
% |\Yboxdim|\meta{dim} with a usual \TeX--dimension.
% The argument has to be appended to the macro: |\Yboxdim13pt|. This
% dimension is the \emph{total} height and width of the boxes --
% \emph{including the lines.} (For small linethicknesses this
% makes of course only a small difference.) Note that the use of |\Yboxdim|
% \emph{implies} |noautoscale|! So to switch from |autoscale| to
% |noautoscale| one call to |\Yboxdim| is sufficient.
%
% There is only one more parameter which determines the appearance of
% the \yt\DescribeMacro{\Ylinethick}: the lines' thickness. This is
% set by |\Ylinethick|\meta{dim}. (The default is $0.3pt$).
%
% You may add space between a tableau and surrounding stuff by
% invoking the macro
% |\Yinterspace|\meta{skip}\DescribeMacro{\Yinterspace}. The advantage
% of using a \emph{skip} is  that this helps \TeX\ to avoid |Over|-
% or |Underful \hbox|es. The default value is |0ex plus 0.3ex|\,.
% (Better take |ex| or |em| for the tableaux are scaleable.)
%
% \subsection{Empty boxes: \texttt{\protect\bslash yng}}
% \DescribeMacro\yng
% The most used variant of \yts\ are those consisting of empty boxes.
% For the tableau \yng(2,1) you have to type
% |\yng(2,1)|. If you want it to appear smaller, change the
% fontsize: |{\tiny\yng(2,1)}| gives \Yautoscale1
% {\tiny\yng(2,1)}; but remember, this only works if |autoscale|
% is turned on (default). (If you are in |noautoscale|-mode, restore
% autoscaling with |\Yautoscale1|.)
%
% Some notes on the usage of |\yng| and |\young| in math or
% text mode\DescribeMacro{math or text?}: You can generate \yts\ in both
% modes, but differences arise from \emph{vertical centering}.
% This only works in math mode (if you have chosen it with
% |\Yvcentermath1|) or |usepackage| option |vcentermath|.
%
% The difference is to be seen here:
% {\tiny\Yvcentermath1 $\yng(1,1)\oplus\yng(1)=$
%   \yng(2,1)}$\oplus$ \dots, which has been generated by
% \begin{verbatim}
% {\tiny\Yvcentermath1 $\yng(1,1)\oplus\yng(1)=$
%   \yng(2,1)}$\oplus$ \dots
% \end{verbatim}
%
% Here the tableau in math are centered with respect to the axis of
% the formula while the one in text mode isn't. Note the
% dimensions of the tableau on the one hand and the |\oplus| on the
% other: The dimensions of the \yts\ are determined by the actual
% text's fontsize (while autoscaling!)\DescribeMacro{sizing}. Try to
% understand what happens in the following example. --- Do you
% understand the sizes of the math symbols? (Compare to the example
% above and have look up the \texttt{.log} file. Don't let \TeX\ fool
% you by messages about invalid |\normalsize|!)
% \begin{verbatim}
% {\tiny\begin{equation}
%     \Yvcentermath1
%     \yng(1,1)\oplus\yng(1)= \Yboxdim{12pt}
%     \yng(2,1)\normalsize\oplus\dots
% \end{equation}}
% \end{verbatim}
% {\tiny\begin{equation}
%     \Yvcentermath1 \yng(1,1)\oplus\yng(1)=
%     \Yboxdim{12pt}\yng(2,1)\normalsize\oplus\dots
% \end{equation}}
% \Yautoscale1
%
% \subsection{Labelled boxes: \texttt{\protect\bslash young}}
% \DescribeMacro\young
% While the sizing of the boxes and the behavior in math/text mode are
% exactly the same as with |\yng|, we have of course a different syntax:\\
% |{\scriptsize\young(aa,b)}| results in
% {\scriptsize\young(aa,b)}. Each line of the tableau is represented
% by a row of single letters (exactly: ``tokens''). The lines
% are separated by commas.
%
% As you see from the example above the letters |a| and |b| come out in
% math italics. This does \emph{not} depend on the \yt\ appearing in
% math or text surround. \emph{The label within a tableau-box is math -- no
%   matter if the tableau is used in text or math mode!} But this is
% only the default setting. Use either the option |stdtext| to the
% |\usepackage| command to switch to roman letters or use the macro
% |\Ystdtext| with an argument of |1|: |\Ystdtext1|. To switch to math
% again use |\Ystdtext0|.
%
% What to do if you don't want to use single letters, but symbols or
% perhaps some white boxes? There are no limits but it's a bit
% complicated. The |\young| algorithm for parsing his argument depends
% strongly on that every label of \emph{one} box,
% \begin{enumerate}
% \item consists of only \emph{one token}. Assume first you had
%   \emph{not} said |\Ystdtext1|.  To get a single roman `a' then you
%   must not say |\mbox{a}|, because this makes \emph{four} tokens (1st
%   is |\mbox|, 2nd is |{|, 3rd is |a|, 4th is |}|). The cure is
%   simply making one token out of |\mbox{a}| by saying
%   |\newcommand{\rma}{\mbox{a}}| and everything is OK:\footnote{Note
%   that the space after \texttt{\bslash rma} belongs to the token itself.}
%   \newcommand{\rma}{\mbox{a}} |\young(\rma lright\bullet)| = \young(\rma
%   lright\bullet)\\
%   After |\Ystdtext1| it is an error to say |$\bullet$|, since the
%   two math delimiters are single tokens. Do it as described above:
%   \Ystdtext1\\ |\newcommand{\ybullet}{$\bullet$}|\\ and
%   everything is OK: \newcommand{\ybullet}{$\bullet$}
%   |\young(\ybullet works)| = \young(\ybullet works)\,.\Ystdtext0\\
%   To use a symbol or special letter in both modes (|\Ystdtext 0 or 1|)
%   put it in a box (here with an extra tuning):\\
%   |\renewcommand{\ybullet}{\raise1.5pt \hbox{$\bullet$}}|
% \item Some characters and macros are not allowed: commas (guess why)
%   and the other punctuation marks, spaces, the macro |\space| and also
%   skips like |\,| and |\:|.\footnote{Write to us if you find more.} If
%   you want to have single empty boxes use (\TeX\ primitive) |\hfil|
%   (For understanding this limitations see also |\y@lastargtest| and
%   |\y@nelettertest| in macro section).
%  \end{enumerate}
%
%
% \subsubsection{Skew \yts\ with \texttt{\protect\bslash young}}
% \newfeature{1998/05/05}
% As far as described above, the rows of a \yt\ are left-aligned. Since
% some authors also assigned a meaning to \emph{``skew''} tableaux, this
% package also supports such along with |\young|. If you want to typeset
% skew tableaux, you have to enable this via the package option
% |enableskew|\DescribeMacro{enableskew}. The default behavior of this
% package is to \emph{dis\/}able skew boxes in order to save \TeX's
% time, however, it's save to include this option even if you do not use
% it.
%
% Here is an example:
% |\young(abcd,:bc,::c)|: \raisebox{-1.9\baselineskip}{\young(abcd,:bc,::c)}
%
% As you see, the Option |enableskew| makes the colon a special
% character (only inside the argument of |\young|). \footnote{If you
%   want a colon to appear as it is (do you??), you have to do the same
%   trick as above with an unpleasant extra: define a macro for the
%   colon using the \TeX-primitive \texttt{\bslash char} like this:
%   \texttt{\bslash newcommand{\bslash mycolon}{\bslash char58}}.} In
% fact all other than the leading colons in a row will simply be
% ignored, while the first will move the row to the right.
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \Yboxdim.4ex
% \raisebox{-1pt}{\young(:\hfil,\hfil,\hfil,\hfil,\hfil,:\hfil)}
% This is a\,
% \young(\hfil,\hfil,\hfil,\hfil,\hfil\hfil\hfil)
% \young(\hfil,\hfil,\hfil,\hfil,\hfil)
% \young(\hfil\hfil\hfil,:\hfil,:\hfil,:\hfil,:\hfil)
% \young(\hfil\hfil\hfil,:\hfil,:\hfil,:\hfil,:\hfil)
% \young(\hfil,\hfil,\hfil,\hfil,\hfil\hfil\hfil)
% \young(\hfil\hfil\hfil,\hfil,\hfil\hfil,\hfil,\hfil\hfil\hfil)
% \hspace{.7ex}
% \young(\hfil\hfil\hfil,:\hfil,:\hfil,:\hfil,:\hfil)
% \young(\hfil\hfil\hfil,\hfil,\hfil\hfil,\hfil,\hfil\hfil\hfil)
% \young(:\hfil\hfil\hfil,\hfil,:\hfil\hfil,:::\hfil,\hfil\hfil\hfil)
% \young(\hfil\hfil\hfil,:\hfil,:\hfil,:\hfil,:\hfil)
% of skew tableaux.
% \raisebox{-1pt}{\young(\hfil,:\hfil,:\hfil,:\hfil,:\hfil,\hfil)}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \Yautoscale1
%
%
% \subsection{The \texttt{youngtab} package and \TeX}\label{compat}
% \DescribeMacro{Compatibility}Because we do not use \PlainTeX, the
% compatibility of this package and \TeX\ is not sufficiently tested.
% However there are some changes necessary in |youngtab.sty| (see file
% \texttt{youngtab.tex}, part of the distribution):
% \begin{itemize}
% \item The macros themselves only use two \LaTeX-commands,
%   |\vspace{|\meta{dim}|}| and |\hspace{|\meta{dim}|}|. One has to
%   replace them with `|\vskip |\meta{dim}' resp.\ `|\hskip|
%   \meta{dim}'\,. (The braces also have to get removed) The
%   \LaTeX-counterparts may be better but no problems should arise
%   from this replacement (we found none).
% \item One has to remove all lines containing \LaTeXe-commands in the
%   preamble of the |.sty| file, e.g.\ comment out every line that
%   contains the following commands: |\DeclareOption|,
%   |\ProcessOptions|, |\NeedsTeXFormat| and |\ProvidesPackage|.
% \item Since \TeX-input files must not contain a |@|,
% |\catcode`\@11\relax| has to be added to the begin of the |.sty| file to 
%   make |@| a |letter| and |\catcode`\@12\relax| at the end right
%   before the |\endinput|, to make it |other| again afterwards.
% \item \textbf{Skew:}\hspace{1em} \TeX\ knows nothing about
%   style-options, we have to find a way to enable skew
%   \yts. (|enableskew| is the only package option that can \emph{not}
%   be accessed by a macro \emph{after loading} the package since
%   almost all according actions will be done at loading time).\\
%   Therefore, we will check if a macro |\enableskew| is defined at loading
%   time:\\[.3ex]
%   |  \expandafter\ifx\csname enableskew\endcsname\relax|\\
%   |   \y@enable@skewfalse \else \y@enable@skewtrue\fi|\\[.3ex]
%   (excerpt from |youngtab.tex|) Then this will enable printing of
%   skew tableaux: \hfil|\def\enableskew{1} \input youngtab|
% \item The autoscaling doesn't work as nice as with \LaTeX\ since if
%   you lower the text's fontsize (which determines the boxsize), you
%   have to lower also the math fontsize. Otherwise the letters in
%   labelled boxes (math!) are too big for the box.
% \end{itemize}
%
% \subsection{To do}
% We have a \textbf{wish list}, things we think the package should be
% capable of:
% \begin{itemize}
% \item A vertical alignment, in the way that the \emph{top}line of the
%   \yts\ and the mathsymbols are on the same height (perhaps using
%   |\vtop|?).
% \item The macros should take notice of math fontsize changes e.g.\ with
%   \texttt{\bslash dis\-play\-style}. (This puts a focus on the autoscale
%   mechanism -- see |\y@setdim| in the macro section.)
% \end{itemize}
% \textbf{If You} have any problems, suggestions, critical remarks -- or
% whatever according this package write to Volker B\"orchers
% (email-adress see title).\\
% {\tiny\yng(61)}
%
% \StopEventually{}
%
% \section{The Macros}
%
%    \begin{macrocode}
%<*package>
%    \end{macrocode}
%
% \begin{macro}{\Yautoscale}
% \begin{macro}{\ify@autoscale}
% If autoscaling is active, the size of the boxes (|\y@boxdim|) is
% determined by the package itselve. The default setting is to
% allow autoscale. |\Yautoscale|\meta{num} serves as the user
% interface.\footnote{I know - it's against the \LaTeXe naming
%   conventions, but it is nicer\dots} We made an option to |\usepackage|
% out of that (see below).
%    \begin{macrocode}
\newif\ify@autoscale \y@autoscaletrue \def\Yautoscale#1{\ifnum #1=0
  \y@autoscalefalse\else\y@autoscaletrue\fi}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \begin{macro}{\Yboxdim}
% \begin{macro}{\y@b@xdim}
% \begin{macro}{\y@boxdim}
% The parameters determining the size of the single boxes and the macro
% to set them. |\Yboxdim|\meta{dim} sets |\y@boxdim| (only used, when
% autoscaling is turned off) and sets |y@autoscale| to
% |false|. |\y@boxdim| is the \emph{total} size of the box (including
% the delimiting lines) while |\y@b@xdim| (to be set in |\y@setdim|) is
% the height and width of the inner of the box.
%    \begin{macrocode}
\newdimen\y@b@xdim
\newdimen\y@boxdim \y@boxdim=13pt
\def\Yboxdim#1{\y@autoscalefalse\y@boxdim=#1}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\Ylinethick}
% \begin{macro}{\y@linethick}
% The line thickness and |\Ylinethick|\meta{dim} as user interface to it.
%    \begin{macrocode}
\newdimen\y@linethick    \y@linethick=.3pt
\def\Ylinethick#1{\y@linethick=#1}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\Yinterspace}
% \begin{macro}{\y@interspace}
% To give the \yts\ extra-space (before and after) |\y@interspace| can
% be set to more than |0pt| by calling |\Yinterspace|. (See |\yng| and
% |\young|.) Note that this is a \emph{skip} and no \emph{dimemsion}.
%    \begin{macrocode}
\newskip\y@interspace \y@interspace=0ex plus 0.3ex
\def\Yinterspace#1{\y@interspace=#1}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\Yvcentermath}
% \begin{macro}{\ify@vcenter}
% The switch to turn vertical centering in math on or off. The default
% is |\y@vcenterfalse|. The second option to |\usepackage|.
%    \begin{macrocode}
\newif\ify@vcenter   \y@vcenterfalse
\def\Yvcentermath#1{\ifnum #1=0 \y@vcenterfalse\else\y@vcentertrue\fi}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\Ystdtext}
% \begin{macro}{\ify@stdtext}
% Normally the inside of the boxes (|\young|) is in math mode. This code
% allows to switch to text mode.
%    \begin{macrocode}
\newif\ify@stdtext   \y@stdtextfalse
\def\Ystdtext#1{\ifnum #1=0 \y@stdtextfalse\else\y@stdtexttrue\fi}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\ify@enable@skew}
% In contrast to the other this \texttt{if} may be set only via the
% package option |enableskew|.
%    \begin{macrocode}
\newif\ify@enable@skew   \y@enable@skewfalse
%    \end{macrocode}
% \end{macro}
% \begin{macro}{noautoscale}
% \begin{macro}{vcentermath}
% \begin{macro}{stdtext}
% \begin{macro}{enableskew}
% Declaration and processing of the options for use with
% \LaTeXe. (For \TeX-users: Comment the following 8 lines out).
%    \begin{macrocode}
\DeclareOption{noautoscale}{\y@autoscalefalse}
\DeclareOption{vcentermath}{\y@vcentertrue}
\DeclareOption{stdtext}{\y@vcentertrue}
\DeclareOption{enableskew}{\y@enable@skewtrue}
\DeclareOption*{\PackageWarning{youngtab}{%
    Unknown option `\CurrentOption' (Known:\MessageBreak
    `vcentermath', `noautoscale', `stdtext', `enableskew'.)}}
\ProcessOptions\relax
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\y@vr}
% A single vertical line to build the boxes. The reason for the depht of
% the line should be clear. (The values for the depth maybe something
% you want to tune)
%    \begin{macrocode}
\def\y@vr{\vrule height0.8\y@b@xdim width\y@linethick depth 0.2\y@b@xdim}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\y@emptybox}
% This macro does less than its name pretend: It only makes one vertical
% line followed by a empty box (width: |\y@boxdim| -- 2|\y@linethick|).
%    \begin{macrocode}
\def\y@emptybox{\y@vr\hbox to \y@b@xdim{\hfil}}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\y@abcbox}
% \begin{macro}{\y@mathabcbox}
% If |enableskew| is not choosen (the package options have been
% parsed now), a |\y@abcbox| or a |\y@mathabcbox| is the simple
% analogue to |\y@emptybox| but it has a \emph{text-font} letter
% centered in it.\\
% For |\y@mathabcbox| the inside is math. We rather want an
% easier access to math italics and symbols than to normal text; so we
% usually use |\y@mathabcbox| instead of |\y@abcbox|.
%
% Skew \yts\ can only be used with |\young|. Then a colon is used to
% \emph{shift} the row to the \emph{right} -- instead of ``inserting
% a box without border'' -- so the colon boxes must be ignored.
%    \begin{macrocode}
\ify@enable@skew
 \def\y@abcbox#1{\if :#1\else
   \y@vr\hbox to \y@b@xdim{\hfil#1\hfil}\fi}
 \def\y@mathabcbox#1{\if :#1\else
   \y@vr\hbox to \y@b@xdim{\hfil$#1$\hfil}\fi}
\else
 \def\y@abcbox#1{\y@vr\hbox to \y@b@xdim{\hfil#1\hfil}}
 \def\y@mathabcbox#1{\y@vr\hbox to \y@b@xdim{\hfil$#1$\hfil}}
\fi
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\y@setdim}
% This macro is called at the beginning of the macros |\yng| and
% |\young|. If |autoscale| is deactivated the box height and width is
% |\y@boxdim| - 2|\y@linethick|. If not we save a box for temporary
% usage, use the height of it to find a good size of the box, fill the
% boxregister with a empty box, and clear the box again by using it.
%
% That's not elegant but I didn't know better\dots How can I determine
% the height of the font in an other way? (I tried it with the \TeX-measure
% |ex| -- but this did not seem to work in any case.) Or -- if I have
% to use setbox -- which boxregister should I use? Is the |\ifvoid| test
% obsolete? (First I used |\box0| -- till I found me competing with
% \AmSTeX\ for this box.)
%    \begin{macrocode}
\def\y@setdim{%
  \ify@autoscale%
   \ifvoid1\else\typeout{Package youngtab: box1 not free! Expect an
     error!}\fi%
   \setbox1=\hbox{A}\y@b@xdim=1.6\ht1 \setbox1=\hbox{}\box1%
  \else\y@b@xdim=\y@boxdim \advance\y@b@xdim by -2\y@linethick
  \fi}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\y@counter}
% A counter for loops.
%    \begin{macrocode}
\newcount\y@counter
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\y@lastargtest}
% This macro is a hack to get \TeX\ to accept a indefinite number of
% arguments (here: the number of \emph{lines} separated by commas). It
% does nothing with its arguments but to see if the second is a space,
% and, if it is to set |\y@islastargtrue|.\footnote{The
%   \texttt{islastarg} conditions are also used if the end of one line
%   of labelled boxes is reached.}
%    \begin{macrocode}
\newif\ify@islastarg
\def\y@lastargtest#1,#2 {\if\space #2 \y@islastargtrue
  \else\y@islastargfalse\fi}
%    \end{macrocode}
% How does it work? An Example:
%
% \verb*+\y@lastargtest first,second +\\
% Here |#1| is |first| and |#2| is |second|. The |\if| construction
% tests if the (expanded) \emph{first} token of |#2| and |\space|
% (here: |s|) are equal. -- They are not. In the next example the
% condition is |true|:
%
% \verb*+\y@lastargtest first, +\\
% Here |#1| is again |first| but |\y@lastargtest| catches the blank
% after the comma to be |#2|. The |\if| condition now is true and
% |\y@islastargtrue| is set. Remember: the blank is essential!
% \end{macro}
%
% \begin{macro}{\y@emptyboxes}
% This macro draws |#1| (this is a number) empty boxes (|\y@emptybox|)
% -- without a top or bottom line:
%
% |:\y@emptyboxes3:| \hspace{0.5em} is
% :$\mid$\hspace{0.8em}$\mid$\hspace{0.8em}$\mid$\hspace{0.8em}:
%    \begin{macrocode}
\def\y@emptyboxes#1{\y@counter=#1\loop\ifnum\y@counter>0
  \advance\y@counter by -1 \y@emptybox\repeat}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\y@nelineemptyboxes}
% This calls |\y@emptyboxes| and adds the top and bottom lines (I think
% this is faster than draw single, complete boxes) and a right closing
% vertical line. Because of the |\vspace| command the top line of the
% eventually following next box-row will be drawn over the bottom line of
% this box-row.
%    \begin{macrocode}
\def\y@nelineemptyboxes#1{%
  \vbox{%
    \hrule height\y@linethick%
    \hbox{\y@emptyboxes{#1}\y@vr}
    \hrule height\y@linethick}\vspace{-\y@linethick}}
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\yng}
% The user-macro for empty \yts. As mentioned above it has only one
% argument, enclosed in brackets. It first calls |\y@setdim| to
% determine the size of the boxes and opens a |\vcenter| if in math mode
% and |vcentermath| is set. Otherwise only a (then obsolet) |{| is
% opened. |\y@lastargtest| determines if the tableau should have only
% one line, setting |\y@islastargtrue| or -|false|. If there is only one
% line, |\yng| does the whole job in calling
% |\y@nelineemptyboxes| once. Otherwise it calls |\y@ungempty| to do the
% real thing. Note the spacing before and after the tableau using
% |\hspace|.
%    \begin{macrocode}
\def\yng(#1){%
  \y@setdim%
  \hspace{\y@interspace}%
  \ifmmode\ify@vcenter\vcenter\fi\fi{%
  \y@lastargtest#1,
  \vbox{\offinterlineskip
    \ify@islastarg
     \y@nelineemptyboxes{#1}
    \else
     \y@ungempty(#1)
    \fi}}\hspace{\y@interspace}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\y@ungempty}
% It is called with |\y@ungempty(#1)| from |\yng|. Now the parsing of
% the arguments starts! As we know from |\y@lastargtest| in
% |\yng|, there really are two arguments left. Explicitely: Let the
% the initial command (given by the user) be |\yng(3,2,1)|; then
% |\yng| calls |\y@ungempty(3,2,1)|. But |\y@ungempty| sees two
% arguments: |#1| is |3| and |#2| is |2,1|! (Note the importance of the
% brackets). |\y@ungempty| then processes the first argument immediately,
% calling |\y@nelineemptyboxes|. (The braces protect numbers with more
% than one digit.)
%
% The next step is to check if |#2| is the last line. If it is, it calls
% \texttt{\bslash y@ne\-line\-empty\-boxes} again. Otherwise it calls
% \emph{recursively itselve}, till all lines are processed.
%    \begin{macrocode}
\def\y@ungempty(#1,#2){%
  \y@nelineemptyboxes{#1}
  \y@lastargtest#2,
  \ify@islastarg
   \y@nelineemptyboxes{#2}
  \else
   \y@ungempty(#2)
  \fi}
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\y@nelettertest}
% The first macro especially for labelled boxes, that is, for
% |\young|. Like \texttt{\bslash y@last\-arg\-test} it is used for
% handling a indefinite number of arguments. (As mentioned before
% \yts\ with labelled boxes have problem double.) |\y@nelettertest|
% determines if the last box of the line has been reached.
%
% Again we will examine it's working method by examples:
%
% |\y@nelettertest ab.|\\
% The period after the argument |ab| (and in the definition of
% |\y@nelettertest|) is merely a mark for the end of the
% arguments. (Otherwise \TeX\ would complain about missing arguments.)
% Here |a| is |#1| and |#2| is |b| -- the |\if|-condition is |false|
% and so |\y@islastargfalse| is set. Now a little miracle:
%
% |\y@nelettertest a.|\\
% In the opposite to the case of |\y@lastargtest| it's not
% understandable for me, why |#2| now is a space -- but it is! (Do
% \emph{you} know the reason why?)
% The rest is known from |\y@lastargtest|.
%    \begin{macrocode}
\def\y@nelettertest#1#2. {\if\space #2 \y@islastargtrue
  \else\y@islastargfalse\fi}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\y@abcboxes}
% Again we use a period to mark the end of arguments. Compare to
% |\y@emptyboxes| -- Now it is more strenuous! The |\y@nelettertest|
% macro makes sure that |\y@abcboxes| is called with at least two boxes
% to process. If there are only two boxes |\y@abcboxes| calls
% |\y@abcbox| two times, otherwise it calls itselve recursively again.
% (The argument-splitting works as in |\y@ungempty|.)
%    \begin{macrocode}
\def\y@abcboxes#1#2.{%
  \ify@stdtext\y@abcbox#1\else\y@mathabcbox#1\fi%
  \y@nelettertest #2.
%    \end{macrocode}
% There must be a space or (equivalently) a carriage return after this
% line!
%    \begin{macrocode}
  \ify@islastarg\unskip%
   \ify@stdtext\y@abcbox{#2}\else\y@mathabcbox{#2}\fi%
  \else\y@abcboxes#2.\fi}
%    \end{macrocode}
% The |\unskip| is needed for the case that |#2| is only one token. Then
% a space appears between two boxes. (I do not understand really what
% happens -- see |\y@nelettertest|.) The |\unskip| resolves this problem.
% \end{macro}
%
% \begin{macro}{\ify@enable@skew}
% \begin{macro}{\y@full@b@xdim}
% \begin{macro}{\y@m@veright@cnt}
% Most of the skew boxes stuff can be found here along the definition
% of \texttt{\bslash y@ne\-line\-abc\-boxes}. We need a further dimension,
% for the effective lenght of one box in a row, |\y@full@b@xdim| =
% |\y@b@xdim| + |1\y@linethick| and one counter for the number of
% boxes to  be left out on the left side of the tableau (determined by
% the number of colons at the beginning of a row), |\y@m@veright@cnt|.
%    \begin{macrocode}
\ify@enable@skew
 \newdimen\y@full@b@xdim
 \newcount\y@m@veright@cnt
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \begin{macro}{\y@get@m@veright@cnt}
% To find out the number of leading colons in a row we have the macro
% \texttt{\bslash y@get@\-m@ve\-right@\-cnt}. Here we use exactly the same
% trick as in |\y@nelettertest|.
%    \begin{macrocode}
 \def\y@get@m@veright@cnt#1#2.{%
   \if :#1 \advance\y@m@veright@cnt by 1\y@get@m@veright@cnt#2.\fi}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\y@setdim}
% Since we now have another dimension that depends on |\y@b@xdim|,
% the dimension of the boxes, we have to extend |\y@setdim| to
% calculate |\y@full@b@xdim| too. (The dummy |\y@setdim@| is used to
% avoid a recursion.)
%    \begin{macrocode}
 \let\y@setdim@=\y@setdim
 \def\y@setdim{%
   \y@setdim@ \y@full@b@xdim=\y@b@xdim
   \advance\y@full@b@xdim by 1\y@linethick}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\y@m@veright@ifskew}
% Now we put it all into the following macro that computes the offset
% and moves the tableau to the right if necessary. If skew \yts\ are
% not enabled, |\y@m@veright@ifskew| will be a null-command (but
% catches the argument).
%    \begin{macrocode}
 \def\y@m@veright@ifskew#1{
   \y@m@veright@cnt=0 \y@get@m@veright@cnt#1.
   \moveright \y@m@veright@cnt\y@full@b@xdim}
\else
 \def\y@m@veright@ifskew#1{}
\fi  
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\y@nelineabcboxes}
% This is the counterpart of |\y@nelineemptyboxes|. The difference
% is the treatment of the case of a row of only one box -- Then only
% |\y@abcbox| is called and not |\y@abcboxes|. If this row must be
% moved to the right, this is done by |\y@m@veright@ifskew|.
%    \begin{macrocode}
\def\y@nelineabcboxes#1{%
  \y@nelettertest #1.
  \ify@islastarg
   \y@m@veright@ifskew{#1}
    \vbox{
      \hrule height\y@linethick%
      \hbox{\ify@stdtext\y@abcbox#1\else\y@mathabcbox#1\fi\y@vr}
      \hrule height\y@linethick}\vspace{-\y@linethick}
  \else
   \y@m@veright@ifskew{#1}
    \vbox{
      \hrule height\y@linethick%
      \hbox{\y@abcboxes #1.\y@vr}%
      \hrule height\y@linethick}\vspace{-\y@linethick}
  \fi}
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\young}
% The user-macro for labelled \yts. It has one argument as |\yng|,
% enclosed in brackets. Everything is identical as in the emptybox case
% (sizing, vcentering, treatment of multiple rows, \dots).
%    \begin{macrocode}
\def\young(#1){%
  \y@setdim%
  \hspace{\y@interspace}%
  \y@lastargtest#1,
  \ifmmode\ify@vcenter\vcenter\fi\fi{%
  \vbox{\offinterlineskip
    \ify@islastarg\y@nelineabcboxes{#1}%
    \else\y@ungabc(#1)%
    \fi}}\hspace{\y@interspace}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\y@ungabc}
% Again nothing new -- see |\y@ungempty|
%    \begin{macrocode}
\def\y@ungabc(#1,#2){%
  \y@nelineabcboxes{#1}%
  \y@lastargtest#2,
  \ify@islastarg\y@nelineabcboxes{#2}%
  \else\y@ungabc(#2)%
  \fi}
%    \end{macrocode}
% \end{macro}
%    \begin{macrocode}
%</package>
%    \end{macrocode}
%
% \Finale
\endinput