<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% \iffalse meta-comment
%
%% File: simples-matrices.dtx 
%% Copyright (C) 2022 Yvon Henel aka Le TeXnicien de surface
%%
%% It may be distributed and/or modified under the conditions of the
%% LaTeX Project Public License (LPPL), either version 1.3c of this
%% license or (at your option) any later version.  The latest version
%% of this license is in the file
%%
%%    http://www.latex-project.org/lppl.txt
%%
%
%&lt;*driver|package|doc&gt;
\RequirePackage{expl3}[2020/01/12]
\GetIdInfo$Id: simples-matrices.dtx 1.0.1 2022-07-03 TdS $
  {}
%&lt;/driver|package|doc&gt;
%&lt;*driver&gt;
\documentclass[full]{l3doc}
% \usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage[french,main=english]{babel}
\usepackage{simples-matrices}
\usepackage{xspace}
\usepackage{csquotes}

\providecommand\darg[3]{\texttt{#1}\meta{#2}\texttt{#3}}

\begin{document}
  \DocInput{\jobname.dtx}
\end{document}
%&lt;/driver&gt;
% \fi
%
% \title{^^A
%   The \pkg{simples-matrices} package^^A
%   \thanks{This file describes v\ExplFileVersion, last revised \ExplFileDate.}^^A
% }
%
% \author{^^A
%  Yvon Henel\thanks^^A
%    {^^A
%      E-mail:
%        \href{mailto:le.texnicien.de.surface@yvon-henel.fr}
%          {le.texnicien.de.surface@yvon-henel.fr}^^A
%    }^^A
% }
%
% \date{Released \ExplFileDate}
%
% \maketitle
% 
% \changes{v1.0}{2022/06/08}{First public version.\foreignlanguage{french}{\emph{Premi��re version publique.}}}
% \changes{v1.0.1}{2022/07/03}{Some improvements in the documentation.\foreignlanguage{french}{\emph{Quelques am��liorations dans la documentation.}}} 
%
% \thispagestyle{empty}
% 
% \noindent\hrulefill
%
% \begin{otherlanguage}{french}
% \begin{abstract}
%   Cette extension fournit des commandes pour d��finir et ��crire des matrices en
%   donnant leurs coefficients, par ligne, dans une vliste (liste de valeurs
%   s��par��es par des virgules).
% 
%   La documentation fran��aise pour l'utilisateur de l'extension
%   \pkg{simples-matrices} est disponible sous le nom de
%   \texttt{simples-matrices-fra}. 
% \end{abstract}
% \end{otherlanguage}
% 
% \noindent\hrulefill
%
% \begin{abstract}
%   This package provides macros to define and write matrices the coefficients
%   of which are given, row by row, in a clist (list of values separated by
%   commas).
%   
%   The English documentation for the final user of the package
%   \pkg{simples-matrices} is available in the file
%   \texttt{simples-matrices-eng}.
% \end{abstract}
% 
% \noindent\hrulefill
% 
% \begin{documentation}
%
%
%\section{Summary of Syntax of Document Commands}
%\label{sec:summary}
%
%
% 
% \begin{function}{\matrice}
% \begin{syntax}
% \cs{matrice}\parg{prefix}\darg{\string&lt;}{clist of key-value pairs}{\string&gt;}\oarg{type}\marg{clist of coefficients}
% \end{syntax}
% \end{function}
% 
% \begin{function}{\declarermatrice}
%   \begin{syntax}
%     \cs{declarermatrice*}\parg{prefix}\darg{\string&lt;}{clist of key-value pairs}{\string&gt;}\marg{matrix name}\oarg{type}\marg{clist of coefficients}
%   \end{syntax}
% \end{function}
% 
% \begin{function}{\lamatrice}
%   \begin{syntax}
%     \cs{lamatrice}\parg{prefix}\darg{\string&lt;}{clist of key-value pairs}{\string&gt;}\marg{matrix name}
%   \end{syntax}
% \end{function}
%
% \begin{function}{\MatriceInterieur}
%   \begin{syntax}
%     \cs{MatriceInterieur}
%   \end{syntax}
% \end{function}
%
% \begin{function}{\LaMatriceInterieur}
%   \begin{syntax}
%     \cs{LaMatriceInterieur}\marg{matrix name}
%   \end{syntax}
% \end{function}
% 
% \begin{function}{\simplesmatricessetup}
%   \begin{syntax}
%     \cs{simplesmatricessetup}\marg{clist of key-value pairs}
%   \end{syntax}
% \end{function}
% 
% \begin{function}{\matid}
%   \begin{syntax}
%     \cs{matid}\oarg{diagonal coefficient, default \(1\)}\marg{size of the square matrix}
%   \end{syntax}
% \end{function}
% 
% \begin{function}{\matnulle}
%   \begin{syntax}
%     \cs{matid}\oarg{diagonal coefficient, default \(0\)}\marg{size of the square matrix}
%   \end{syntax}
% \end{function}
% 
% \end{documentation}
%
% \iffalse
%&lt;*doc&gt; 
\documentclass[full]{l3doc}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
%&lt;FRA&gt;\usepackage[english,main=french]{babel}
%&lt;ENG&gt;\usepackage[french,main=english]{babel}
\usepackage{xparse}
\usepackage{simples-matrices}
\newcommand\BOP{\discretionary{}{}{}}
\usepackage{xspace}
\usepackage{csquotes}
\usepackage{fancyvrb,fancyvrb-ex}
\usepackage{listings}
\usepackage{mathtools}
\usepackage{delarray}
\usepackage{nicematrix}

\providecommand\darg[3]{ \texttt{#1} \meta{#2} \texttt{#3} }

% \colorlet{option}{olive!75!black}
% Couleur des mots-cl��s de niveau 1
\colorlet{keyword20}{cyan} %!75!black
% Couleur des mots-cl��s de niveau 2
\colorlet{keyword30}{teal}
\colorlet{keycolor}{green!50!black}
\colorlet{dollarcolor}{violet}
\colorlet{cmdmuette}{blue}
\colorlet{cmdcausante}{red}

\lstset{frame=single,%
  language=[LaTeX]{TeX},%
  showspaces=false,%
  breaklines=true,%
  breakatwhitespace=true,% 
  basicstyle=\ttfamily\bfseries,%
  alsoletter={*-$},% 
  texcsstyle=*[2]\color{cmdcausante},%
  texcs=[2]{matrice,declarermatrice*,lamatrice,matid,matnulle,MatriceInterieur,LaMatriceInterieur},% 
  texcsstyle=*[3]\color{cmdmuette},%
  texcs=[3]{declarermatrice,simplesmatricessetup},% 
  keywordstyle=[20]\color{keyword20},%
  keywordstyle=[30]\color{keyword30},%
  keywordstyle=[40]\color{keycolor},%
  keywordstyle=[50]\color{dollarcolor},%
  keywords=[20]{tabular,array,matrix,matrix*,NiceArray},%
  keywords=[30]{x,S,T,I,J,C,O,D},%
  keywords=[40]{out-of-box,prefix,envir,typeord,argopt},%
  keywords=[50]{$},%
  escapeinside={\%*@}{@*)}%
}

\newcommand{\MacroPres}[2]{\textcolor{#1}{\textbf{\cs{#2}}}}
\newcommand{\csmute}{\MacroPres{cmdmuette}}
\newcommand{\csprint}{\MacroPres{cmdcausante}}
\newcommand{\ObjetPres}[2]{\textcolor{#1}{\textbf{\texttt{#2}}}}
\newcommand{\keyname}{\ObjetPres{keycolor}}
\newcommand{\envir}{\ObjetPres{keyword20}}
\newcommand{\TypeMat}{\ObjetPres{keyword30}}

\newcommand{\UnExemple}{%
  \par \medskip \par \noindent
  \begin{minipage}[c]{0.66\linewidth}
    \lstinputlisting[gobble=0, frame=single, numbers=left, numberstyle={\small}]{code00.tex}
  \end{minipage}
  \hspace{\stretch{1}}
  \begin{minipage}[c]{0.32\linewidth}
    \small 
    \input{code00}
  \end{minipage}
  \par \medbreak}

\newcommand*{\vliste}{liste\xspace}

%&lt;FRA&gt; \newcommand{\VoirEx}[1]{(voir exemple en page~\pageref{#1})}
%&lt;ENG&gt; \newcommand{\VoirEx}[1]{(see example on page~\pageref{#1})}

\begin{document}
%&lt;*FRA&gt;
\title{Guide de l'utilisateur de \pkg{simples-matrices}\thanks{Ce fichier d��crit
    la version~\ExplFileVersion, derni��re r��vision~\ExplFileDate.\\
    \emph{En souvenir de ma grand-m��re maternelle}, Adrienne \textsc{Binaut}
    (1908-03-23 -- 1997-06-08).}  }
%&lt;/FRA&gt;
%&lt;*ENG&gt;
\title{\pkg{simples-matrices} user guide\thanks{This file describes
    version~\ExplFileVersion, last revised~\ExplFileDate.\\
    \emph{In memory of my maternal grandmother} Adrienne \textsc{Binaut}
    (1908-03-23 -- 1997-06-08).}  }
%&lt;/ENG&gt;
\author{Yvon Henel\thanks{E-mail:
    \href{mailto:le.texnicien.de.surface@yvon-henel.fr}
    {le.texnicien.de.surface@yvon-henel.fr}}}
\maketitle
\noindent\hrulefill

\begin{abstract}
%&lt;*FRA&gt;
Une extension pour ��crire des matrices en donnant les coefficients par ligne
sous la forme d'une liste de valeurs s��par��es par des virgules.

Une macro permet de d��finir des matrices nomm��es et une autre permet d'��crire
les matrices nomm��es. L'extension fournit ��galement quelques raccourcis pour les
matrices identit�� et les matrices nulles.
%&lt;/FRA&gt;
%&lt;*ENG&gt;
A package to write matrices which are defined with a list of comma separated
coefficients read by row.

A macro enables the definition of a named matrix, another enables the writing of
a named matrix. This package provides also some shortcuts for identity matrices
and null matrices.

The name of this package and of its macros are French based for there are
already too many macros using the word ``matrix'' itself. The French
``\foreignlanguage{french}{simples matrices}'' means ``simple
matrices''. \emph{Just a letter apart!}
%&lt;/ENG&gt;
\end{abstract}

\noindent\hrulefill

%&lt;FRA&gt; \begin{otherlanguage}{english}
%&lt;ENG&gt; \begin{otherlanguage}{french}
\begin{abstract}
%&lt;*FRA&gt; 
A package to write matrices which are defined with a list of comma separated
coefficients read by row.

A macro enables the definition of a named matrix, another enables the writing of
a named matrix. This package provides also some shortcuts for identity matrices
and null matrices.

The name of this package and of its macros are French based for there are
already too many macros using the word ``matrix'' itself. The French
``\foreignlanguage{french}{simples matrices}'' means ``simple
matrices''. \emph{Just a letter apart!}

The English documentation for the final user of the package
\pkg{simples-matrices} is available in the file \texttt{simples-matrices-eng}. 
%&lt;/FRA&gt;
%&lt;*ENG&gt;
Une extension pour ��crire des matrices en donnant les coefficients par ligne
sous la forme d'une liste de valeurs s��par��es par des virgules.

Une macro permet de d��finir des matrices nomm��es et une autre permet d'��crire
les matrices nomm��es. L'extension fournit ��galement quelques raccourcis pour les
matrices identit�� et les matrices nulles.


La documentation fran��aise pour l'utilisateur de l'extension
\pkg{simples-matrices} est disponible sous le nom de \texttt{simples-matrices-fra}. 
%&lt;/ENG&gt;
\end{abstract}
\end{otherlanguage}

\noindent\hrulefill

\tableofcontents{}

\vspace{3\baselineskip}


%&lt;*ENG&gt;
The package \pkg{simples-matrices} requires \pkg{xparse} and \pkg{l3keys2e} used
to define macros and manage key-options. It loads \pkg{amsmath} as well for
ensuring a correct presentation of matrices.

\textbf{Beware}: you have to provide the suitable mathematical environment to
use the macros which print a matrix. Only the unstarred version of
\csmute{declarermatrice} may be used outside math-mode.

%&lt;/ENG&gt;
%&lt;*FRA&gt;
L'extension \pkg{simples-matrices} utilise \pkg{xparse} et \pkg{l3keys2e} pour
d��finir ses macros et g��rer les cl��s d'option. Elle charge ��galement
\pkg{amsmath} pour obtenir une pr��sentation convenable des matrices.

\textbf{Attention}: vous devez fournir l'environnement math��matique ad��quat pour
utiliser les macros qui ��crivent les matrices. Seule la version non-��toil��e de
\csmute{declarermatrice} peut ��tre utilis��e en dehors du mode math��matique.
%&lt;/FRA&gt;

%&lt;*ENG&gt;
\section{The Macros}
\label{sec:macros}

\pkg{simples-matrices} offers nine document macros.

%&lt;/ENG&gt;
%&lt;*FRA&gt;
\section{Les macros}
\label{sec:macros}

L'extension \pkg{simples-matrices} offre neuf macros de document.

%&lt;/FRA&gt;

%&lt;*ENG&gt;
In the main text (syntaxes and examples), the name of a macro of this package is
printed in red if the macro produces some text in the document, otherwise it is
printed in blue.
%&lt;/ENG&gt;
%&lt;*FRA&gt;
Dans le texte principal (syntaxes et exemples), le nom d'une macro de cette
extension est ��crit en rouge si la macro produit du texte dans le document,
autrement il est ��crit en bleu.
%&lt;/FRA&gt;

%&lt;*ENG&gt;
\subsection{Main Macros}
\label{sec:main}

The six main document macros are the following: 
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\subsection{Macros principales}
\label{sec:principales}

Les six macros principales sont les suivantes: 
%&lt;/FRA&gt; 
%&lt;*ENG&gt;

\begin{function}{\matrice}
  \begin{syntax}
    \csprint{matrice}\parg{prefix}\darg{\string&lt;}{clist of key-value pairs}{\string&gt;}\oarg{type}\marg{clist of coefficients}
  \end{syntax}
  where \meta{prefix} has the same meaning as the key \keyname{prefix} (see page~\pageref{key-prefix});
  \meta{clist of key-value pairs} ---optional and void by default--- can be used to
  redefined the \envir{matrix}-like environment; \meta{type} is a string of character
  the usage of which is explained later ---see \ref{sec:matrix-type}--- and
  \meta{clist of coefficients} is a clist of the coefficients of the matrix
  given by row order.

  The French \emph{matrice} means ``matrix''.
\end{function}
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\begin{function}{\matrice}
  \begin{syntax}
    \csprint{matrice}\parg{prefixe}\darg{\string&lt;}{\vliste de paires de cl��-valeur}{\string&gt;}\oarg{type}\marg{\vliste des coefficients}
  \end{syntax}
  o�� \meta{prefixe} a la m��me fonction que la cl�� \keyname{prefix} (voir page~\pageref{key-prefix});
  \meta{\vliste de paires de cl��-valeur} --- optionnel et vide par d��faut ---
  peut ��tre utilis�� pour red��finir l'environnement de type \envir{matrix};
  \meta{type} est une chaine de caract��re dont l'utilisation sera expliqu��e
  ci-dessous --- voir~\ref{sec:matrix-type} --- et \meta{\vliste des
    coefficients} est la \vliste des coefficients de la matrice donn��s ligne par
  ligne.
\end{function}
%&lt;/FRA&gt;

%&lt;ENG&gt; With
%&lt;FRA&gt; Avec
\lstinline+$\matrice{1, 2, 3, 4}$+
%&lt;ENG&gt; we obtain 
%&lt;FRA&gt; on obtient 
\(\matrice{1, 2, 3, 4}\).

%&lt;ENG&gt; With
%&lt;FRA&gt; Avec
\lstinline+$\matrice(b)[3]{1, 2, 3, 4, 5, 6}$+
%&lt;ENG&gt; we obtain 
%&lt;FRA&gt; on obtient 
\(\matrice(b)[3]{1, 2, 3, 4, 5, 6}\).

%&lt;*ENG&gt;
\begin{function}{\declarermatrice}
  \begin{syntax}
    \csmute{declarermatrice}\parg{prefix}\darg{\string&lt;}{clist of key-value pairs}{\string&gt;}\marg{matrix name}\oarg{type}\marg{clist of coefficients}
  \end{syntax}
\end{function}

\begin{function}{\declarermatrice*}
  \begin{syntax}
    \csprint{declarermatrice*}\parg{prefix}\darg{\string&lt;}{clist of key-value pairs}{\string&gt;}\marg{matrix name}\oarg{type}\marg{clist of coefficients}
  \end{syntax}
  where \meta{matrix name} is the name of the matrix to be used afterwards. The
  other arguments, optional or mandatory, have the same meaning than above. The
  starred version defines and prints the matrix. The unstarred version only
  defines it.

  The definition is global but one can redefine an existing named matrix with
  the same function. \textbf{No check is done} to ensure that one is not
  redefining a previously defined matrix.

  With the macro \csmute{declarermatrice}, the first two optional arguments have
  no effect for they are not take into account to define the matrix \VoirEx{sec:declar}.

  The French \emph{d��clarer une matrice} means ``declare a matrix''.
\end{function}
%&lt;/ENG&gt;

%&lt;*FRA&gt;
\begin{function}{\declarermatrice}
  \begin{syntax}
    \csmute{declarermatrice}\parg{prefixe}\darg{\string&lt;}{\vliste de paires de cl��-valeur}{\string&gt;}\marg{nom}\oarg{type}\marg{\vliste des coefficients}
  \end{syntax}
\end{function}


\begin{function}{\declarermatrice*}
  \begin{syntax}
    \csprint{declarermatrice*}\parg{prefixe}\darg{\string&lt;}{\vliste de paires de cl��-valeur}{\string&gt;}\marg{nom}\oarg{type}\marg{\vliste des coefficients}
  \end{syntax}
  o�� \meta{nom} est le nom de la matrice pour utilisation future. Les autres
  arguments, optionnels ou obligatoires, ont la m��me signification que
  ci-dessus. La version ��toil��e d��finit et ��crit la matrice. La version
  non-��toil��e ne fait que la d��finir.

  La d��finition est globale mais on peut red��finir une matrice nomm��e existante
  avec la m��me fonction. \textbf{Aucun contr��le} n'est exerc�� pour s'assurer que
  l'on n'est pas en train de red��finir une matrice nomm��e pr��c��demment d��finie.

  Avec la macro \csmute{declarermatrice}, les deux premiers arguments optionnels
  n'ont aucun effet car la d��finition de la matrice n'en tient pas compte \VoirEx{sec:declar}.
\end{function}
%&lt;/FRA&gt; 

%&lt;*ENG&gt; 
\begin{function}{\lamatrice}
  \begin{syntax}
    \csprint{lamatrice}\parg{prefix}\darg{\string&lt;}{clist of key-value pairs}{\string&gt;}\marg{matrix name}
  \end{syntax}
  prints the previously defined matrix the name of which is given by
  \meta{matrix name}. The two optional arguments have the meaning as before \VoirEx{sec:declar}.

  The French \emph{la matrice} means ``the matrix''.
\end{function}
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\begin{function}{\lamatrice}
  \begin{syntax}
    \csprint{lamatrice}\parg{prefixe}\darg{\string&lt;}{\vliste de paires de cl��-valeur}{\string&gt;}\marg{nom}
  \end{syntax}
  ��crit la matrice nomm��e de nom \meta{nom}.
  Les deux arguments optionnels ont la m��me signification que ci-dessus \VoirEx{sec:declar}.
\end{function}
%&lt;/FRA&gt;

%&lt;*ENG&gt;
\begin{function}{\MatriceInterieur}
  \begin{syntax}
    \csprint{MatriceInterieur}
  \end{syntax}
  gives the inner part of the last printed ---via \csprint{matrice} or
  \csprint{declarermatrice*}--- or defined ---via \csmute{declarermatrice}---
  matrix. It can be used inside an \envir{array}-like environment
  \VoirEx{sec:matint}.

  The French should be \emph{\foreignlanguage{french}{int��rieur de la matrice}}
  which means ``inside of the matrix''. What is implicit is the adjective
  ``anonymous''. For named matrix see below.
\end{function}
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\begin{function}{\MatriceInterieur}
  \begin{syntax}
    \csprint{MatriceInterieur}
  \end{syntax}
  donne l'int��rieur de la derni��re matrice ��crite --- via \csprint{matrice} ou
  \csprint{declarermatrice*} --- ou d��finie --- via \csmute{declarermatrice}. On
  peut l'utiliser dans un environnement du genre \envir{array} \VoirEx{sec:matint}.
\end{function}
%&lt;/FRA&gt;

%&lt;*ENG&gt;
\begin{function}{\LaMatriceInterieur}
  \begin{syntax}
    \csprint{LaMatriceInterieur}\marg{matrix name}
  \end{syntax}
  gives the inner part of the matrix with name \meta{matrix name}. It can be
  used inside an \envir{array}-like environment \VoirEx{sec:matint}.

  Again false French but the parallel with \csprint{lamatrice} should suggest that,
  now, the matrix has a name and we have to use it. 
\end{function}

%&lt;/ENG&gt;
%&lt;*FRA&gt;
\begin{function}{\LaMatriceInterieur}
  \begin{syntax}
    \csprint{LaMatriceInterieur}\marg{nom}
  \end{syntax}
  donne l'int��rieur de la matrice de nom \meta{nom}. On peut l'utiliser dans un
  environnement du genre \envir{array} \VoirEx{sec:matint}.
\end{function}

%&lt;/FRA&gt; 

%&lt;*ENG&gt;
\subsection{Setting the Keys}
\label{sec:setting-keys}

One can change the values of the keys of \pkg{simples-matrices} with 
\begin{function}{\simplesmatricessetup}
  \begin{syntax}
    \csmute{simplesmatricessetup}\marg{clist of key-value pairs}
  \end{syntax}
  where \meta{clist of key-value pairs} is the usual clist of key-value pairs
  setting one or many of the three keys of the package as presented on
  page~\pageref{sec:keys}.

  To stick to established convention the name of this macro is created from the
  name of the package (reduced to \TeX{} letters) followed by \emph{setup}. I
  apologize for that strange linguistic mixture.
\end{function}
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\subsection{Valuer les cl��s}
\label{sec:setting-keys}

On peut changer les valeurs des cl��s de \pkg{simples-matrices} avec
\begin{function}{\simplesmatricessetup}
  \begin{syntax}
    \csmute{simplesmatricessetup}\marg{\vliste de paires de cl��-valeur}
  \end{syntax}
  o�� \meta{\vliste de paires de cl��-valeur} est l'habituelle \vliste de paires de
  cl��-valeur valuant une ou plusieurs des trois cl��s de cette extension
  telles que pr��sent��es ci-dessous en page~\pageref{sec:clefs}. 

  Pour suivre une convention d��sormais bien ��tablie le nom de cette macro
  consiste en le nom de l'extension --- r��duite �� ces lettres \TeX{}iennes ---
  suivi de l'anglais \emph{setup}. Je demande pardon pour cette ��trange mixture
  linguistique. 
\end{function}
%&lt;/FRA&gt;

%&lt;*ENG&gt;
\newpage{}
\subsection{Shortcuts}
\label{sec:shortcuts}

There are also two \emph{shortcut} macros: 
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\subsection{Raccourcis}
\label{sec:shortcuts}

L'extension propose deux macros \emph{raccourcis}:
%&lt;/FRA&gt;

%&lt;*ENG&gt;
\begin{function}{\matid}
  \begin{syntax}
    \csprint{matid}\parg{prefix}\darg{\string&lt;}{clist of key-value pairs}{\string&gt;}\oarg{coefficient}\marg{number of columns}
  \end{syntax}
  which write the identity matrix --- by default --- with \meta{number of
    columns} columns. If \meta{coefficient} is given, we obtain a diagonal
  matrix with all its coefficients equal to \meta{coefficient}.

  The two first optional arguments have the same functionality as in the
  preceding macros.

  \emph{matid} stands for \emph{\foreignlanguage{French}{matrice identit��}} which means
  ``identity matrix''.
\end{function}
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\begin{function}{\matid}
  \begin{syntax}
    \csprint{matid}\parg{prefixe}\darg{\string&lt;}{\vliste de paires de cl��-valeur}{\string&gt;}\oarg{coefficient}\marg{nombre de colonnes}
  \end{syntax}
  qui imprime la matrice identit�� --- par d��faut --- avec
  \meta{nombre de colonnes} colonnes.
  Si \meta{coefficient} est fourni, on obtient une matrice diagonale
  dont tous les coefficients non-nuls sont ��gaux �� \meta{coefficient}.

  Les deux premiers arguments optionnels ont la m��me fonction que dans les
  macros pr��c��dentes.
\end{function}
%&lt;/FRA&gt;

%&lt;*ENG&gt;
\begin{function}{\matnulle}
  \begin{syntax}
    \csprint{matnulle}\parg{prefix}\darg{\string&lt;}{clist of key-value pairs}{\string&gt;}\oarg{coefficient}\marg{number of columns}
  \end{syntax}
  writes the null matrix with \meta{number of columns} columns ---by default---
  or a matrix containing with \meta{number of columns} columns and all
  coefficients equal to \meta{coefficient}.

  The two first optional arguments have the same functionality as in the
  preceding macros.

  \emph{matnulle} stands for \emph{\foreignlanguage{French}{matrice nulle}} which means
  ``null matrix''.
\end{function}
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\begin{function}{\matnulle}
  \begin{syntax}
    \csprint{matnulle}\parg{prefixe}\darg{\string&lt;}{\vliste de paires de cl��-valeur}{\string&gt;}\oarg{coefficient}\marg{nombre de colonnes}
  \end{syntax}
  imprime la matrice nulle \meta{nombre de colonnes} colonnes --- par d��faut ---
  ou une matrice de \meta{nombre de colonnes} colonnes dont tous les
  coefficients sont ��gaux �� \meta{coefficient}.

  Les deux premiers arguments optionnels ont la m��me fonction que dans les
  macros pr��c��dentes.
\end{function}
%&lt;/FRA&gt;

\begin{VerbatimOut}[gobble=0]{code00.tex}
$\matid{3}$\qquad $\matid[9]{3}$
\par \medskip
$\matnulle{3}$\qquad $\matnulle[2]{3}$
\end{VerbatimOut}
\UnExemple{}

%&lt;*ENG&gt;
\section{The Package Options}
\label{sec:keys}

The package uses key-value options. There are four keys:
\keyname{envir}, 
\keyname{prefix},
\keyname{typeord}
and
\keyname{argopt}.

\begin{description}
\item[\keyname{envir} (\textit{\texttt{string}})] the main and last part of the
  name of the environment used to print the matrix. Its initial value is
  \texttt{matrix}.\label{key-envir}
  
\item[\keyname{prefix} (\textit{\texttt{string}})] a string which is prefixed to
  \texttt{envir} to obtain the complete name of the environment. Its initial
  value is \texttt{p}. Therefore, by default, the environment used to print the
  matrix is \envir{pmatrix} as defined by \pkg{amsmath}.\label{key-prefix}

\item[\keyname{typeord} (\textit{\texttt{string}})] a string which is the
  ordinary ---i.~e. default--- value of the \meta{type} optional argument. The
  initial value of the key is \TypeMat{C}.\label{key-typeord}

\item[\keyname{argopt} (\textit{\texttt{token list}})] for French
  \foreignlanguage{french}{\emph{argument optionnel}} (optional argument). That
  key is initially void. See page~\pageref{sec:delarray} for usage.\label{key-argopt}
\end{description}

Moreover, an other key is available which is not an option of the package:
\keyname{out-of-box} which is a metakey.
%&lt;/ENG&gt;

%&lt;*FRA&gt;
\section{Les options de l'extension} 
\label{sec:clefs} 

L'extension utilise le syst��me de clefs-valeurs pour ses options. Elle poss��de
quatre cl��s: \keyname{envir}, \keyname{prefix}, \keyname{typeord} et \keyname{argopt}.

\begin{description}
\item[\keyname{envir} (\textit{\texttt{chaine de caract��res}})] est la partie
  finale du nom de l'environnement utilis�� pour imprimer la matrice. Sa valeur
  initiale est \texttt{matrix}.\label{key-envir}
  
\item[\keyname{prefix} (\textit{\texttt{chaine de caract��res}})] contient les
  caract��res plac��s devant \texttt{envir} pour fournir le nom complet de
  l'environnement utilis�� pour imprimer la matrice. Sa valeur initiale est
  \texttt{p}. Cela fait que l'environnement par d��faut est \envir{pmatrix}
  fourni par \pkg{amsmath}.\label{key-prefix}

\item[\keyname{typeord} (\textit{\texttt{chaine de caract��res}})] d��finit la
  valeur ordinaire --- c.-��-d. par d��faut --- de l'argument optionnel
  \meta{type}. La valeur initiale de la cl�� est \TypeMat{C}.\label{key-typeord}

\item[\keyname{argopt} (\textit{\texttt{liste de lex��mes}}, anglais:
  \foreignlanguage{english}{token list})] est vide par d��faut. Voir
  page~\pageref{sec:delarray} pour son utilisation.\label{key-argopt}
\end{description}

De plus, une cl�� suppl��mentaire existe qui est une m��tacl��:
\keyname{out-of-box}.
%&lt;/FRA&gt;


%&lt;ENG&gt; With 
%&lt;FRA&gt; Avec
\lstinline|\simplesmatricessetup{out-of-box}| 
%&lt;ENG&gt; we obtain the same effect as with
%&lt;FRA&gt; on obtient le m��me effet qu'avec
\lstinline|\simplesmatricessetup{prefix=p,|\BOP\lstinline| envir=matrix,|%
  \BOP\lstinline| argopt=,|\BOP\lstinline| typeord=C}|.

%&lt;*ENG&gt;
\newpage{}
\section{Examples}
\label{sec:examples}
\subsection{Without any special package}
\label{sec:amsmath}

That is with only \pkg{amsmath} loaded as done by this package.

\subsubsection{Declaration and Usage}
\label{sec:declar}
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\section{Exemples}
\label{sec:exemples}
\subsection{Sans extension particuli��re}
\label{sec:amsmath}

C'est-��-dire en chargeant uniquement \pkg{amsmath} comme le fait cette extension.

\subsubsection{D��claration et utilisation}
\label{sec:declar}
%&lt;/FRA&gt; 

\begin{VerbatimOut}[gobble=0]{code00.tex}
\declarermatrice{A}{1, 2, 300, 400}
$\declarermatrice*{B}{a, b, c, d}$
\quad $\lamatrice{A}$ \par \bigskip
$\lamatrice(V){A}$
\quad $\lamatrice(b){B}$
\end{VerbatimOut}
\UnExemple{}

%&lt;*ENG&gt;
On the first line of this example, the matrix~\texttt{A} is defined but not
printed. Then, on the second line, the matrix~\texttt{B} is defined and
printed. We can afterwards call the~\texttt{A} or \texttt{B}-matrix with
\csprint{lamatrice}.
%&lt;/ENG&gt;
%&lt;*FRA&gt;
Sur la premi��re ligne de l'exemple, la matrice~\texttt{A} est d��finie mais pas
��crite. Ensuite, sur la seconde ligne, la matrice~\texttt{B} est d��finie et
��crite. Nous pouvons ensuite appeler les matrices~\texttt{A} ou~\texttt{B} ��
l'aide de \csprint{lamatrice}.
%&lt;/FRA&gt;

%&lt;*ENG&gt;
\subsubsection{The ``\texttt{type}'' argument}
\label{sec:matrix-type}

The last but one --- optional --- argument of macros \csprint{matrice}, 
\csmute{declarermatrice} and \csprint{declarermatrice*}
defaults to \TypeMat{O}. In that case the value of the key
\keyname{typeord} is used to determine the \emph{type} of the matrix input,
see~\pageref{sec:matrix-type-key}.

Its value can be a number, in which case it is the number of columns, or a
string ---presently a one letter string--- among: \TypeMat{C}, \TypeMat{D},
\TypeMat{I}, \TypeMat{J}, \TypeMat{S}, \TypeMat{T} and \TypeMat{x}.
%&lt;/ENG&gt;

%&lt;*FRA&gt;
\subsubsection{L'argument \og \texttt{type}\fg}
\label{sec:matrix-type}

L'avant dernier argument --- optionnel --- des macros \csprint{matrice},
\csmute{declarermatrice} et \csprint{declarermatrice*} vaut par d��faut
\TypeMat{O}. Dans ce cas, c'est la valeur de la cl�� \keyname{typeord} qui est
utilis��e pour d��terminer le \emph{type} des donn��es de la matrice,
voir~\pageref{sec:matrix-type-key}.

Sinon, il peut prendre une valeur num��rique qui est le nombre de colonnes de la
matrice ou encore une chaine de caract��res --- �� ce jour, une seule lettre ---
parmi: \TypeMat{C}, \TypeMat{D}, \TypeMat{I}, \TypeMat{J}, \TypeMat{S}, \TypeMat{T} et
\TypeMat{x}.
%&lt;/FRA&gt;

\medskip{}

%&lt;FRA&gt; \TypeMat{C} signifie matrice \textbf{carr��e}.
%&lt;ENG&gt; \TypeMat{C} means square matrix for French ``\texttt{C}arr��'' means ``square''.
\begin{VerbatimOut}[gobble=0]{code00.tex}
\[
 \matrice{1, 2, 3, 4, 5, 6, 7, 8, 9}
 \quad 
 \matrice[C]{1, 2, 3, 4, 5, 6, 7, 8, 9}
\]
\end{VerbatimOut}
\UnExemple{}

%&lt;FRA&gt; \TypeMat{D} signifie matrice \textbf{diagonale}.
%&lt;ENG&gt; \TypeMat{D} means \textbf{diagonal} matrix.
\begin{VerbatimOut}[gobble=0]{code00.tex}
\[
 \matrice{1, 2, 3, 4}\quad 
 \matrice[D]{1, 2, 3, 4}
\]
\end{VerbatimOut}
\UnExemple{}

%&lt;*FRA&gt;
\TypeMat{I} signifie matrice triangulaire \textbf{inf��rieure}; \TypeMat{J}
signifie matrice triangulaire inf��rieure avec des z��ros sur la diagonale.
%&lt;/FRA&gt;
%&lt;*ENG&gt;
\TypeMat{I} means lower triangular matrix. French ``\texttt{I}nf��rieur'' means
``lower''; \TypeMat{J} means lower triangular matrix with zeros on the diagonal.
%&lt;/ENG&gt;
\begin{VerbatimOut}[gobble=0]{code00.tex}
\[
 \matrice[I]{1, 2, 3}\quad 
 \matrice[J]{1, 2, 3}
\]
\end{VerbatimOut}
\UnExemple{}

%&lt;*FRA&gt;
\TypeMat{S} signifie matrice triangulaire \textbf{sup��rieure}; \TypeMat{T}
signifie matrice triangulaire sup��rieure avec des z��ros sur la diagonale.
%&lt;/FRA&gt;
%&lt;*ENG&gt;
\TypeMat{S} means upper triangular matrix. French ``\texttt{S}up��rieur'' means
``upper''; \TypeMat{T} means upper triangular matrix with zeros on the diagonal.
%&lt;/ENG&gt;
\begin{VerbatimOut}[gobble=0]{code00.tex}
\[
 \matrice[S]{1, 2, 3}\quad 
 \matrice[T]{1, 2, 3}
\]
\end{VerbatimOut}
\UnExemple{}

%&lt;*FRA&gt;
\TypeMat{x} signifie \texttt{xcas}\footnote{Syst��me de calcul formel libre
  disponible ici:
  \url{https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac_fr.html}}. Avec
cette valeur, on peut copier-coller de \texttt{xcas} dans le document \LaTeX{}.
%&lt;/FRA&gt;
%&lt;*ENG&gt;
\TypeMat{x} means \texttt{xcas}\footnote{Free computer algebra system, see here:
\url{https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac.html}.}. With that value, one can copy-paste from
\texttt{xcas} into the \LaTeX{} document.
%&lt;/ENG&gt;
\begin{VerbatimOut}[gobble=0]{code00.tex}
\[
 \matrice[x]{[[7,1,3],[1,0,3],[5,1,2]]}
\]
\end{VerbatimOut}
\UnExemple{}

\pagebreak[3]
%&lt;*FRA&gt;
Un nombre donne le nombre de colonnes de la matrice.
%&lt;/FRA&gt;
%&lt;*ENG&gt;
A number sets up the number of columns of the matrix.
%&lt;/ENG&gt;
\begin{VerbatimOut}[gobble=0]{code00.tex}
\[
 \matrice[2]{1, 2, 3, 4, 5, 6}
 \quad
 \matrice[3]{1, 2, 3, 4, 5, 6}
\]
\end{VerbatimOut}
\UnExemple{}


%&lt;*ENG&gt;
\subsubsection{Using the ``\keyname{typeord}'' Key}
\label{sec:matrix-type-key}

In this document, the key \keyname{typeord} has the initial value of~\TypeMat{C}.
%&lt;/ENG&gt;

%&lt;*FRA&gt;
\subsubsection{Utilisation de la cl�� \og \keyname{typeord}\fg}
\label{sec:matrix-type-key}

Dans ce document, la cl�� \keyname{typeord} a comme valeur initiale~\TypeMat{C}.
%&lt;/FRA&gt;

\medskip{}

\begin{VerbatimOut}[gobble=0]{code00.tex}
\simplesmatricessetup{typeord=3}
$\matrice{1, 2, 3, 4, 5, 6}$\quad 
\simplesmatricessetup{typeord=2}
$\matrice{1, 2, 3, 4, 5, 6}$\quad  
\simplesmatricessetup{typeord=C}
$\matrice{1, 2, 3, 4}$
\end{VerbatimOut}
\UnExemple{}

%&lt;*FRA&gt;
Le code pr��c��dent n'est, bien entendu, donn�� qu'�� titre d'illustration. Pour une
d��claration de type ne concernant qu'une seule matrice, on aura int��r��t ��
utiliser l'argument optionnel. Cependant si on veut r��diger un cours sur les
matrices triangulaires sup��rieures\dots{}
%&lt;/FRA&gt;
%&lt;*ENG&gt;
The preceding code is but a mere illustration. In order to declare a type for
one matrix it's more convenient to use the optional argument. However if one
wants to write a lesson about upper triangular matrices\dots{}
%&lt;/ENG&gt;

%&lt;*ENG&gt;
\subsubsection{Using the \csprint{(La)MatriceInterieur} Macros}
\label{sec:matint}
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\subsubsection{Utilisation des macros \csprint{(La)MatriceInterieur}}
\label{sec:matint}
%&lt;/FRA&gt;

\begin{VerbatimOut}[gobble=0]{code00.tex}
\declarermatrice{B}[4]{
 \hline ein, zwei, drei, vier, 
 \hline unos, dos, tres, cuatro, 
 \hline unu, du, tri, kvar}%
\declarermatrice{A}[3]{
 one, two, three, 
 un, deux, trois, 
 uno, due, tre}%
\begin{tabular}{*{3}{l}}
  \MatriceInterieur %*@\label{anonyme}@*)
\end{tabular}
\par \bigskip *** \par \bigskip
\begin{tabular}{*{3}{l}}
  \LaMatriceInterieur{A} %*@\label{parnom}@*)
\end{tabular}
\par \bigskip
\begin{tabular}{|*{4}{l|}}
  \LaMatriceInterieur{B}\hline 
\end{tabular}
\end{VerbatimOut}
\UnExemple{}

%&lt;*ENG&gt;
On lines~\ref{anonyme} and~\ref{parnom} we use the same \emph{internal} because
the \texttt{A}-matrix is the last defined before line~\ref{anonyme}. 
%&lt;/ENG&gt;
%&lt;*FRA&gt;
En lignes~\ref{anonyme} et~\ref{parnom}, nous acc��dons aux m��mes
\emph{entrailles} car la matrice~\texttt{A} est la derni��re d��finie avant la
ligne~\ref{anonyme}.
%&lt;/FRA&gt;

%&lt;*ENG&gt;
\subsection{Changing the Look}
\label{sec:changelook}

We can load other packages which deal with matrices such as \pkg{mathtools}, 
\pkg{delarray} or \pkg{nicematrix}. In that case we can change the look of our
matrices thanks to the option-key \keyname{envir}, \keyname{prefix} and
\keyname{argopt}.

This document loads the three packages \pkg{mathtools}, \pkg{delarray} and
\pkg{nicematrix} in order to give the following examples.

%&lt;/ENG&gt;

%&lt;*FRA&gt;
\subsection{Changer l'aspect}
\label{sec:aspect}

On peut charger d'autres extensions qui permettent de pr��senter des matrices
comme \pkg{mathtools}, \pkg{delarray} ou \pkg{nicematrix}. Dans ce cas on peut
changer l'aspect de nos matrices grace aux cl��s d'option \keyname{envir},
\keyname{prefix} et \keyname{argopt}.

Ce document charge les trois extensions \pkg{mathtools}, \pkg{delarray} et
\pkg{nicematrix} pour pr��senter les exemples suivants.

%&lt;/FRA&gt;

%&lt;*ENG&gt;
\subsubsection{With \pkg{mathtools}}
\label{sec:mathtools}

As already stated above there are two ways to use the option-keys: through
\csmute{simples}\BOP\ObjetPres{cmdmuette}{matrices}\BOP\ObjetPres{cmdmuette}{setup}
or through the optional argument \darg{\string&lt;}{clist of pairs of
  key-value}{\string&gt;}. I show both.
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\subsubsection{Avec \pkg{mathtools}}
\label{sec:mathtools}

Comme d��j�� signal��, il y a deux fa��ons d'utiliser les cl��s d'option: �� l'aide de
\csmute{simplesmatricessetup} ou en utilisant l'argument optionnel
\darg{\string&lt;}{\vliste de paires de cl��-valeur}{\string&gt;}.  Je montre les deux. 
%&lt;/FRA&gt;

\begin{VerbatimOut}[gobble=0]{code00.tex}
\simplesmatricessetup{
  envir=matrix*, prefix=p, argopt=[r]}
$\matrice{1, 2, 30, 40}$ \quad
\simplesmatricessetup{out-of-box}
$\matrice{1, 2, 30, 40}$ 
\par \medskip
$\matrice(b)&lt;envir=matrix*,argopt=[l]&gt; {1, 2, 30, 40}$
\end{VerbatimOut}
\UnExemple{}

%&lt;*ENG&gt;
\subsubsection{With \pkg{delarray}}
\label{sec:delarray}

%&lt;/ENG&gt;
%&lt;*FRA&gt;
\subsubsection{Avec \pkg{delarray}}
\label{sec:delarray}

%&lt;/FRA&gt;

\begin{VerbatimOut}[gobble=0]{code00.tex}
\simplesmatricessetup{
  envir=array, prefix=, 
  argopt=[c][{l r}\}}
$\matrice{1, 2, 30, 40}$ \quad
$\matid()&lt;envir=array, 
  argopt={[c][{@{}c c c@{}}\}}&gt;{3}$
\end{VerbatimOut}
\UnExemple{}
\simplesmatricessetup{out-of-box}


%&lt;*ENG&gt;
\subsubsection{With \pkg{nicematrix}}
\label{sec:nicematrix}
%&lt;/ENG&gt;
%&lt;*FRA&gt;
\subsubsection{Avec \pkg{nicematrix}}
\label{sec:nicematrix}
%&lt;/FRA&gt;

\begin{VerbatimOut}[gobble=0]{code00.tex}
$\matrice&lt;prefix=b, envir=NiceArray, 
argopt={ {cc||rl} }&gt;{1, 2, 3, 4, 5, 6, 
  7, 8, 9, 10, 11, 12, 13, 14, 15, 16}$
\end{VerbatimOut}
\UnExemple{}

%&lt;*ENG&gt; 
In that case we need to double the curly braces around the column descriptors of
the \envir{array} environment because the first level is stripped off by
\LaTeX{} when valuating the key.

\medskip{}

In the following example, for the second matrix, it is not necessary to surround
the value of \keyname{argopt} with an extra pair of curly braces (see
line~\ref{sansaccol}) ---even if it is not dangerous (see
line~\ref{avecaccol})--- for the presence of \texttt{[margin]} prevents \LaTeX{}
to strip off the curly braces.
%&lt;/ENG&gt;
%&lt;*FRA&gt;
Dans ce cas il faut doubler les accolades entourant les descripteurs de colonnes
de l'environnement \envir{array} car \LaTeX{} retire un niveau d'accolades en
valuant la cl��.

\medskip{}

Dans l'exemple suivant, pour la deuxi��me matrice, il n'est pas n��cessaire
d'entourer la valeur de \keyname{argopt} d'une paire d'accolades (voir
ligne~\ref{sansaccol}) --- m��me si ��a n'est pas dangereux (voir
ligne~\ref{avecaccol}) --- car la pr��sence de \texttt{[margin]} emp��che \LaTeX{}
de supprimer une paire d'accolades.
%&lt;/FRA&gt;

\begin{VerbatimOut}[gobble=0]{code00.tex}
$\matrice&lt;prefix=b, envir=NiceArray, 
argopt={{l c r}}&gt;{1, 2, 3, 40, 50, 60, 
  700, 800, 900}$
\par \medskip
$\matrice&lt;prefix=b, envir=NiceArray, 
argopt={l c r}[margin]&gt;{1, 2, 3, %*@\label{sansaccol}@*)
  40, 50, 60, 700, 800, 900}$
\par \medskip
$\matrice&lt;prefix=b, envir=NiceArray, 
argopt={{l c r}[margin]}&gt;{1, 2, 3, %*@\label{avecaccol}@*)
  40, 50, 60, 700, 800, 900}$
\end{VerbatimOut}
\UnExemple{}

%&lt;ENG&gt; \section{Thanks}
%&lt;FRA&gt; \section{Remerciements}
%&lt;*ENG&gt;
Many thanks to Denis \textsc{Bitouz��} for his remarks about the initial state of
this documentation. Thanks to him, some colours have appeared on these pages.
%&lt;/ENG&gt;
%&lt;*FRA&gt;
Mille mercis �� Denis \textsc{Bitouz��} pour ses remarques �� propos de l'��tat
initial de cette documentation. C'est gr��ce �� lui que quelques couleurs sont 
apparues sur ces pages.
%&lt;/FRA&gt;


\vspace{\stretch{2}}

\noindent\hspace*{0.2\textwidth}\hrulefill\hspace*{0.2\textwidth}
\begin{center}
  \textsl{Le TeXnicien de Surface scripsit.}
\end{center}
\noindent\hspace*{0.2\textwidth}\hrulefill\hspace*{0.2\textwidth}

\vspace*{\stretch{2}}

\end{document}
%&lt;/doc&gt; 
% \fi
% \begin{implementation}
%
% \section{\pkg{simples-matrices} implementation}
%
% 
% \iffalse
%&lt;*package&gt;
% \fi
% 
%\subsection{Loading And Greeting}
%\label{sec:loading}
% 
%    \begin{macrocode}
%&lt;@@=SMPLMTRC&gt;
%    \end{macrocode}
%  
%    \begin{macrocode}
\RequirePackage{l3keys2e,xparse}
\ProvidesExplPackage
{simples-matrices} {2022/06/08} {1.0} {defining and printing matrices}
\RequirePackage{amsmath}
%    \end{macrocode}
% 
% \pkg{amsmath} is the only auxiliary package loaded. We need it to write the
% matrices.
%
%\subsection{Keys And Options}
%\label{sec:keysandoptions}
%
% I'm using the key management mechanism of \LaTeX3.  
% 
%    \begin{macrocode}
\keys_define:nn {simples-matrices}
{
  envir .tl_set:N = \g_@@_nom_environnement_tl,
  envir .initial:n = {matrix},  
  prefix .tl_set:N = \g_@@_prefix_environnement_tl,
  prefix .initial:n = {p},
  argopt .tl_set:N = \g@@_argument_environnement_tl,
  argopt .initial:n = { },
  typeord .str_set:N = \g_@@_type_ordinaire_str,
  typeord .initial:n = { C },
}
\ProcessKeysOptions {simples-matrices}
%    \end{macrocode}
% 
% The keys above defined the package options. The next one may be usefull to
% return to a kind of neutral state.
% 
%    \begin{macrocode}
\keys_define:nn {simples-matrices}
{
  out-of-box .meta:n = {prefix=p, envir=matrix, argopt=, typeord=C},  
}
%    \end{macrocode}
% 
%
%\subsection{Constants And Variables}
%\label{sec:const-var}
%
% To handle the syntax of \texttt{xcas} matrices, I resort to \emph{regex} so I
% have to create some constant \emph{regexes}. Some comments are just there to
% prevent \texttt{emacs} to go too far in formating the code.
% 
%    \begin{macrocode}
\regex_const:Nn \c_@@_xcas_debut_regexp {\[\[} %\]\]
\regex_const:Nn \c_@@_xcas_fin_regexp {\]\]}
\regex_const:Nn \c_@@_xcas_milieu_regexp{\],\ *\[} %\]
%    \end{macrocode}
% 
% Now come error messages: the first deals with bad numbers of coefficient for
% matrices of type I, J, S or T; the second appears when dealing with an x~type
% matrix.
% 
%    \begin{macrocode}
\msg_new:nnnn{simples-matrices}{errorIJST}
{The~number~of~coefficients~does~not~fit~the~matrix-type}
{I~was~expecting~#1~coefficients~and~obtain~only~#2.}

\msg_new:nnnn{simples-matrices}{errorx}
{The~data~do~not~seem~to~match~the~x-type}
{I~was~expecting~the~data~to~begin~with~"[["}
%    \end{macrocode}
% 
% To contain the inner part of the matrix, we need a token list global
% variable. I chose to built it with a non-letter to try to prevent name clash.
% 
%    \begin{macrocode}
\tl_new:c {g_@@_contenu_anonyme*_tl}
%    \end{macrocode}
% 
% \begin{macro}{\@@_creer_matrice_aux:}
% 
% When this macro is called, \cs{g_tmpa_int} contains the number of columns of
% the matrix and \cs{g_tmpa_seq} the \emph{sequence} of coefficients.
% 
%    \begin{macrocode}
\cs_new:Nn \@@_creer_matrice_aux:
{
  \tl_gclear:c {g_@@_contenu_anonyme*_tl}

  \seq_map_indexed_inline:Nn \g_tmpa_seq
  {
    \tl_gput_right:cn {g_@@_contenu_anonyme*_tl} { ##2  }
    \int_compare:nNnTF { \int_mod:nn {##1} { \g_tmpa_int } } = { 0 }
    {
      \tl_gput_right:cn {g_@@_contenu_anonyme*_tl} { \\ }
    }
    {
      \tl_gput_right:cn {g_@@_contenu_anonyme*_tl} { &amp;  }
    }
  }
}
%    \end{macrocode}
% 
% At the end of this macro, \cs{g_@@_contenu_anonyme*_tl} contains the inner
% part of the matrix.
% 
% \end{macro}  
% 
% For I need to match a text against a regex constant, I create a variant of one
% of the function of \LaTeX3: 
%    \begin{macrocode}
\cs_generate_variant:Nn \regex_match:nnF { nVF }
%    \end{macrocode}
% 
% The next macro does the bulk of the work in reading the coefficients in the
% second argument and managing them according to the data-type which is given in
% the first argument.
% 
% \begin{macro}{\@@_creer_matrice:nn}
% 
%  To be on the safe side, I begin with clearing the variable. 
%    \begin{macrocode}
\cs_new:Nn \@@_creer_matrice:nn
{
  \tl_gclear:c {g_@@_contenu_anonyme*_tl}
%    \end{macrocode}
%  I then read the first argument inside \cs{l_tmpa_str} with \cs{str_set:Nx} in
%  case the string is contained in a variable.
%    \begin{macrocode}
  \str_set:Nx \l_tmpa_str { #1 }
%    \end{macrocode}
%  If \verb|#1| is equal to \texttt{O}, I fetch the data-type in the string valued
%  through the key \texttt{typeord}. 
%    \begin{macrocode}
  \str_if_eq:VnT \l_tmpa_str { O }
  {
    \str_set:NV \l_tmpa_str \g_@@_type_ordinaire_str
  }
%    \end{macrocode}
%  We enter now the first \texttt{case} which depends on the data-type. The
%  first case deals with the \texttt{x}-type. Here we obtain the inner part of
%  the matrix by replacing, according to \emph{regex}. There is no need to
%  calculate anything. 
% 
% If ever there are other types of the same kind ---e.~g. to deal with
% \texttt{maxima} syntax or the like--- those types would be dealt with here. 
% 
%    \begin{macrocode}
  \str_case:VnF \l_tmpa_str
  { 
    { x } {
      \tl_set:Nn \l_tmpa_tl { #2 }

      \regex_match:nVF {\A\s*\[\[} %\]\]
      \l_tmpa_tl 
      {
          \msg_fatal:nn{simples-matrices} {errorx}
      }
      
      \regex_replace_all:NnN \c_@@_xcas_debut_regexp { } \l_tmpa_tl
      \regex_replace_all:NnN \c_@@_xcas_fin_regexp { \c{\\} } \l_tmpa_tl
      \regex_replace_all:NnN \c_@@_xcas_milieu_regexp { \c{\\} } \l_tmpa_tl
      \regex_replace_all:nnN { , }{ &amp; } \l_tmpa_tl

      \tl_set_eq:cN {g_@@_contenu_anonyme*_tl} \l_tmpa_tl
    } 
  }
%    \end{macrocode}
% The \texttt{x} -type is done. Now for the \texttt{false} part of the
% \texttt{case} where I will take care of the other kind of data-types, those
% which require calculations.
% 
% I prepare the work by reading the second argument inside the \emph{sequence}
% \cs{g_tmpa_seq} and cleaning \cs{g_tmpb_seq}.
%    \begin{macrocode}
  { 
    \seq_set_from_clist:Nn \g_tmpa_seq { #2 }
    \seq_clear:N \l_tmpb_seq
%    \end{macrocode}
%  Now come the second \texttt{case}: 
%    \begin{macrocode}
    \str_case:VnF \l_tmpa_str
    { 
%    \end{macrocode}
%  The first case is that of the square matrices. I calculate the number of
%  columns as the square root of the number of coefficients. There is, as for
%  now, no check for correctness because in case of bad number of coefficients
%  there will just be a strange matrix, with void cells. 
%    \begin{macrocode}
      { C } { 
        \int_set:Nn \g_tmpb_int { \seq_count:N \g_tmpa_seq }
        \int_set:Nn \g_tmpa_int { \fp_to_int:n { sqrt(\g_tmpb_int) } }
      }
%    \end{macrocode}
% In case of a diagonal matrix, the number of columns is simply the number of
% coefficients but we have to create the suitable \emph{sequence}. The trick is
% just to add as many zeros as there are columns between each given coefficient.
%    \begin{macrocode}
      { D } {
        \int_set:Nn \g_tmpa_int { \seq_count:N \g_tmpa_seq }
        \seq_pop_left:NN \g_tmpa_seq \l_tmpa_tl
        \seq_put_right:NV \l_tmpb_seq \l_tmpa_tl

        \bool_until_do:nn { \seq_if_empty_p:N \g_tmpa_seq }
        {
          \int_step_inline:nn { \g_tmpa_int } 
          {
            \seq_put_right:Nn \l_tmpb_seq { 0 }
          }
          \seq_pop:NN \g_tmpa_seq \l_tmpa_tl
          \seq_put_right:NV \l_tmpb_seq \l_tmpa_tl
        }
        \seq_set_eq:NN \g_tmpa_seq \l_tmpb_seq
      } 
%    \end{macrocode}
%  The code for the next four cases is very similar. We have to calculate the
%  number of columns from the number of coefficient and then complete the
%  \emph{sequence} of coefficients.
% 
%  Here I check the correctness because, otherwise, in case of error \LaTeX{}
%  doesn't behave kindly.
% 
%  The number of coefficients \emph{non-necessarily} null in a triangular matrix
%  with \(n\)~columns is \(n(n+1)/2\) or \(n(n-1)/2\) if the diagonal is
%  \emph{null}. Therefore the computing of \cs{g_tmpa_int} from \cs{g_tmpb_int}
%  which is equal to the number of coefficients, that is the number of items in
%  the \emph{sequence} \cs{g_tmpa_seq}.
% 
% In the first case (upper triangular) there are coefficients on the diagonal so
% we have to append \(L-1\) zeros before \(N+1-L\) coefficients where \(L\) is
% the line number and \(N\) the number of columns.
% 
%    \begin{macrocode}
      { S } {
        \int_set:Nn \g_tmpb_int { \seq_count:N \g_tmpa_seq }
        \int_set:Nn \g_tmpa_int
        {
          \fp_to_int:n { ( sqrt(1 + 8*\g_tmpb_int) - 1 ) / 2 }
        }
%    \end{macrocode}
%  We check for correctness and abort in case of discrepancy.
%    \begin{macrocode}
        \int_compare:nNnF
        {2*\g_tmpb_int} = { \g_tmpa_int * (\g_tmpa_int + 1)}
        {
          \msg_fatal:nnxx{simples-matrices}
          {errorIJST}
          {\int_to_arabic:n{(\g_tmpa_int * (\g_tmpa_int + 1))/2}}
          {\int_to_arabic:n{\g_tmpb_int}}
        }
%    \end{macrocode}
%  \verb|##1| is the line number of the matrix
%    \begin{macrocode}
        
        \int_step_inline:nn { \g_tmpa_int } 
        {
          \int_step_inline:nn { ##1 - 1 }
          {
            \seq_put_right:Nn \l_tmpb_seq {0}
          }
          \int_step_inline:nn { \g_tmpa_int - ##1 + 1 }
          {
            \seq_pop:NN \g_tmpa_seq \l_tmpa_tl
            \seq_put_right:NV \l_tmpb_seq \l_tmpa_tl
          }
        }
        
        \seq_set_eq:NN \g_tmpa_seq \l_tmpb_seq
        
      } 
%    \end{macrocode}
%  When there are zeros on the diagonal, the formula changes a tiny bit: append
%  \(L\) zeros before \(N-L\) coefficients. 
%    \begin{macrocode}
      { T } {
        \int_set:Nn \g_tmpb_int { \seq_count:N \g_tmpa_seq }
        \int_set:Nn \g_tmpa_int
        {
          \fp_to_int:n { (1 + sqrt(1 + 8*\g_tmpb_int) ) / 2 }
        }
        \int_compare:nNnF
        {2*\g_tmpb_int} = { \g_tmpa_int * (\g_tmpa_int - 1)}
        {
          \msg_fatal:nnxx{simples-matrices}
          {errorIJST}
          {\int_to_arabic:n{(\g_tmpa_int * (\g_tmpa_int - 1))/2}}
          {\int_to_arabic:n{\g_tmpb_int}}
        }
        \int_step_inline:nn { \g_tmpa_int } 
        {
          \int_step_inline:nn { ##1 }
          {
            \seq_put_right:Nn \l_tmpb_seq {0}
          }
          \int_step_inline:nn { \g_tmpa_int - ##1 }
          {
            \seq_pop:NN \g_tmpa_seq \l_tmpa_tl
            \seq_put_right:NV \l_tmpb_seq \l_tmpa_tl
          }
        }
        \seq_set_eq:NN \g_tmpa_seq \l_tmpb_seq
      } 
%    \end{macrocode}
%  Now come the cases for lower triangular matrices. First \emph{with diagonal}.
%    \begin{macrocode}
      { I } {
        \int_set:Nn \g_tmpb_int { \seq_count:N \g_tmpa_seq }
        \int_set:Nn \g_tmpa_int
        {
          \fp_to_int:n { ( sqrt(1 + 8*\g_tmpb_int) - 1 ) / 2 }
        }
        \int_compare:nNnF
        {2*\g_tmpb_int} = { \g_tmpa_int * (\g_tmpa_int + 1)}
        {
          \msg_fatal:nnxx{simples-matrices}
          {errorIJST}
          {\int_to_arabic:n{(\g_tmpa_int * (\g_tmpa_int + 1))/2}}
          {\int_to_arabic:n{\g_tmpb_int}}
        }
        \int_step_inline:nn { \g_tmpa_int } 
        {
          \int_step_inline:nn { ##1 }
          {
            \seq_pop:NN \g_tmpa_seq \l_tmpa_tl
            \seq_put_right:NV \l_tmpb_seq \l_tmpa_tl
          }
          \int_step_inline:nn { \g_tmpa_int - ##1 }
          {
            \seq_put_right:Nn \l_tmpb_seq {0}
          }
        }
        \seq_set_eq:NN \g_tmpa_seq \l_tmpb_seq
      }
%    \end{macrocode}
%  Secondly \emph{without diagonal}.
%    \begin{macrocode}
      { J } {
        \int_set:Nn \g_tmpb_int { \seq_count:N \g_tmpa_seq }
        \int_set:Nn \g_tmpa_int
        {
          \fp_to_int:n { (1 + sqrt(1 + 8*\g_tmpb_int) ) / 2 }
        }
        \int_compare:nNnF
        {2*\g_tmpb_int} = { \g_tmpa_int * (\g_tmpa_int - 1)}
        {
          \msg_fatal:nnxx{simples-matrices}
          {errorIJST}
          {\int_to_arabic:n{(\g_tmpa_int * (\g_tmpa_int - 1))/2}}
          {\int_to_arabic:n{\g_tmpb_int}}
        }
        \int_step_inline:nn { \g_tmpa_int } 
        {
          \int_step_inline:nn { ##1 -1}
          {
            \seq_pop:NN \g_tmpa_seq \l_tmpa_tl
            \seq_put_right:NV \l_tmpb_seq \l_tmpa_tl
          }
          \int_step_inline:nn { \g_tmpa_int - ##1 + 1}
          {
            \seq_put_right:Nn \l_tmpb_seq {0}
          }
        }
        \seq_set_eq:NN \g_tmpa_seq \l_tmpb_seq
      }
    }
%    \end{macrocode}
%  Here we attain the \texttt{false} part of the second \texttt{case}. We assume
%  that we have a number in \verb|#1|.
%    \begin{macrocode}
    { 
      \int_set:Nn \g_tmpa_int { \l_tmpa_str }
    }
%    \end{macrocode}
%  If all is well, here it ends well with the number of columns in
%  \cs{g_tmpa_int} and all the coefficients of the matrix in \cs{g_tmpa_seq}. So
%  it's time to call 
%    \begin{macrocode}
    \@@_creer_matrice_aux:
  } 
}
%    \end{macrocode}
% \end{macro} 
% 
% \begin{macro}{\MatriceInterieur}
%   A document command to access the inner part of the \textbf{last} printed
%   ---via \cs{matrice}--- or defined ---via \cs{declarermatrice}--- matrix. 
% 
%   This macro can be placed inside an \env{array}-like environment.
%    \begin{macrocode}
\cs_new:Npn \MatriceInterieur
{
  \tl_use:c { g_@@_contenu_anonyme*_tl }
}
%    \end{macrocode}
% \end{macro} 
% 
% 
% \begin{macro}{\LaMatriceInterieur}
% A version to access the inner part of a named matrix: 
% 
%    \begin{macrocode}
\cs_new:Npn \LaMatriceInterieur #1
{
  \tl_use:c { g_@@_contenu_nom_#1_tl }
}
%    \end{macrocode}
% \end{macro} 
% 
% 
% The next macro is used to print a matrix. Its name means \emph{prepare (the)
% presentation} of the matrix. It builds the name of the environment, taking
% care of possible arguments of the said environment. 
% 
% \begin{macro}{\@@_preparer_presentation:nn}
% At the end of the macro, \cs{g_tmpa_tl} contains the \emph{overture} of the
% environment and \cs{g_tmpb_tl} the \emph{grand final}.
% 
%    \begin{macrocode}
\cs_new:Nn \@@_preparer_presentation:nn
{
  \IfValueT{#1}
  {
    \keys_set:nn {simples-matrices} {prefix = #1}
  }
  \IfValueT{#2}
  {
    \keys_set:nn {simples-matrices} { #2 }
  }
  \tl_set:NV \l_tmpa_tl \g_@@_prefix_environnement_tl
  \tl_put_right:NV \l_tmpa_tl \g_@@_nom_environnement_tl      
  \tl_set:Nn \g_tmpa_tl { \begin{\l_tmpa_tl} }
  \tl_put_right:NV \g_tmpa_tl \g@@_argument_environnement_tl
  \tl_set:Nn \g_tmpb_tl {\end{\l_tmpa_tl} }
}
%    \end{macrocode}
% \end{macro}
% 
% Now comes the first main document command which prints the matrix from the
% data-type and coefficients. It assigns the different arguments to the
% auxiliary macros and finishes with using the token lists created by the
% auxiliaries.
% 
% \begin{macro}{\matrice}
%    \begin{macrocode}
\NewDocumentCommand{\matrice}{ d() d&lt;&gt; O{O} m }
{
  \@@_creer_matrice:nn { #3 } { #4 }
  \@@_preparer_presentation:nn { #1 } { #2 }
  \tl_use:N \g_tmpa_tl
  \tl_use:c { g_@@_contenu_anonyme*_tl }
  \tl_use:N \g_tmpb_tl
}
%    \end{macrocode}
% \end{macro} 
% 
% I provide a way of changing the keys inside the document with the usual
% \emph{setup} macro:
% \begin{macro}{\simplesmatricessetup}
%    \begin{macrocode}
\NewDocumentCommand{\simplesmatricessetup}{m}
{
  \keys_set:nn {simples-matrices} { #1 }
}
%    \end{macrocode}
% \end{macro}
% 
% Another main document command to define a named matrix. The starred version
% defines and prints.
% 
% The first mandatory argument ---the 4th of all--- should contain the ``name''
% of the matrix with which one can recall the matrix using \cs{lamatrice}.
% \begin{macro}{\declarermatrice}
%    \begin{macrocode}
\NewDocumentCommand{\declarermatrice}{ s d() d&lt;&gt; m  O{O} m }
{
  \@@_creer_matrice:nn { #5 } { #6 }
  \tl_gset_eq:cc {g_@@_contenu_nom_#4_tl} {g_@@_contenu_anonyme*_tl}
  \IfBooleanT { #1 }
  {
    \@@_preparer_presentation:nn { #2 } { #3 }
    \tl_use:N \g_tmpa_tl
    \tl_use:c { g_@@_contenu_anonyme*_tl }
    \tl_use:N \g_tmpb_tl
  }
}
%    \end{macrocode}
% \end{macro}
% 
% To print a named matrix: 
% \begin{macro}{\lamatrice}
%    \begin{macrocode}
\NewDocumentCommand{\lamatrice}{ d() d&lt;&gt; m }
{
  \@@_preparer_presentation:nn { #1 } { #2 }
  \tl_use:N \g_tmpa_tl
  \tl_use:c { g_@@_contenu_nom_#3_tl }
  \tl_use:N \g_tmpb_tl
}
%    \end{macrocode}
% \end{macro}  
% 
% For the next commands, I need a variant:  
%    \begin{macrocode}
\cs_generate_variant:Nn \@@_creer_matrice:nn { nV }
%    \end{macrocode}
% 
% The auxiliary macro to print an identity matrix. \verb|#1| will receive the value
% to print in the diagonal ---defaulting to \(1\)--- and \verb|#2| the number of
% columns. 
% \begin{macro}{\@@_creer_matrice_identite:nn}
%    \begin{macrocode}
\cs_new:Nn \@@_creer_matrice_identite:nn
{
  \clist_clear:N \l_tmpa_clist 
  \int_step_inline:nn { #2 }
  {
    \clist_put_left:Nn \l_tmpa_clist { #1 }
  }
  \@@_creer_matrice:nV {D} \l_tmpa_clist
}
%    \end{macrocode}
% \end{macro}
% 
% I can then use it to define the document command: 
% \begin{macro}{\matid}
%    \begin{macrocode}
\NewDocumentCommand{\matid}{ d() d&lt;&gt; O{1} m}
{
  \@@_creer_matrice_identite:nn { #3 } { #4 }
  \@@_preparer_presentation:nn  { #1 } { #2 }
  \tl_use:N \g_tmpa_tl
  \tl_use:c { g_@@_contenu_anonyme*_tl }
  \tl_use:N \g_tmpb_tl
}
%    \end{macrocode}
% \end{macro}
% 
% I follow the same pattern for null matrices. First the auxiliary macro, \verb|#2|
% is the number of columns, \verb|#1| the value of all the coefficients ---defaulting
% to \(0\)---.
% \begin{macro}{\@@_creer_matrice_nulle:nn}
%    \begin{macrocode}
\cs_new:Nn \@@_creer_matrice_nulle:nn
{
  \clist_clear:N \l_tmpa_clist 
  \int_step_inline:nn { #2*#2 }
  {
    \clist_put_left:Nn \l_tmpa_clist { #1 }
  }
  \@@_creer_matrice:nV {C} \l_tmpa_clist
}
%    \end{macrocode}
% \end{macro}
% 
% I can again use it to define the document command: 
% \begin{macro}{\matnulle}
%    \begin{macrocode}
\NewDocumentCommand{\matnulle}{ d() d&lt;&gt; O{0} m}
{
  \@@_creer_matrice_nulle:nn {#3} {#4}
  \@@_preparer_presentation:nn { #1 } { #2 }
  \tl_use:N \g_tmpa_tl
  \tl_use:c { g_@@_contenu_anonyme*_tl }
  \tl_use:N \g_tmpb_tl
}
%    \end{macrocode}
% \end{macro}
% 
% \iffalse
%&lt;/package&gt;
% \fi
% 
% \end{implementation}
%
% \Finale \PrintChanges\PrintIndex
% 
\endinput
%%% Local Variables: 
%%% mode: doctex
%%% coding: utf-8
%%% fill-column: 80
%%% TeX-master: t
%%% End: 
</pre></body></html>