nicematrix (13feb18)

git-svn-id: svn://tug.org/texlive/trunk@46627 c570f23f-e606-0410-a88d-b1316a301751

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diff --git a/Master/texmf-dist/doc/latex/nicematrix/README.md b/Master/texmf-dist/doc/latex/nicematrix/README.md
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+The LaTeX extension nicematrix is distributed under the LPPL 1.3 license.
+
+This extension has been written by F. Pantigny (fpantigny@wanadoo.fr).
+
+This extension is entirely contained in a single file : nicematrix.sty
+
+The LaTeX package nicematrix gives an environment NiceMatrix which is similar to environment
+matrix of mathtools but gives the possibility to draw beautiful ellipis dots between the cells 
+of the matrix.
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/nicematrix/nicematrix.pdf b/Master/texmf-dist/doc/latex/nicematrix/nicematrix.pdf
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diff --git a/Master/texmf-dist/source/latex/nicematrix/nicematrix.dtx b/Master/texmf-dist/source/latex/nicematrix/nicematrix.dtx
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+% \iffalse meta-comment
+%
+% Copyright (C) 2017 by F. Pantigny
+% -----------------------------------
+%
+% This file may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in:
+%
+% http://www.latex-project.org/lppl.txt
+%
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% \fi
+% \iffalse
+\def\myfileversion{1.0}
+\def\myfiledate{2018/02/13}
+%
+%
+%<*batchfile>
+\begingroup
+\input l3docstrip.tex
+\keepsilent
+\usedir{tex/latex/nicematrix}
+\preamble
+
+Copyright (C) 2017 by F. Pantigny
+-----------------------------------
+
+This file may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3
+of this license or (at your option) any later version.
+The latest version of this license is in:
+
+http://www.latex-project.org/lppl.txt
+
+and version 1.3 or later is part of all distributions of LaTeX
+version 2005/12/01 or later.
+
+\endpreamble
+\askforoverwritefalse
+\endgroup
+%</batchfile>
+%
+%<@@=nm>
+%<*driver>
+\documentclass{l3doc} % load fancyvrb, amsmath, array, color, etc.
+\VerbatimFootnotes
+\usepackage{xltxtra}
+\usepackage{lmodern}
+\usepackage{geometry}
+\usepackage[dvipsnames]{xcolor} % color is already loaded with l3doc (?)
+\geometry{left=2.8cm,right=2.8cm,top=2.5cm,bottom=2.5cm,papersize={21cm,29.7cm}}
+\usepackage{mathtools}
+\usepackage{amsfonts}
+\usepackage{stmaryrd}
+\usepackage{nicematrix}
+\NewDocumentEnvironment {scope} {} {} {}
+\def\interitem{\vskip 7mm plus 2 mm minus 3mm}          
+\def\emphase#1{{\color{RoyalPurple}#1}}
+\fvset{commandchars=\~\#\@,formatcom={\color{gray}}}
+\parindent 0pt
+\DisableCrossrefs
+\begin{document}
+\DocInput{nicematrix.dtx}
+\end{document}
+%</driver>
+% \fi 
+% \title{The package \pkg{nicematrix}\thanks{This document corresponds to the version~\myfileversion\space of \pkg{nicematrix},
+% at the date of~\myfiledate.}} \author{F. Pantigny \\ \texttt{fpantigny@wanadoo.fr}}
+%
+% \maketitle
+%
+% \begin{abstract}
+% The LaTeX package \pkg{nicematrix} gives an environment |{NiceMatrix}| which is similar to the environment
+% |{matrix}| but gives the possibility to draw ellipis dots between the cells of the matrix.
+% \end{abstract}
+%
+% \vspace{1cm}
+% \section{Presentation}
+%
+% This package can be used with |xelatex|, |lualatex|, |pdflatex| but also by the classical workflow
+% |latex|-|dvips|-|ps2pdf| (or Adobe Distiller). Two compilations may be necessary. This package requires the
+% packages \pkg{expl3}, \pkg{l3keys2e}, \pkg{xparse}, \pkg{array}, \pkg{mathtools} and \pkg{tikz}. The Tikz
+% libraries \pkg{calc} and \pkg{math} are also required.
+%
+% \medskip
+% The package \pkg{nicematrix} aims to draw beautiful matrices in a way almost transparent for the user.
+% 
+% \medskip
+% Consider, for exemple, the matrix\enskip
+% $A = \begin{pmatrix}
+% 1      &\cdots &\cdots &1      \\
+% 0      &\ddots &       &\vdots \\
+% \vdots &\ddots &\ddots &\vdots \\
+% 0      &\cdots &0      &1
+% \end{pmatrix}$
+%
+% \medskip
+% Usually, when using LaTeX and \pkg{amsmath} (or \pkg{mathtools}), such a matrix is composed with an environment
+% |{pmatrix}| and the following code:
+% \begin{Verbatim}
+% $A = \begin{pmatrix}
+% 1      & \cdots & \cdots & 1      \\
+% 0      & \ddots &        & \vdots \\
+% \vdots & \ddots & \ddots & \vdots \\
+% 0      & \cdots & 0      & 1
+% \end{pmatrix}$
+% \end{Verbatim}
+% 
+% \medskip 
+% If we load the package \pkg{nicematrix} with the option |Transparent|, the same code will give the
+% following result:
+% 
+% \begin{scope}
+% \NiceMatrixOptions{Transparent}
+% \[A = \begin{pmatrix}
+% 1      & \cdots & \cdots & 1      \\
+% 0      & \ddots &        & \vdots \\
+% \vdots & \ddots & \ddots & \vdots \\
+% 0      & \cdots & 0      & 1
+% \end{pmatrix}\]
+% \end{scope}
+%
+% \medskip
+% The dotted lines are drawn with Tikz. Two compilations may be necessary.
+%
+%
+% \section{How to use nicematrix for new code}
+%
+% \subsection{The environment NiceMatrix and its variants} 
+%
+% The package \pkg{nicematrix} gives six new environments |{NiceMatrix}|, |{pNiceMatrix}|, |{bNiceMatrix}|,
+% |{BNiceMatrix}|, |{vNiceMatrix}| and |{VNiceMatrix}|. By default, these environments behave almost exactly as the
+% corresponding environments of \pkg{amsmath} (and \pkg{mathtools}): |{matrix}|, |{pmatrix}|, |{bmatrix}|,
+% |{Bmatrix}|, |{vmatrix}| and |{Vmatrix}|.
+%
+% \smallskip
+% Inside these environments, five new commands are defined: |\Ldots|, |\Cdots|, |\Vdots|, |\Ddots| and |\Iddots|.
+% These commands are intended to be used in place of |\dots|, |\cdots|, |\vdots|, |\ddots| and
+% |\iddots|.\footnote{The command |\iddots|, defined in \pkg{nicematrix}, is a variant of 
+% |\ddots| with dots going forward: \smash{$\iddots$}. If |mathdots| is loaded, the version of |mathdots| is used.}
+%
+% \smallskip
+% Each of them must be used alone in the cell of the array and it draws a dotted line between the first non-empty
+% cells\footnote{The precise definition of a ``non-empty cell'' is given below.} on both sides of the current cell.
+% Of course, for |\Ldots| and |\Cdots|, it's an horizontal line; for |\Vdots|, it's a vertical line and for
+% |\Ddots| and |\Iddots| diagonals ones.\par\nobreak
+% \bigskip
+% \begin{BVerbatim}[baseline=c,boxwidth=10cm]
+% \begin{bNiceMatrix}
+% a_1      & \Cdots &        & & a_1 \\
+% \Vdots   & a_2    & \Cdots & & a_2 \\
+%          & \Vdots & \Ddots \\
+% \\
+% a_1      & a_2    &        & & a_n \\ 
+% \end{bNiceMatrix}
+% \end{BVerbatim}
+% $\begin{bNiceMatrix}
+% a_1      & \Cdots &        & & a_1 \\
+% \Vdots   & a_2    & \Cdots & & a_2 \\
+%          & \Vdots & \Ddots \\
+% \\
+% a_1      & a_2    &        & & a_n \\ 
+% \end{bNiceMatrix}$
+% 
+% \interitem
+% In order to represent the null matrix, one can use the following codage:\par\nobreak
+% \bigskip
+% \begin{BVerbatim}[baseline=c,boxwidth=10cm]
+% \begin{bNiceMatrix}
+% 0      & \Cdots & 0      \\
+% \Vdots &        & \Vdots \\
+% 0      & \Cdots & 0 
+% \end{bNiceMatrix}
+% \end{BVerbatim}
+% $\begin{bNiceMatrix}
+% 0      & \Cdots & 0      \\
+% \Vdots &        & \Vdots \\
+% 0      & \Cdots & 0 
+% \end{bNiceMatrix}$
+%
+% \bigskip
+% However, one may want a larger matrix. Usually, in such a case, the users of LaTeX add a new row and a new
+% column. It's possible to use the same method with \pkg{nicematrix}:\par\nobreak
+% \bigskip
+% \begin{BVerbatim}[baseline=c,boxwidth=10cm]
+% \begin{bNiceMatrix}
+% 0      & \Cdots & \Cdots & 0      \\
+% \Vdots &        &        & \Vdots \\
+% \Vdots &        &        & \Vdots \\
+% 0      & \Cdots & \Cdots & 0 
+% \end{bNiceMatrix}
+% \end{BVerbatim}
+% $\begin{bNiceMatrix}
+% 0      & \Cdots & \Cdots & 0      \\
+% \Vdots &        &        & \Vdots \\
+% \Vdots &        &        & \Vdots \\
+% 0      & \Cdots & \Cdots & 0 
+% \end{bNiceMatrix}$
+% 
+% \bigskip
+% In the first column of this exemple, there are two instructions |\Vdots| but only one dotted line is drawn (there
+% is no overlapping graphic objects in the resulting \textsc{pdf}).
+%
+% However, useless computations are performed by TeX before detecting that both instructions would eventually yield
+% the same dotted line. That's why the package \pkg{nicematrix} provides starred versions of |\Ldots|, |\Cdots|,
+% etc.: |\Ldots*|, |\Cdots*|, etc.. These versions are simply equivalent to |\hphantom{\ldots}|,
+% |\hphantom{\cdots}|, etc. The user should use these starred versions whenever a classical version has already
+% been used for the same dotted line.\par\nobreak
+% \bigskip
+% \begin{BVerbatim}[baseline=c,boxwidth=10cm]
+% \begin{bNiceMatrix}
+% 0       & \Cdots & ~emphase#\Cdots*@ & 0       \\
+% \Vdots  &        &         & \Vdots  \\
+% ~emphase#\Vdots*@ &        &         & ~emphase#\Vdots*@ \\
+% 0       & \Cdots & ~emphase#\Cdots*@ & 0 
+% \end{bNiceMatrix}
+% \end{BVerbatim}
+% $\begin{bNiceMatrix}
+% 0       & \Cdots &        & 0      \\
+% \Vdots  &        &        &        \\
+%         &        &        & \Vdots \\
+% 0       &        & \Cdots & 0 
+% \end{bNiceMatrix}$
+%
+% \bigskip
+% In fact, in this example, it would be possible to draw the same matrix without starred commands with the
+% following code:\par\nobreak
+% \bigskip
+% \begin{BVerbatim}[baseline=c,boxwidth=10cm]
+% \begin{bNiceMatrix}
+% 0       & \Cdots &        & 0      \\
+% \Vdots  &        &        &        \\
+%         &        &        & \Vdots \\
+% 0       &        & \Cdots & 0 
+% \end{bNiceMatrix}
+% \end{BVerbatim}
+% $\begin{bNiceMatrix}
+% 0       & \Cdots &        & 0      \\
+% \Vdots  &        &        &        \\
+%         &        &        & \Vdots \\
+% 0       &        & \Cdots & 0 
+% \end{bNiceMatrix}$
+%
+% \bigskip
+% There are also other means to change the size of the matrix. Someone might want to use the optional argument of
+% the command~|\\| for the vertical dimension and a command~|\hspace*| in a cell for the horizontal dimension.
+% However, a command~|\hspace*| might interfer with the construction of the dotted lines. That's why the package
+% \pkg{nicematrix} provides a command~|\Hspace| which is a variant of |\hspace| transparent for the dotted lines of
+% \pkg{nicematrix}.\par\nobreak
+% \bigskip
+% \begin{BVerbatim}[baseline=c,boxwidth=10cm]
+% \begin{bNiceMatrix}
+% 0      & \Cdots & ~emphase#\Hspace*{1cm}@ & 0      \\
+% \Vdots &        &               & \Vdots \\~emphase#[1cm]@
+% 0      & \Cdots &               & 0    
+% \end{bNiceMatrix}
+% \end{BVerbatim}
+% $\begin{bNiceMatrix}
+% 0      & \Cdots & \Hspace*{1cm} & 0      \\
+% \Vdots &        &               & \Vdots \\[1cm]
+% 0      & \Cdots &               & 0    
+% \end{bNiceMatrix}$
+% 
+% \vskip1cm
+% \subsection{The option NullifyDots}
+%
+% Consider the following matrix composed classicaly with the environment |{pmatrix}|.\par\nobreak
+% \medskip
+% \begin{BVerbatim}[baseline=c,boxwidth=7cm]
+% $A = \begin{pmatrix}
+% a_0 & b \\
+% a_1 &   \\
+% a_2 &   \\
+% a_3 &   \\
+% a_4 &   \\
+% a_5 & b
+% \end{pmatrix}$
+% \end{BVerbatim}
+% $A = \begin{pmatrix}
+% a_0 & b \\
+% a_1 &   \\
+% a_2 &   \\
+% a_3 &   \\
+% a_4 &   \\
+% a_5 & b
+% \end{pmatrix}$
+%
+%
+% \bigskip
+% If we add |\vdots| instructions in the second column, the geometry of the matrix is modified.\par\nobreak
+% \medskip
+% \begin{BVerbatim}[baseline=c,boxwidth=7cm]
+% $B = \begin{pmatrix}
+% a_0 & b      \\
+% a_1 & \vdots \\
+% a_2 & \vdots \\
+% a_3 & \vdots \\
+% a_4 & \vdots \\
+% a_5 & b
+% \end{pmatrix}$
+% \end{BVerbatim}
+% $B = \begin{pmatrix}
+% a_0 & b      \\
+% a_1 & \vdots \\
+% a_2 & \vdots \\
+% a_3 & \vdots \\
+% a_4 & \vdots \\
+% a_5 & b
+% \end{pmatrix}$
+%
+% \bigskip
+% By default, with \pkg{nicematrix}, if we replace |{pmatrix}| by |{pNiceMatrix}| and |\vdots| by
+% |\Vdots| (or |\Vdots*| for efficiency), the geometry of the matrix is not changed.\par\nobreak
+% \medskip
+% \begin{BVerbatim}[baseline=c,boxwidth=7cm]
+% $C = \begin{pNiceMatrix}
+% a_0 & b       \\
+% a_1 & \Vdots  \\
+% a_2 & \Vdots* \\
+% a_3 & \Vdots* \\
+% a_4 & \Vdots* \\
+% a_5 & b
+% \end{pNiceMatrix}$
+% \end{BVerbatim}
+% $C = \begin{pNiceMatrix}
+% a_0 & b       \\
+% a_1 & \Vdots  \\
+% a_2 & \Vdots* \\
+% a_3 & \Vdots* \\
+% a_4 & \Vdots* \\
+% a_5 & b
+% \end{pNiceMatrix}$
+%
+% \bigskip
+% However, one may prefer the geometry of the first matrix $A$ and would like to have such a geometry with a dotted
+% line in the second column. It's possible by using the option |NullifyDots| (and only one instruction |\Vdots| is
+% necessary).\par\nobreak
+% \medskip
+% \begin{BVerbatim}[baseline=c,boxwidth=7cm]
+% ~emphase#\NiceMatrixOptions{NullifyDots}@
+% $D = \begin{pNiceMatrix}
+% a_0 & b      \\
+% a_1 & \Vdots \\
+% a_2 &        \\
+% a_3 &        \\
+% a_4 &        \\
+% a_5 & b
+% \end{pNiceMatrix}$
+% \end{BVerbatim}
+% {\NiceMatrixOptions{NullifyDots}
+% $D = \begin{pNiceMatrix}
+% a_0 & b      \\
+% a_1 & \Vdots \\
+% a_2 &        \\
+% a_3 &        \\
+% a_4 &        \\
+% a_5 & b
+% \end{pNiceMatrix}$}
+%
+% \medskip
+% The option |NullifyDots| smashes the instructions |\Ldots| (and the variants) vertically but also horizontally.
+%
+% \section{How to use nicematrix for existing code}
+%
+% The package \pkg{nicematrix} provides an option called |Transparent| for using existing code transparently (this
+% option --- and the others --- can be set with the |\usepackage| command but \pkg{nicematrix} provides also a
+% dedicated command called |\NiceMatrixOptions|).
+%
+% In fact, this option is an alias for the conjonction of two options : |RenewDots| and |RenewMatrix|.
+%
+% \smallskip
+%
+% \begin{itemize}
+% \item The option |RenewDots|\par\nobreak
+% With this option, the commands |\ldots|, |\cdots|, |\vdots|, |\ddots| and |\iddots|\footnote{The command
+% |\iddots| is not a command of LaTeX but is defined by the package \pkg{nicematrix}. If |mathdots| is loaded, the
+% version of |mathdots| is used.} are redefined within the environments |{NiceMatrix}| and behave like |\Ldots|,
+% |\Cdots|, |\Vdots|, |\Ddots| and |\Iddots|; the command |\dots| (``automatic dots'' of |amsmath| --- and
+% |mathtools|) is also redefined to behave like |\Ldots|.
+%
+% \item  The option |RenewMatrix|\par\nobreak
+% With this option, the environment |{matrix}| is redefined and behave like |{NiceMatrix}|, and so on for the five
+% variants.
+% \end{itemize}
+%
+% \bigskip 
+% Therefore, with the option |Transparent|, a classical code gives directly the ouput of \pkg{nicematrix}.\par\nobreak
+% \bigskip
+% \begin{BVerbatim}[baseline=c]
+% ~emphase#\NiceMatrixOptions{Transparent}@
+% \begin{pmatrix}
+% 1      & \cdots & \cdots & 1      \\
+% 0      & \ddots &        & \vdots \\
+% \vdots & \ddots & \ddots & \vdots \\
+% 0      & \cdots & 0      & 1
+% \end{pmatrix}
+% \end{BVerbatim}
+% \hspace{2cm}
+% \begin{scope}
+% \NiceMatrixOptions{Transparent}
+% $\begin{pmatrix}
+% 1      & \cdots & \cdots & 1      \\
+% 0      & \ddots &        & \vdots \\
+% \vdots & \ddots & \ddots & \vdots \\
+% 0      & \cdots & 0      & 1
+% \end{pmatrix}$
+% \end{scope}
+%
+% 
+% \section{Technical remarks}
+%
+% \subsection{Diagonal lines} 
+%
+% By default, all the diagonal lines of a same matrix are ``parallelized''. That means that the first diagonal line
+% is drawn and, then, the other lines are drawn parallel to the first one (by rotation around the left-most
+% extremity of the line). That's why the position of the instructions |\Ddots| in the matrix can have a marked
+% effect on the final result.
+%
+% \medskip
+% In the following examples, the first |\Ddots| instruction is written in color:
+% 
+% \medskip
+% \begin{scope}
+% \begin{minipage}{9.5cm}
+% Example with parallelization (default):
+% \begin{Verbatim}
+% $A = \begin{pNiceMatrix}
+% 1      & \Cdots &        & 1      \\
+% a+b    & ~emphase#\Ddots@~ &        & \Vdots \\
+% \Vdots & \Ddots &        &        \\
+% a+b    & \Cdots & a+b    & 1
+% \end{pNiceMatrix}$
+% \end{Verbatim}
+% \end{minipage}
+% $A = \begin{pNiceMatrix}
+% 1      & \Cdots &     & 1      \\
+% a+b    & \Ddots &     & \Vdots \\
+% \Vdots & \Ddots &     &        \\
+% a+b    & \Cdots & a+b & 1
+% \end{pNiceMatrix}$
+% 
+% \bigskip
+% \NiceMatrixOptions{ParallelizeDiagonals=true}%
+% \begin{minipage}{9.5cm}
+% % \begin{Verbatim}
+% $A = \begin{pNiceMatrix}
+% 1      & \Cdots &        & 1      \\
+% a+b    &        &        & \Vdots \\
+% \Vdots & ~emphase#\Ddots@~ & \Ddots &        \\
+% a+b    & \Cdots & a+b    & 1
+% \end{pNiceMatrix}$
+% \end{Verbatim}
+% \end{minipage}
+% $A = \begin{pNiceMatrix}
+% 1      & \Cdots &        & 1      \\
+% a+b    &        &        & \Vdots \\
+% \Vdots & \Ddots & \Ddots &        \\
+% a+b    & \Cdots & a+b    & 1
+% \end{pNiceMatrix}$
+%
+% \bigskip
+% It's possible to turn off the parallelization with the option |ParallelizeDiagonals| set to |false|: \par\nobreak 
+%
+% \medskip
+% \NiceMatrixOptions{ParallelizeDiagonals=false}%
+% \begin{minipage}{9.5cm}
+% The same example without parallelization:\\
+% |\NiceMatrixOptions{ParallelizeDiagonals=false}|. 
+% \end{minipage}
+% $A = \begin{pNiceMatrix}
+% 1      & \Cdots  &     & 1      \\
+% a+b    & \Ddots  &     & \Vdots \\
+% \Vdots & \Ddots  &     &        \\
+% a+b    & \Cdots  & a+b & 1
+% \end{pNiceMatrix}$
+%
+%
+% \end{scope}
+%
+% \vskip1cm
+% \subsection{The ``empty'' cells}
+% 
+% An instruction like |\Ldots|, |\Cdots|, etc. tries to determine the first non-empty cell on both sides. However,
+% a empty cell is not necessarily a cell with no TeX content (that is to say a cell with no token between the two
+% ampersands~|&|). Indeed, a cell with contents |\hspace*{1cm}| may be considered as empty.
+%
+% \interitem
+% For \pkg{nicematrix}, the precise rules are as follow.
+%
+% \begin{itemize}
+% \item An implicit cell is empty. For example, in the following matrix:
+%
+% \begin{Verbatim}
+% \begin{pmatrix}
+% a & b \\
+% c \\
+% \end{pmatrix}
+% \end{Verbatim}
+% 
+% the last cell (second row and second column) is empty.
+%
+% \medskip
+% \item Each cell whose TeX ouput has a width less than 0.5~pt is empty.
+%
+% \medskip
+% \item A cell which contains a command |\Ldots|, |\Cdots|, |\Vdots|, |\Ddots| or |\Iddots| and their starred
+% versions is empty. We recall that theses commands should be used alone in a cell.
+%
+% \medskip
+% \item A cell with a command |\Hspace| (or |\Hspace*|) is empty. This command |\Hspace| is a command defined by
+% the package \pkg{nicematrix} with the same meaning that |\hspace| except that the cell where it is used is
+% considered as empty. This command can be used to fix the width of some columns of the matrix without interfering
+% with \pkg{nicematrix}.
+% % \end{itemize}
+%
+% \interitem
+% A dotted line must be delimited by two non-empty cells. If it's not possible to find one of these cells whitin
+% the boudaries of the matrix, an error is issued and the instruction is ignored.
+%
+%
+%
+% \section{Examples}
+%
+%
+% \bigskip
+% A tridiagonal matrix :
+% 
+% \bigskip
+% \begin{BVerbatim}[baseline=c]
+% \NiceMatrixOptions{NullifyDots}
+% $\begin{pNiceMatrix}
+% a      & b      & 0      &        & \Cdots & 0      \\ 
+% b      & a      & b      & \Ddots &        & \Vdots \\
+% 0      & b      & a      & \Ddots &        &        \\
+%        & \Ddots & \Ddots & \Ddots &        & 0      \\
+% \Vdots &        &        &        &        & b      \\
+% 0      & \Cdots &        & 0      & b      & a
+% \end{pNiceMatrix}$
+% \end{BVerbatim}
+% \hspace{1.5cm}
+% \begin{scope}
+% \NiceMatrixOptions{NullifyDots}
+% $\begin{pNiceMatrix}
+% a      & b      & 0      &        & \Cdots & 0      \\ 
+% b      & a      & b      & \Ddots &        & \Vdots \\
+% 0      & b      & a      & \Ddots &        &        \\
+%        & \Ddots & \Ddots & \Ddots &        & 0      \\
+% \Vdots &        &        &        &        & b      \\
+% 0      & \Cdots &        & 0      & b      & a
+% \end{pNiceMatrix}$
+% \end{scope}
+%
+% \vspace{2cm}
+%
+% A permutation matrix :
+%
+% \bigskip
+% \begin{BVerbatim}[baseline=c]
+% $\begin{pNiceMatrix}
+% 0       & 1 & 0 &        & \Cdots &   0    \\
+% \Vdots  &   &   & \Ddots &        & \Vdots \\
+%         &   &   & \Ddots &        &        \\
+%         &   &   & \Ddots &        &   0    \\
+% 0       & 0 &   &        &        &   1    \\
+% 1       & 0 &   & \Cdots &        &   0    
+% \end{pNiceMatrix}$
+% \end{BVerbatim}
+% \hspace{2.5cm}
+% $\begin{pNiceMatrix}
+% 0       & 1 & 0 &        & \Cdots &   0    \\
+% \Vdots  &   &   & \Ddots &        & \Vdots \\
+%         &   &   & \Ddots &        &        \\
+%         &   &   & \Ddots &        &   0    \\
+% 0       & 0 &   &        &        &   1    \\
+% 1       & 0 &   & \Cdots &        &   0    
+% \end{pNiceMatrix}$
+%
+% \vspace{2cm}
+%
+% An example with |\Iddots|: 
+% 
+% \bigskip
+% \begin{BVerbatim}[baseline=c]
+% $\begin{pNiceMatrix}
+% 1       & \Cdots  &         & 1      \\
+% \Vdots  &         &         & 0      \\
+%         & ~emphase#\Iddots@ & ~emphase#\Iddots@ & \Vdots \\
+% 1       & 0       & \Cdots  & 0 
+% \end{pNiceMatrix}$
+% \end{BVerbatim}
+% \hspace{4cm}
+% $\begin{pNiceMatrix}
+% 1       & \Cdots  &         & 1      \\
+% \Vdots  &         &         & 0      \\
+%         & \Iddots & \Iddots & \Vdots \\
+% 1       & 0       & \Cdots  & 0 
+% \end{pNiceMatrix}$
+%
+%
+% 
+% \vspace{1cm}
+%
+% \section{Implementation}
+%
+% \subsection{Declaration of the package and extensions loaded}
+%
+%
+% First, Tikz and the Tikz libraries \pkg{calc} and \pkg{math} are loaded before the |\ProvidesExplPackage|. They
+% are loaded this way because |\usetikzlibrary| in |expl3| code fails.\footnote{cf.
+% |tex.stackexchange.com/questions/57424/using-of-usetikzlibrary-in-an-expl3-package-fails|}
+% 
+%    \begin{macrocode}
+\RequirePackage{tikz}
+\usetikzlibrary{calc,math}
+%    \end{macrocode}
+%
+% \bigskip
+% Then, we can give the traditionnal declaration of a package written with |expl3|:
+%    \begin{macrocode}
+\RequirePackage{l3keys2e}
+\ProvidesExplPackage
+  {nicematrix}
+  {\myfiledate}
+  {\myfileversion}
+  {Draws nice dotted lines in matrix environments}
+%    \end{macrocode}
+% 
+% The command for the treatment of the options of |\usepackage| is at the end of this package for technical reasons.
+%
+% \bigskip
+% We load \pkg{array} and \pkg{mathtools} (\pkg{mathtools} may be considered as the successor of \pkg{amsmath}).
+%    \begin{macrocode}
+\RequirePackage{array}
+\RequirePackage{mathtools}
+%    \end{macrocode}
+%
+% \bigskip 
+% The package \pkg{xparse} will be used to define the environment |{NiceMatrix}|, its variants and the
+% document-level commands (|\NiceMatrixOptions|, etc.).
+% \begin{macrocode}
+\RequirePackage{xparse}
+%    \end{macrocode}
+%
+% \bigskip
+% \subsection{Technical  definitions}
+%
+% First, we define a command |\iddots| similar to |\ddots| ($\ddots$) but with dots going forward ($\iddots$). We
+% use |\ProvideDocumentCommand|, and so, if the command |\iddots| has already been defined (for example by the
+% package \pkg{mathdots}), we don't define it again.
+% 
+%    \begin{macrocode}
+\ProvideDocumentCommand \iddots {}
+      {\mathinner{\mkern 1mu 
+                  \raise 1pt \hbox{.}
+                  \mkern 2mu
+                  \raise 4pt\hbox{.}
+                  \mkern 2mu
+                  \raise7pt \vbox{\kern 7pt 
+                                  \hbox{.}}
+                  \mkern1mu}}
+%    \end{macrocode}
+%
+% This definition is a variant of the standard definition of |\ddots|.
+%
+% \bigskip
+% In the environment |{NiceMatrix}|, the command |\multicolumn| will be linked to the following command
+% |\@@_multicolumn:| but only if the option |RenewMatrix| is not set. Indeed, if the option |RenewMatrix| is used,
+% we want to let the possibility to the user to use |\multicolumn| (or |\hdotsfor| of \pkg{amsmath}) in some
+% matrices without dotted lines and to have the automatic dotted lines of \pkg{nicematrix} in other matrices.
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_multicolumn:nn
+       {\msg_error:nn {nicematrix} {multicolumn~forbidden}}
+%    \end{macrocode}
+% This command |\@@_multicolumn:nn| takes two arguments, and therefore, the first two arguments of |\column| will
+% be gobbled.
+%
+% \bigskip 
+% The following counter will count the environments |{NiceMatrix}|. The value of this counter will be used to
+% prefix the names of the Tikz nodes created in the matrix.
+%    \begin{macrocode}
+\int_new:N \g_@@_env_int
+%    \end{macrocode}
+%
+% \bigskip
+% \subsection{The options}
+%
+% The flag |\l_@@_parallelize_diags_bool| controls wether the diagonals are parallelized. The default
+% is~|true|.
+%    \begin{macrocode}
+\bool_new:N \l_@@_parallelize_diags_bool
+\bool_set_true:N \l_@@_parallelize_diags_bool
+%    \end{macrocode}
+%
+% \bigskip
+% The flag |\l_@@_nullify_dots_bool| corresponds to the option |NullifyDots|. When the flag is down, the
+% instructions like |\vdots| are inserted within a |\hphantom| (and so the constructed matrix has exactly the same
+% size as a matrix constructed with the classical |{matrix}| and |\ldots|, |\vdots|, etc.)
+%    \begin{macrocode}
+\bool_new:N \l_@@_nullify_dots_bool
+%    \end{macrocode}
+%
+% \bigskip
+% The flag |\l_@@_renew_matrix_bool| will be raised if the option |RenewMatrix| is used.
+%    \begin{macrocode}
+\bool_new:N \l_@@_renew_matrix_bool
+%    \end{macrocode}
+%
+% \bigskip
+% We define a set of options which will be used with the command |NiceMatrixOptions|.
+%    \begin{macrocode}
+\keys_define:nn {NiceMatrix}
+     {ParallelizeDiagonals .bool_set:N = \l_@@_parallelize_diags_bool,
+      ParallelizeDiagonals .default:n  = true,
+%    \end{macrocode}
+%
+% \bigskip
+% With the option |RenewDots|, the command |\cdots|, |\ldots|, |\vdots| and |\ddots| are redefined and behave like the
+% commands |\Cdots|, |\Ldots|, |\Vdots| and |\Ddots|.
+%    \begin{macrocode}
+      RenewDots            .bool_set:N = \l_@@_renew_dots_bool,
+      RenewDots            .default:n  = true,
+%    \end{macrocode}
+%
+% \bigskip
+% With the option |RenewMatrix|, the environment |{matrix}| of \pkg{amsmath} and its variants are redefined to
+% behave like the environment |{NiceMatrix}| and its variants.
+%    \begin{macrocode}
+      RenewMatrix          .code:n     = {\cs_set_eq:NN \env@matrix \NiceMatrix
+                                          \bool_set_true:N \l_@@_renew_matrix_bool}, 
+      RenewMatrix          .default:n  = true,
+      Transparent          .meta:n     = {RenewDots,RenewMatrix},
+      Transparent          .value_forbidden:n = true,
+%    \end{macrocode}
+%
+% \bigskip
+% Without the option |NullifyDots|, the instructions like |\vdots| are inserted within a
+% |\hphantom| (and so the constructed matrix has exactly the same size as a matrix constructed with the
+% classical |{matrix}| and |\ldots|, |\vdots|, etc.). This option is set by default.
+%    \begin{macrocode}
+      NullifyDots          .bool_set:N = \l_@@_nullify_dots_bool ,
+      NullifyDots          .default:n  = true}
+%    \end{macrocode}
+%
+% \bigskip
+% |\NiceMatrixOptions| is the command of the \pkg{nicematrix} package to fix options at the document level. The
+% scope of these specification is the current TeX group.
+%    \begin{macrocode}
+\NewDocumentCommand \NiceMatrixOptions {m}
+    {\keys_set:nn {NiceMatrix} {#1}}
+%    \end{macrocode}
+%
+% \bigskip
+% \subsection{The main functions}
+%
+% The pseudo-environment |\@@_Cell:|--|\@@_end_Cell:| is used to format the cells of the array (except the cells of
+% the first column: see below). 
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_Cell:
+   {
+%    \end{macrocode}
+% We increment |\g_@@_column_int|, which is the counter of the columns. We need a global affectation because this
+% command will be used in the cell of a |\halign| (via an environment |{array}|).
+%    \begin{macrocode}
+    \int_gincr:N \g_@@_column_int
+%    \end{macrocode}
+% At the end of the array, the counter |\g_@@_nb_column_int| will contain the total number of columns of the array
+% (even if all the lines don't have the same number of ampersands).
+%    \begin{macrocode}
+    \int_gset:Nn \g_@@_nb_column_int {\int_max:nn \g_@@_nb_column_int \g_@@_column_int}
+%    \end{macrocode}
+% We create a Tikz node for the current cell of the array. 
+%    \begin{macrocode}
+    \tikz[remember~picture, inner~sep = 0pt, minimum~width = 0pt, baseline]
+       \node [anchor=base] (nm-\int_use:N \g_@@_env_int-
+                               \int_use:N \g_@@_line_int-
+                               \int_use:N \g_@@_column_int)
+       \bgroup $} % $
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_end_Cell:
+   {$\egroup ;} % $
+%    \end{macrocode}
+%
+% \interitem 
+% The pseudo-environment |\@@_Cell_First_Column:|--|\@@_end_Cell:| is used to format the cells of the first column
+% of the array. For such a column, we have to increment the counter of the lines (|\g_@@_line_int|) and to
+% initialize the counter of the columns (|\g_@@_column_int|).
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_Cell_First_Column:
+   {\int_gincr:N \g_@@_line_int
+    \int_gset:Nn \g_@@_column_int 0
+    \@@_Cell:}
+%    \end{macrocode}
+%
+%
+% \interitem
+% The environment |{NiceMatrix}| is the main environment of the package |nicematrix|. This environment creates an
+% array similar to the array created by the environment |{matrix}| of \pkg{amsmath} but with Tikz nodes for each
+% cell of the matrix.
+%    \begin{macrocode}
+\NewDocumentEnvironment {NiceMatrix} {}
+   {
+%    \end{macrocode}
+% We use a |\aftergroup| to execute |\@@_draw_lines| at the end of the environment (all the LaTeX environments are
+% TeX groups). With this technic, the second part of the environment is the same that the second part of the
+% environment |{matrix}| of \pkg{amsmath}. Therefore, it's easier to redefine the environment |{matrix}| (when the
+% option |RenewMatrix| is used).
+%    \begin{macrocode}
+    \aftergroup \@@_draw_lines:
+%    \end{macrocode}
+%
+% The commands |\Ldots|, |\Cdots|, etc. will be defined only within the environment |{NiceMatrix}|.
+%    \begin{macrocode}
+    \cs_set_eq:NN \Ldots \@@_Ldots
+    \cs_set_eq:NN \Cdots \@@_Cdots
+    \cs_set_eq:NN \Vdots \@@_Vdots
+    \cs_set_eq:NN \Ddots \@@_Ddots
+    \cs_set_eq:NN \Iddots \@@_Iddots
+    \cs_set_eq:NN \Hspace \@@_Hspace:
+    \cs_set_eq:NN \NiceMatrixEndPoint \@@_NiceMatrixEndPoint:
+    \bool_if:NF \l_@@_renew_matrix_bool
+        {\cs_set_eq:NN \multicolumn \@@_multicolumn:nn}
+%    \end{macrocode}
+% If the option |RenewDots| is used, we redefine the commands |\ldots|, |\cdots|, etc.
+%    \begin{macrocode}
+    \bool_if:NT \l_@@_renew_dots_bool
+       {\cs_set_eq:NN \ldots \@@_Ldots
+        \cs_set_eq:NN \cdots \@@_Cdots
+        \cs_set_eq:NN \vdots \@@_Vdots
+        \cs_set_eq:NN \ddots \@@_Ddots
+        \cs_set_eq:NN \iddots \@@_Iddots
+        \cs_set_eq:NN \dots  \@@_Ldots}
+%    \end{macrocode}
+%
+% We increment the counter |\g_@@_env_int| which counts the environments |{NiceMatrix}|.
+%    \begin{macrocode}
+    \int_gincr:N \g_@@_env_int
+%    \end{macrocode}
+% 
+% The sequence |\g_@@_empty_cells_seq| will contains a list of ``empty'' cells (not all the empty cells of the
+% matrix). If we want to indicate that the cell in line~$i$ and line~$j$ must be considered as empty, the token
+% list ``|i-j|'' will be put in this sequence.
+%    \begin{macrocode}
+    \seq_gclear_new:N  \g_@@_empty_cells_seq
+%    \end{macrocode}
+%
+% The counter |\g_@@_instruction_int| will count the instructions (|\Cdots|, |\Vdots|, |\Ddots|, etc.) in the matrix.
+%    \begin{macrocode}
+    \int_gzero_new:N \g_@@_instruction_int
+%    \end{macrocode}
+% The counter |\g_@@_line_int| will be used to count the lines of the array. At the end of the environment
+% |{array}|, this counter will give the total number of lines of the matrix.
+%    \begin{macrocode}
+    \int_gzero_new:N \g_@@_line_int 
+%    \end{macrocode}
+% The counter |\g_@@_column_int| will be used to count the colums of the array. Since we want to known the total
+% number of columns of the matrix, we also create a counter |\g_@@_nb_column_int|. These counters are updated in
+% the command |\@@_Cell:| executed at the beginning of each cell.
+%    \begin{macrocode}
+    \int_gzero_new:N \g_@@_column_int 
+    \int_gzero_new:N \g_@@_nb_column_int
+%    \end{macrocode}
+% The next two lines are the same as in the command |\env@matrix| of \pkg{amsmath} on which all the matrix
+% constructions are built.
+%    \begin{macrocode}
+    \hskip -\arraycolsep
+    \cs_set_eq:NN \@ifnextchar \new@ifnextchar
+%    \end{macrocode}
+% Eventually, the environment |{NiceMatrix}| is defined upon the environment |{array}|. We maintain the
+% signification of the counter |\c@MaxMatrixCols| of \pkg{amsmath}.
+%    \begin{macrocode}
+    \int_set:Nn \l_tmpa_int {\c@MaxMatrixCols - 1}
+    \array{>{\@@_Cell_First_Column:}c<{\@@_end_Cell:}
+                  *\l_tmpa_int{>{\@@_Cell:}c<{\@@_end_Cell:}}}}
+%    \end{macrocode}
+% \bigskip
+% The second part of the environment |{NiceMatrix}| is the same as the second part of the environment |{matrix}| of
+% \pkg{amsmath}. However, at the end of the environment, the instruction |\@@_draw_lines:| will
+% be executed because we have put a ``|\aftergroup \@@_draw_lines:|'' in the beginning of the environment
+% (therefore, it's possible to implement the option |RenewMatrix| with |\cs_set_eq:NN \env@matrix \NiceMatrix|).
+%    \begin{macrocode}
+   {\endarray
+    \hskip -\arraycolsep}
+%    \end{macrocode}
+%
+% \interitem
+% We create the variants of the environment |{NiceMatrix}|.
+%    \begin{macrocode}
+\NewDocumentEnvironment {pNiceMatrix} {}
+   {\left(\begin{NiceMatrix}}
+   {\end{NiceMatrix}\right)}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\NewDocumentEnvironment {bNiceMatrix} {}
+   {\left[\begin{NiceMatrix}}
+   {\end{NiceMatrix}\right]}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\NewDocumentEnvironment {BNiceMatrix} {}
+   {\left\{\begin{NiceMatrix}}
+   {\end{BNiceMatrix}\right\}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\NewDocumentEnvironment {vNiceMatrix} {}
+   {\left\lvert\begin{NiceMatrix}}
+   {\end{BNiceMatrix}\right\rvert}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\NewDocumentEnvironment {VNiceMatrix} {}
+   {\left\lVert\begin{NiceMatrix}}
+   {\end{BNiceMatrix}\right\rVert}
+%    \end{macrocode}
+%
+% \interitem
+% The conditionnal |\@@_if_not_empty_cell:nnT| test wether a cell is empty. The first two arguments must be LaTeX3
+% counters for the row and the column of the considered cell.
+%    \begin{macrocode}
+\prg_set_conditional:Npnn \@@_if_not_empty_cell:nn #1#2 {T}
+%    \end{macrocode}
+% If the cell is a implicit cell (that is after the symbol |\\| of end of row), the cell must, of course, be
+% considered as empty. It's easy to check wether we are in this situation considering the correspondant Tikz node.
+%    \begin{macrocode}
+       {\cs_if_exist:cTF {pgf@sh@ns@nm-
+                                    \int_use:N \g_@@_env_int-
+                                    \int_use:N #1-
+                                    \int_use:N #2}
+%    \end{macrocode}
+% We manage a list of ``empty cells'' called |\g_@@_empty_cells_seq|. In fact, this list is not a list of all the
+% empty cells of the array but only those explicitely declared empty for some reason. It's easy to check if the
+% current cell is in this list.
+%    \begin{macrocode}
+          {\seq_if_in:NxTF \g_@@_empty_cells_seq
+                           {\int_use:N #1-\int_use:N #2}
+             {\prg_return_false:}
+%    \end{macrocode}
+% In the general case, we consider the width of the Tikz node corresponding to the cell. In order to compute this
+% width, we have to extract the coordinate of the west and east anchors of the node. This extraction needs a
+% command |\tikz| but, in fact, nothing is drawn.
+%    \begin{macrocode}
+             {\tikz[remember~picture]
+                \path let \p1 = (nm-
+                                 \int_use:N \g_@@_env_int-
+                                 \int_use:N #1-
+                                 \int_use:N #2.east),
+                          \p2 = (nm-
+                                 \int_use:N \g_@@_env_int-
+                                 \int_use:N #1-
+                                 \int_use:N #2.west)
+                      in \pgfextra {\dim_gset:Nn \g_tmpa_dim {\x1}
+                                    \dim_gset:Nn \g_tmpb_dim {\x2}} ;
+%    \end{macrocode}
+% We compute in |\g_tmpa_dim| the width of the Tikz node.
+%    \begin{macrocode}
+              \dim_gsub:Nn \g_tmpa_dim \g_tmpb_dim
+              \dim_compare:nNnTF {\dim_abs:n \g_tmpa_dim} < {0.5 pt}
+                    {\prg_return_false:}
+                    {\prg_return_true:}}}
+          {\prg_return_false:}
+       }
+%    \end{macrocode}
+%
+% \interitem
+% For each drawing instruction in the matrix (like |\Cdots|, etc.), we create a global property list to store the
+% informations corresponding to the instruction. Such an property list will have three fields:
+% \begin{itemize}
+% \item a field ``type'' with the type of the instruction (|cdots|, |vdots|, |ddots|, etc.);
+% \item a field ``line'' with the number of the line of the matrix where the instruction appeared;
+% \item a field ``column'' with the number of the column of the matrix where the instruction appeared.
+% \end{itemize}
+%
+% \interitem
+% The argument of the following command |\@@_instruction_of_type:n| is the type of the instruction (|cdots|,
+% |vdots|, |ddots|, etc.). This command creates the corresponding property list.
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_instruction_of_type:n 
+%    \end{macrocode}
+% First, we increment the counter of the instructions (this counter is initialized in the beginning of the
+% environment |{NiceMatrix}|). This incrementation is global because the command will be used in the cell of a |\halign|).
+%    \begin{macrocode}
+     {\int_gincr:N \g_@@_instruction_int
+      \prop_put:Nnn \l_tmpa_prop {type} {#1}
+      \prop_put:NnV \l_tmpa_prop {line} \g_@@_line_int
+      \prop_put:NnV \l_tmpa_prop {column} \g_@@_column_int
+%    \end{macrocode}
+% The property list has been created in a local variable for convenience. Now, it will be stored in a
+% global variable indicating the number of the instruction.
+%    \begin{macrocode}
+      \prop_gclear_new:c 
+         {g_@@_instruction_\int_use:N\g_@@_instruction_int _prop}
+      \prop_gset_eq:cN
+         {g_@@_instruction_\int_use:N\g_@@_instruction_int _prop}
+         \l_tmpa_prop
+      }
+%    \end{macrocode}
+%
+% 
+% \bigskip
+% \subsection{We draw the lines in the matrix}
+
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_draw_lines:
+    {
+%    \end{macrocode}
+%
+% The sequence |\l_@@_yet_drawn_seq| contains a list of lines which have been drawn previously in the matrix. We
+% maintain this sequence because we don't want to draw two overlapping lines.
+%    \begin{macrocode}
+     \seq_clear_new:N \l_@@_yet_drawn_seq
+%    \end{macrocode}
+%
+%
+% The following variables will be used further.
+%    \begin{macrocode}
+     \int_zero_new:N \l_@@_type_int
+     \int_zero_new:N \l_@@_line_int
+     \int_zero_new:N \l_@@_column_int
+     \int_zero_new:N \l_@@_di_int
+     \int_zero_new:N \l_@@_dj_int
+%    \end{macrocode}
+%
+% By befault, the diagonal lines will be parallelized\footnote{It's possible to use the option
+% |ParallelizeDiagonals| to disable this parallelization.}. There are two types of diagonals lines: the $|\Ddots|$
+% diagonals and the |\Iddots| diagonals. We have to count the both types in order to known wether a diagonal is the
+% first of its type in the current |{NiceMatrix}| environment.
+%    \begin{macrocode}
+     \bool_if:NT \l_@@_parallelize_diags_bool
+          {\int_zero_new:N \l_@@_ddots_int
+           \int_zero_new:N \l_@@_iddots_int
+%    \end{macrocode}
+%
+% The dimensions |\l_@@_delta_x_one_dim| and |\l_@@_delta_y_one_dim| will contains the $\Delta_x$ and $\Delta_y$ of the
+% first |\Ddots| diagonal. We have to store these values in order to draw the others |\Ddots| diagonals parallel to
+% the first one. Similarly |\l_@@_delta_x_two_dim| and |\l_@@_delta_y_two_dim| are the $\Delta_x$ and $\Delta_y$ of
+% the first |\Iddots| diagonal.
+%    \begin{macrocode}
+           \dim_zero_new:N \l_@@_delta_x_one_dim
+           \dim_zero_new:N \l_@@_delta_y_one_dim
+           \dim_zero_new:N \l_@@_delta_x_two_dim
+           \dim_zero_new:N \l_@@_delta_y_two_dim}
+%    \end{macrocode}
+% 
+% \interitem
+% The counter |\l_@@_instruction_int| will be the index of the loop over the instructions. The first value is~$1$.
+%    \begin{macrocode}
+     \int_zero_new:N \l_@@_instruction_int
+     \int_incr:N \l_@@_instruction_int
+%    \end{macrocode}
+%
+% \interitem
+% We begin the loop over the instructions (the incrementation is at the end of the loop).
+%    \begin{macrocode}
+     \int_until_do:nNnn \l_@@_instruction_int > \g_@@_instruction_int
+        {
+%    \end{macrocode}
+%
+% \interitem
+% We extract from the property list of the current instruction the fields ``type'', ``line'' and ``column''and we
+% store these values. We have to do a conversion because the components of a property list are token lists (and not
+% integers).
+%    \begin{macrocode}
+         \prop_get:cnN {g_@@_instruction_\int_use:N \l_@@_instruction_int _prop}
+                        {type} \l_tmpa_tl
+         \int_set:Nn \l_@@_type_int {\l_tmpa_tl}
+         \prop_get:cnN {g_@@_instruction_\int_use:N \l_@@_instruction_int _prop}
+                        {line} \l_tmpa_tl
+         \int_set:Nn \l_@@_line_int {\l_tmpa_tl}
+         \prop_get:cnN {g_@@_instruction_\int_use:N \l_@@_instruction_int _prop}
+                        {column} \l_tmpa_tl
+         \int_set:Nn \l_@@_column_int {\l_tmpa_tl}
+%    \end{macrocode}
+%
+% \interitem
+% We fix the values of |\l_@@_di_int| and |\l_@@_dj_int| which indicate the direction of the dotted line to draw in
+% the matrix.
+%    \begin{macrocode}
+           \int_case:nn \l_@@_type_int
+             { 0 {\int_set:Nn \l_@@_di_int 0
+                  \int_set:Nn \l_@@_dj_int 1}
+               1 {\int_set:Nn \l_@@_di_int 0
+                  \int_set:Nn \l_@@_dj_int 1}
+               2 {\int_set:Nn \l_@@_di_int 1
+                  \int_set:Nn \l_@@_dj_int 0}
+               3 {\int_set:Nn \l_@@_di_int 1
+                  \int_set:Nn \l_@@_dj_int 1}
+               4 {\int_set:Nn \l_@@_di_int 1
+                  \int_set:Nn \l_@@_dj_int {-1}}}
+%    \end{macrocode}
+%
+% \interitem 
+% An instruction for a dotted line must have a initial cell and a final cell which are both not empty. If it's not
+% the case, the instruction is said \emph{impossible}. An error will be raised if an impossible instruction is
+% encountered.
+%    \begin{macrocode}
+           \bool_if_exist:NTF \l_@@_impossible_instruction_bool
+               {\bool_set_false:N \l_@@_impossible_instruction_bool}
+               {\bool_new:N \l_@@_impossible_instruction_bool}
+%    \end{macrocode}
+%
+% \interitem
+% We will determine |\l_@@_final_i_int| and |\l_@@_final_j_int| which will be the ``coordinates'' of the end of the
+% dotted line we have to draw.
+%    \begin{macrocode}
+           \int_zero_new:N  \l_@@_final_i_int
+           \int_zero_new:N  \l_@@_final_j_int
+           \int_set:Nn \l_@@_final_i_int \l_@@_line_int
+           \int_set:Nn \l_@@_final_j_int \l_@@_column_int
+           \bool_if_exist:NTF \l_@@_stop_loop_bool
+                  {\bool_set_false:N \l_@@_stop_loop_bool}
+                  {\bool_new:N \l_@@_stop_loop_bool}
+           \bool_do_until:Nn \l_@@_stop_loop_bool 
+              {\int_add:Nn \l_@@_final_i_int \l_@@_di_int
+               \int_add:Nn \l_@@_final_j_int \l_@@_dj_int
+%    \end{macrocode}
+% We test if we are still in the matrix. 
+%    \begin{macrocode}
+               \bool_if:nTF { \int_compare_p:nNn \l_@@_final_i_int < 1
+                           || \int_compare_p:nNn \l_@@_final_i_int > \g_@@_line_int
+                           || \int_compare_p:nNn \l_@@_final_j_int < 1
+                           || \int_compare_p:nNn \l_@@_final_j_int > \g_@@_nb_column_int}
+%    \end{macrocode}
+% If we are outside the matrix, the instruction is impossible and, of course, we stop the loop.
+%    \begin{macrocode}
+                       {\bool_set_true:N \l_@@_impossible_instruction_bool
+                        \bool_set_true:N \l_@@_stop_loop_bool}
+%    \end{macrocode}
+% If we are in the matrix, we test if the cell is empty. If it's not the case, we stop the loop because we have
+% found the correct values for |\l_@@_final_i_int| and |\l_@@_final_j_int|.
+%    \begin{macrocode}
+                       {\@@_if_not_empty_cell:nnT \l_@@_final_i_int \l_@@_final_j_int
+                              {\bool_set_true:N \l_@@_stop_loop_bool}}
+               }
+%    \end{macrocode}
+% 
+% \interitem
+% We will determine |\l_@@_initial_i_int| and |\l_@@_initial_j_int| which will be the ``coordinates'' of the
+% beginning of the dotted line we have to draw. The programmation is similar to the previous one.
+%    \begin{macrocode}
+           \int_zero_new:N  \l_@@_initial_i_int
+           \int_zero_new:N  \l_@@_initial_j_int
+           \int_set:Nn \l_@@_initial_i_int \l_@@_line_int
+           \int_set:Nn \l_@@_initial_j_int \l_@@_column_int
+%    \end{macrocode}
+% If we known that the instruction is impossible (because it was not possible to found the correct value for 
+% |\l_@@_final_i_int| and |\l_@@_final_j_int|), we don't do this loop.
+%    \begin{macrocode}
+           \bool_set_eq:NN \l_@@_stop_loop_bool \l_@@_impossible_instruction_bool
+           \bool_do_until:Nn \l_@@_stop_loop_bool 
+              {\int_sub:Nn \l_@@_initial_i_int \l_@@_di_int
+               \int_sub:Nn \l_@@_initial_j_int \l_@@_dj_int
+               \bool_if:nTF 
+                       {   \int_compare_p:nNn \l_@@_initial_i_int < 1
+                        || \int_compare_p:nNn \l_@@_initial_i_int > \g_@@_line_int
+                        || \int_compare_p:nNn \l_@@_initial_j_int < 1
+                        || \int_compare_p:nNn \l_@@_initial_j_int > \g_@@_nb_column_int}
+                       {\bool_set_true:N \l_@@_impossible_instruction_bool
+                        \bool_set_true:N \l_@@_stop_loop_bool}
+                       {\@@_if_not_empty_cell:nnT \l_@@_initial_i_int \l_@@_initial_j_int
+                              {\bool_set_true:N \l_@@_stop_loop_bool}}
+               }
+%    \end{macrocode}
+%
+% \interitem
+% Now, we can determine wether we have to draw a line. 
+% If the line is impossible, of course, we won't draw any line.
+%    \begin{macrocode}
+          \bool_if:NTF \l_@@_impossible_instruction_bool
+            {\msg_error:nn {nicematrix} {Impossible~instruction}}
+%    \end{macrocode}
+%
+% If the dotted line to draw is in the list of the previously drawn lines (|\l_@@_yet_drawn_seq|), we don't draw
+% (so, we won't have overlapping lines in the \textsc{pdf}). The token list |\l_tmpa_tl| is the $4$-uplet
+% characteristic of the line.
+%    \begin{macrocode}
+            {\tl_set:Nx \l_tmpa_tl {\int_use:N \l_@@_initial_i_int-
+                                    \int_use:N \l_@@_initial_j_int-
+                                    \int_use:N \l_@@_final_i_int-
+                                    \int_use:N \l_@@_final_j_int}
+             \seq_if_in:NVF \l_@@_yet_drawn_seq \l_tmpa_tl
+%    \end{macrocode}
+%
+% If the dotted line to draw is not in the list, we add it the list |\l_@@_yet_drawn_seq|.
+%    \begin{macrocode}
+              {\seq_put_left:NV \l_@@_yet_drawn_seq \l_tmpa_tl
+%    \end{macrocode}
+%
+% \medskip
+% The four following variables are global because we will have to do affectations in a Tikz instruction (in order
+% to extract the coordinates of two extremities of the line to draw).
+%    \begin{macrocode}
+               \dim_zero_new:N \g_@@_x_initial_dim 
+               \dim_zero_new:N \g_@@_y_initial_dim 
+               \dim_zero_new:N \g_@@_x_final_dim 
+               \dim_zero_new:N \g_@@_y_final_dim
+%    \end{macrocode}
+%
+% 
+% We draw the line.
+%    \begin{macrocode}
+               \int_case:nn \l_@@_type_int 
+                {0  \@@_draw_ldots_line:
+                 1  \@@_draw_cdots_line:
+                 2  \@@_draw_vdots_line:
+                 3  \@@_draw_ddots_line:
+                 4  \@@_draw_iddots_line:}}}
+%    \end{macrocode}
+%
+% \bigskip
+% Incrementation of the index of the loop (and end of the loop).
+%    \begin{macrocode}
+            \int_incr:N \l_@@_instruction_int
+         }
+}
+%    \end{macrocode}
+%
+%
+% \interitem 
+% The command |\@@_retrieve_coords:nn| retrieves the Tikz coordinates of the two extremities of the dotted line we
+% will have to draw \footnote{In fact, with diagonals lines, a adjustment of one of the coordinates may be done.}.
+% This command has four implicit arguments which are |\l_@@_initial_i_int|, |\l_@@_initial_j_int|,
+% |\l_@@_final_i_int| and |\l_@@_final_j_int|.
+%
+% The two arguments of the command |\@@_retrieve_coords:nn| are the anchors that must be used for the two nodes.
+% These anchors must be given with the point (e.g.: |.north|, |.south|, etc.).
+%
+% The coordinates are stored in |\g_@@_x_initial_dim|, |\g_@@_y_initial_dim|, |\g_@@_x_final_dim|,
+% |\g_@@_y_final_dim|. These variables are global for technical reasons: we have to do an affectation in a Tikz
+% picture.
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_retrieve_coords:nn
+     {\tikz[remember~picture]
+       \path let \p1 = (nm-\int_use:N \g_@@_env_int-
+                           \int_use:N \l_@@_initial_i_int-
+                           \int_use:N \l_@@_initial_j_int #1),
+                 \p2 = (nm-\int_use:N \g_@@_env_int-
+                           \int_use:N \l_@@_final_i_int-
+                           \int_use:N \l_@@_final_j_int #2)
+             in \pgfextra {\dim_gset:Nn \g_@@_x_initial_dim {\x1}
+                           \dim_gset:Nn \g_@@_y_initial_dim {\y1}
+                           \dim_gset:Nn \g_@@_x_final_dim {\x2}
+                           \dim_gset:Nn \g_@@_y_final_dim {\y2}} ; }
+%    \end{macrocode}
+%
+% \interitem
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_draw_ldots_line:
+      {\@@_retrieve_coords:nn {.south~east} {.south~west}
+       \@@_draw_tikz_line:}
+%    \end{macrocode}
+%
+% \bigskip
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_draw_cdots_line:
+      {\@@_retrieve_coords:nn {.mid~east} {.mid~west}
+       \@@_draw_tikz_line:}
+%    \end{macrocode}
+%
+% \bigskip
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_draw_vdots_line:
+      {\@@_retrieve_coords:nn {.south} {.north}
+       \@@_draw_tikz_line:}
+%    \end{macrocode}
+%
+% \interitem
+% For the diagonal lines, the situation is a bit more complicated because, by default, we parallelize the diagonals
+% lines. The first diagonal line is drawn and then, all the other diagonal lines are drawn parallel to the first
+% one.
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_draw_ddots_line:
+   {\@@_retrieve_coords:nn {.south~east} {.north~west}
+%    \end{macrocode}
+% We have retrieved the coordinates in the usual way (they are stored in |\g_@@_x_initial_dim|, etc.).
+% If the parallelization of the diagonals is set, we will have (maybe) to adjust the fourth coordinate.
+%    \begin{macrocode}
+    \bool_if:NT \l_@@_parallelize_diags_bool
+       {\int_incr:N \l_@@_ddots_int
+%    \end{macrocode}
+% We test if the diagonal line is the first one (the counter |\l_@@_ddots_int| is created for this usage).
+%    \begin{macrocode}
+        \int_compare:nNnTF \l_@@_ddots_int = 1
+%    \end{macrocode}
+% If the diagonal line is the first one, we have no adjustment of the line to do but we store the $\Delta_x$ and the
+% $\Delta_y$ of the line because these values will be used to draw the others diagonal lines parallels to the first one.
+%    \begin{macrocode}
+          {\dim_set:Nn \l_@@_delta_x_one_dim {\g_@@_x_final_dim - \g_@@_x_initial_dim }
+           \dim_set:Nn \l_@@_delta_y_one_dim {\g_@@_y_final_dim - \g_@@_y_initial_dim }}
+%    \end{macrocode}
+% If the diagonal line is not the first one, we have to adjust the second extremity of the line by modifying 
+% the coordinate |\g_@@_y_initial_dim|.
+%    \begin{macrocode}
+          {\dim_gset:Nn \g_@@_y_final_dim          
+                  {\g_@@_y_initial_dim +
+                      (\g_@@_x_final_dim - \g_@@_x_initial_dim)
+                      * \dim_ratio:nn \l_@@_delta_y_one_dim \l_@@_delta_x_one_dim }}}
+%    \end{macrocode}
+% Now, we can draw the dotted line (after a possible change of |\g_@@_y_initial_dim|).
+%    \begin{macrocode}
+    \@@_draw_tikz_line:}
+%    \end{macrocode}
+%
+% \bigskip
+% We draw the |\Iddots| diagonals in the same way.
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_draw_iddots_line:
+   {\_@@_retrieve_coords:nn {.south~west} {.north~east} 
+    \bool_if:NT \l_@@_parallelize_diags_bool
+       {\int_incr:N \l_@@_iddots_int
+        \int_compare:nNnTF \l_@@_iddots_int = 1
+          {\dim_set:Nn \l_@@_delta_x_two_dim {\g_@@_x_final_dim - \g_@@_x_initial_dim }
+           \dim_set:Nn \l_@@_delta_y_two_dim {\g_@@_y_final_dim - \g_@@_y_initial_dim }}
+          {\dim_gset:Nn \g_@@_y_final_dim
+                  {\g_@@_y_initial_dim +
+                      (\g_@@_x_final_dim - \g_@@_x_initial_dim)
+                      * \dim_ratio:nn \l_@@_delta_y_two_dim \l_@@_delta_x_two_dim }}}
+    \@@_draw_tikz_line:}
+%    \end{macrocode}
+%
+% \bigskip
+% \subsection{The actual instructions for drawing the dotted line with Tikz}
+%
+% The command |\@@_draw_tikz_line:| draws the line using four implicit arguments: 
+%
+% \quad |\g_@@_x_initial_dim|, |\g_@@_y_initial_dim|, |\g_@@_x_final_dim| and |\g_@@_y_final_dim|. 
+
+% These variables are global for technical reasons: we have to do affectations in an instruction |\tikz|.
+%
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_draw_tikz_line:
+                     {\begin{tikzpicture}[overlay]
+                        \tikzmath{
+                           coordinate~\a , \b ;
+                           real~\l, \x, \d ;
+                           integer~\n ; 
+                           \a = (\g_@@_x_initial_dim, \g_@@_y_initial_dim) ;
+                           \b = (\g_@@_x_final_dim,  \g_@@_y_final_dim) ;
+                           \l = veclen(\bx-\ax,\by-\ay) ;
+                           \n = (\l - 0.54em)/(0.45em) ;
+                           \x = (\l - \n*0.45em)/(2*\l) ;
+                           \d = 0.45em / \l ; 
+                           if~\n>0
+                           then~{ for~\k in~{0,...,\n}
+                                  { {\node at ($(\a)!\x+\k*\d!(\b)$) {.} ; } ; } ;
+                            }  ;
+                           }
+                      \end{tikzpicture}}
+%    \end{macrocode}
+%
+% \bigskip
+% \subsection{User commands available in environments {NiceMatrix}}
+%
+% We give new names for the commands |\ldots|, |\cdots|, |\vdots| and |\ddots| because these commands will be
+% redefined (if the option |RenewDots| is used).
+%    \begin{macrocode}
+\cs_set_eq:NN \@@_ldots \ldots
+\cs_set_eq:NN \@@_cdots \cdots
+\cs_set_eq:NN \@@_vdots \vdots
+\cs_set_eq:NN \@@_ddots \ddots
+\cs_set_eq:NN \@@_iddots \iddots
+%    \end{macrocode}
+%
+% \interitem
+% The command |\@@_add_to_empty_cells:| adds the current cell to |\g_@@_empty_cells_seq| which is the list of the
+% empty cells (the cells explicitly declared ``empty'': there may be, of course, other empty cells in the matrix).
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_add_to_empty_cells:
+    {\seq_gput_right:Nx \g_@@_empty_cells_seq
+          {\int_use:N \g_@@_line_int-
+           \int_use:N \g_@@_column_int}}
+%    \end{macrocode}
+%
+% \interitem 
+% The commands |\@@_Ldots|, |\@@_Cdots|, |\@@_Vdots|, |\@@_Ddots| and |\@@_Iddots| will be linked to |\Ldots|,
+% |\Cdots|, |\Vdots|, |\Ddots| and |\Iddots| in the environment |{NiceMatrix}|.
+%    \begin{macrocode}
+\NewDocumentCommand \@@_Ldots {s}
+    {\IfBooleanF {#1} {\@@_instruction_of_type:n 0}
+     \bool_if:NF \l_@@_nullify_dots_bool {\phantom \@@_ldots}
+     \@@_add_to_empty_cells:}
+%    \end{macrocode}
+%
+% \bigskip
+%    \begin{macrocode}
+\NewDocumentCommand \@@_Cdots {s}
+    {\IfBooleanF {#1} {\@@_instruction_of_type:n 1}
+     \bool_if:NF \l_@@_nullify_dots_bool {\phantom \@@_cdots}
+     \@@_add_to_empty_cells:}
+%    \end{macrocode}
+%
+% \bigskip
+%    \begin{macrocode}
+\NewDocumentCommand \@@_Vdots {s}
+    {\IfBooleanF {#1} {\@@_instruction_of_type:n 2}
+     \bool_if:NF \l_@@_nullify_dots_bool {\phantom \@@_vdots}
+     \@@_add_to_empty_cells:}
+%    \end{macrocode}
+%
+% \bigskip
+%    \begin{macrocode}
+\NewDocumentCommand \@@_Ddots {s}
+    {\IfBooleanF {#1} {\@@_instruction_of_type:n 3}
+     \bool_if:NF \l_@@_nullify_dots_bool {\phantom \@@_ddots}
+     \@@_add_to_empty_cells:}
+%    \end{macrocode}
+%
+% \bigskip
+%    \begin{macrocode}
+\NewDocumentCommand \@@_Iddots {s}
+    {\IfBooleanF {#1} {\@@_instruction_of_type:n 4}
+     \bool_if:NF \l_@@_nullify_dots_bool {\phantom \@@_iddots}
+     \@@_add_to_empty_cells:}
+%    \end{macrocode}
+%
+%
+% \bigskip
+% The command |\@@_Hspace:| will be linked to |\hspace| in the environment |{NiceMatrix}|.
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_Hspace:
+  {\@@_add_to_empty_cells:
+   \hspace}
+%    \end{macrocode}
+%
+% \bigskip
+% The command |\@@_NiceMatrixEndPoint:| will be linked to |\NiceMatrixEndPoint| in the environment |{NiceMatrix}|.
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_NiceMatrixEndPoint:
+     {\kern 0.5pt}
+%    \end{macrocode}
+%
+% \bigskip
+% \subsection{We process the options}
+%
+% We process the options when the package is loaded (with |\usepackage|) but we recommend to use
+% |\NiceMatrixOptions| instead. 
+%
+% We must process these options after the definition of the environment |{NiceMatrix}| because the option
+% |RenewMatrix| execute the code |\cs_set_eq:NN \env@matrix \NiceMatrix|. 
+%
+% Of course, the command |\NiceMatrix| must be defined before such an instruction is executed.
+%    \begin{macrocode}
+\ProcessKeysOptions {NiceMatrix}
+%    \end{macrocode}
+%
+%
+% \bigskip
+% \subsection{The error messages}
+%    \begin{macrocode}
+\msg_new:nnnn {nicematrix}
+              {Impossible~instruction}
+              {It's~not~possible~to~execute~the~instruction~
+               \int_case:nn \l_@@_type_int
+                 {0 {\token_to_str:N \Ldots}
+                  1 {\token_to_str:N \Cdots}
+                  2 {\token_to_str:N \Vdots}
+                  3 {\token_to_str:N \Ddots}}~in~the~line~\int_use:N\l_@@_line_int\ 
+               ~and~the~column~\int_use:N\l_@@_column_int\space of~the~matrix~
+               because~it's~impossible~to~find~one~of~its~extremities~  
+               (both~extremities~must~be~non~empty~cells~of~the~matrix).~
+               If~you~go~on,~the~instruction~will~be~ignored.}
+              {You~can~specify~a~end~of~line~on~a~empty~cell~
+               with~\token_to_str:N \NiceMatrixEndPoint.}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\msg_new:nnn {nicematrix}
+             {multicolumn~forbidden}
+             {The~command~\token_to_str:N \multicolumn\ 
+              is~forbidden~in~the~environment~\{NiceMatrix\}~ 
+              and~its~variants.~The~command~\token_to_str:N \hdotsfor\ 
+              of~amsmath~is~also~forbidden~since~it~uses~
+              \token_to_str:N \multicolumn.~You~can~go~on~but~your~line~will~
+              probably~be~wrong.}
+%    \end{macrocode}
+%
+% \endinput
+%
+% Local Variables:
+% TeX-fold-mode: nil
+% End:
diff --git a/Master/texmf-dist/source/latex/nicematrix/nicematrix.ins b/Master/texmf-dist/source/latex/nicematrix/nicematrix.ins
new file mode 100644
index 00000000000..ce8a59e12b8
--- /dev/null
+++ b/Master/texmf-dist/source/latex/nicematrix/nicematrix.ins
@@ -0,0 +1,47 @@
+%%
+%% Copyright (C) 2017 by F. Pantigny
+%%
+%%
+%% This file may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either
+%% version 1.3 of this license or (at your option) any later
+%% version.  The latest version of this license is in:
+%%
+%%      http://www.latex-project.org/lppl.txt
+%%
+%% and version 1.3 or later is part of all distributions of
+%% LaTeX version 2005/12/01 or later.
+%%
+\input l3docstrip.tex
+\keepsilent
+\usedir{tex/latex/nicematrix}
+\preamble
+
+Copyright (C) 2017 by F. Pantigny
+
+This file may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either
+version 1.3 of this license or (at your option) any later
+version.  The latest version of this license is in:
+
+     http://www.latex-project.org/lppl.txt
+
+and version 1.3 or later is part of all distributions of
+LaTeX version 2005/12/01 or later.
+
+\endpreamble
+\generate{\file{nicematrix.sty}{\from{nicematrix.dtx}{package}}}
+\Msg{*********************************************************}
+\Msg{*}
+\Msg{* To finish the installation you have to move the}
+\Msg{* following file into a directory searched by TeX:}
+\Msg{*}
+\Msg{* \space\space nicematrix.sty}
+\Msg{*}
+\Msg{* To produce the documentation run the file nicematrix.dtx}
+\Msg{* through XeLaTeX.}
+\Msg{*}
+\Msg{* Happy TeXing!}
+\Msg{*********************************************************}
+\endbatchfile
+
diff --git a/Master/texmf-dist/tex/latex/nicematrix/nicematrix.sty b/Master/texmf-dist/tex/latex/nicematrix/nicematrix.sty
new file mode 100644
index 00000000000..d0c2e771cc6
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/nicematrix/nicematrix.sty
@@ -0,0 +1,386 @@
+%%
+%% This is file `nicematrix.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% nicematrix.dtx  (with options: `package')
+%% 
+%% Copyright (C) 2017 by F. Pantigny
+%% 
+%% This file may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either
+%% version 1.3 of this license or (at your option) any later
+%% version.  The latest version of this license is in:
+%% 
+%%      http://www.latex-project.org/lppl.txt
+%% 
+%% and version 1.3 or later is part of all distributions of
+%% LaTeX version 2005/12/01 or later.
+%% 
+\def\myfileversion{1.0}
+\def\myfiledate{2018/02/13}
+\RequirePackage{tikz}
+\usetikzlibrary{calc,math}
+\RequirePackage{l3keys2e}
+\ProvidesExplPackage
+  {nicematrix}
+  {\myfiledate}
+  {\myfileversion}
+  {Draws nice dotted lines in matrix environments}
+\RequirePackage{array}
+\RequirePackage{mathtools}
+\RequirePackage{xparse}
+\ProvideDocumentCommand \iddots {}
+      {\mathinner{\mkern 1mu
+                  \raise 1pt \hbox{.}
+                  \mkern 2mu
+                  \raise 4pt\hbox{.}
+                  \mkern 2mu
+                  \raise7pt \vbox{\kern 7pt
+                                  \hbox{.}}
+                  \mkern1mu}}
+\cs_new_protected:Nn \__nm_multicolumn:nn
+       {\msg_error:nn {nicematrix} {multicolumn~forbidden}}
+\int_new:N \g__nm_env_int
+\bool_new:N \l__nm_parallelize_diags_bool
+\bool_set_true:N \l__nm_parallelize_diags_bool
+\bool_new:N \l__nm_nullify_dots_bool
+\bool_new:N \l__nm_renew_matrix_bool
+\keys_define:nn {NiceMatrix}
+     {ParallelizeDiagonals .bool_set:N = \l__nm_parallelize_diags_bool,
+      ParallelizeDiagonals .default:n  = true,
+      RenewDots            .bool_set:N = \l__nm_renew_dots_bool,
+      RenewDots            .default:n  = true,
+      RenewMatrix          .code:n     = {\cs_set_eq:NN \env@matrix \NiceMatrix
+                                          \bool_set_true:N \l__nm_renew_matrix_bool},
+      RenewMatrix          .default:n  = true,
+      Transparent          .meta:n     = {RenewDots,RenewMatrix},
+      Transparent          .value_forbidden:n = true,
+      NullifyDots          .bool_set:N = \l__nm_nullify_dots_bool ,
+      NullifyDots          .default:n  = true}
+\NewDocumentCommand \NiceMatrixOptions {m}
+    {\keys_set:nn {NiceMatrix} {#1}}
+\cs_new_protected:Nn \__nm_Cell:
+   {
+    \int_gincr:N \g__nm_column_int
+    \int_gset:Nn \g__nm_nb_column_int {\int_max:nn \g__nm_nb_column_int \g__nm_column_int}
+    \tikz[remember~picture, inner~sep = 0pt, minimum~width = 0pt, baseline]
+       \node [anchor=base] (nm-\int_use:N \g__nm_env_int-
+                               \int_use:N \g__nm_line_int-
+                               \int_use:N \g__nm_column_int)
+       \bgroup $} % $
+\cs_new_protected:Nn \__nm_end_Cell:
+   {$\egroup ;} % $
+\cs_new_protected:Nn \__nm_Cell_First_Column:
+   {\int_gincr:N \g__nm_line_int
+    \int_gset:Nn \g__nm_column_int 0
+    \__nm_Cell:}
+\NewDocumentEnvironment {NiceMatrix} {}
+   {
+    \aftergroup \__nm_draw_lines:
+    \cs_set_eq:NN \Ldots \__nm_Ldots
+    \cs_set_eq:NN \Cdots \__nm_Cdots
+    \cs_set_eq:NN \Vdots \__nm_Vdots
+    \cs_set_eq:NN \Ddots \__nm_Ddots
+    \cs_set_eq:NN \Iddots \__nm_Iddots
+    \cs_set_eq:NN \Hspace \__nm_Hspace:
+    \cs_set_eq:NN \NiceMatrixEndPoint \__nm_NiceMatrixEndPoint:
+    \bool_if:NF \l__nm_renew_matrix_bool
+        {\cs_set_eq:NN \multicolumn \__nm_multicolumn:nn}
+    \bool_if:NT \l__nm_renew_dots_bool
+       {\cs_set_eq:NN \ldots \__nm_Ldots
+        \cs_set_eq:NN \cdots \__nm_Cdots
+        \cs_set_eq:NN \vdots \__nm_Vdots
+        \cs_set_eq:NN \ddots \__nm_Ddots
+        \cs_set_eq:NN \iddots \__nm_Iddots
+        \cs_set_eq:NN \dots  \__nm_Ldots}
+    \int_gincr:N \g__nm_env_int
+    \seq_gclear_new:N  \g__nm_empty_cells_seq
+    \int_gzero_new:N \g__nm_instruction_int
+    \int_gzero_new:N \g__nm_line_int
+    \int_gzero_new:N \g__nm_column_int
+    \int_gzero_new:N \g__nm_nb_column_int
+    \hskip -\arraycolsep
+    \cs_set_eq:NN \@ifnextchar \new@ifnextchar
+    \int_set:Nn \l_tmpa_int {\c@MaxMatrixCols - 1}
+    \array{>{\__nm_Cell_First_Column:}c<{\__nm_end_Cell:}
+                  *\l_tmpa_int{>{\__nm_Cell:}c<{\__nm_end_Cell:}}}}
+   {\endarray
+    \hskip -\arraycolsep}
+\NewDocumentEnvironment {pNiceMatrix} {}
+   {\left(\begin{NiceMatrix}}
+   {\end{NiceMatrix}\right)}
+\NewDocumentEnvironment {bNiceMatrix} {}
+   {\left[\begin{NiceMatrix}}
+   {\end{NiceMatrix}\right]}
+\NewDocumentEnvironment {BNiceMatrix} {}
+   {\left\{\begin{NiceMatrix}}
+   {\end{BNiceMatrix}\right\}}
+\NewDocumentEnvironment {vNiceMatrix} {}
+   {\left\lvert\begin{NiceMatrix}}
+   {\end{BNiceMatrix}\right\rvert}
+\NewDocumentEnvironment {VNiceMatrix} {}
+   {\left\lVert\begin{NiceMatrix}}
+   {\end{BNiceMatrix}\right\rVert}
+\prg_set_conditional:Npnn \__nm_if_not_empty_cell:nn #1#2 {T}
+       {\cs_if_exist:cTF {pgf@sh@ns@nm-
+                                    \int_use:N \g__nm_env_int-
+                                    \int_use:N #1-
+                                    \int_use:N #2}
+          {\seq_if_in:NxTF \g__nm_empty_cells_seq
+                           {\int_use:N #1-\int_use:N #2}
+             {\prg_return_false:}
+             {\tikz[remember~picture]
+                \path let \p1 = (nm-
+                                 \int_use:N \g__nm_env_int-
+                                 \int_use:N #1-
+                                 \int_use:N #2.east),
+                          \p2 = (nm-
+                                 \int_use:N \g__nm_env_int-
+                                 \int_use:N #1-
+                                 \int_use:N #2.west)
+                      in \pgfextra {\dim_gset:Nn \g_tmpa_dim {\x1}
+                                    \dim_gset:Nn \g_tmpb_dim {\x2}} ;
+              \dim_gsub:Nn \g_tmpa_dim \g_tmpb_dim
+              \dim_compare:nNnTF {\dim_abs:n \g_tmpa_dim} < {0.5 pt}
+                    {\prg_return_false:}
+                    {\prg_return_true:}}}
+          {\prg_return_false:}
+       }
+\cs_new_protected:Nn \__nm_instruction_of_type:n
+     {\int_gincr:N \g__nm_instruction_int
+      \prop_put:Nnn \l_tmpa_prop {type} {#1}
+      \prop_put:NnV \l_tmpa_prop {line} \g__nm_line_int
+      \prop_put:NnV \l_tmpa_prop {column} \g__nm_column_int
+      \prop_gclear_new:c
+         {g__nm_instruction_\int_use:N\g__nm_instruction_int _prop}
+      \prop_gset_eq:cN
+         {g__nm_instruction_\int_use:N\g__nm_instruction_int _prop}
+         \l_tmpa_prop
+      }
+
+\cs_new_protected:Nn \__nm_draw_lines:
+    {
+     \seq_clear_new:N \l__nm_yet_drawn_seq
+     \int_zero_new:N \l__nm_type_int
+     \int_zero_new:N \l__nm_line_int
+     \int_zero_new:N \l__nm_column_int
+     \int_zero_new:N \l__nm_di_int
+     \int_zero_new:N \l__nm_dj_int
+     \bool_if:NT \l__nm_parallelize_diags_bool
+          {\int_zero_new:N \l__nm_ddots_int
+           \int_zero_new:N \l__nm_iddots_int
+           \dim_zero_new:N \l__nm_delta_x_one_dim
+           \dim_zero_new:N \l__nm_delta_y_one_dim
+           \dim_zero_new:N \l__nm_delta_x_two_dim
+           \dim_zero_new:N \l__nm_delta_y_two_dim}
+     \int_zero_new:N \l__nm_instruction_int
+     \int_incr:N \l__nm_instruction_int
+     \int_until_do:nNnn \l__nm_instruction_int > \g__nm_instruction_int
+        {
+         \prop_get:cnN {g__nm_instruction_\int_use:N \l__nm_instruction_int _prop}
+                        {type} \l_tmpa_tl
+         \int_set:Nn \l__nm_type_int {\l_tmpa_tl}
+         \prop_get:cnN {g__nm_instruction_\int_use:N \l__nm_instruction_int _prop}
+                        {line} \l_tmpa_tl
+         \int_set:Nn \l__nm_line_int {\l_tmpa_tl}
+         \prop_get:cnN {g__nm_instruction_\int_use:N \l__nm_instruction_int _prop}
+                        {column} \l_tmpa_tl
+         \int_set:Nn \l__nm_column_int {\l_tmpa_tl}
+           \int_case:nn \l__nm_type_int
+             { 0 {\int_set:Nn \l__nm_di_int 0
+                  \int_set:Nn \l__nm_dj_int 1}
+               1 {\int_set:Nn \l__nm_di_int 0
+                  \int_set:Nn \l__nm_dj_int 1}
+               2 {\int_set:Nn \l__nm_di_int 1
+                  \int_set:Nn \l__nm_dj_int 0}
+               3 {\int_set:Nn \l__nm_di_int 1
+                  \int_set:Nn \l__nm_dj_int 1}
+               4 {\int_set:Nn \l__nm_di_int 1
+                  \int_set:Nn \l__nm_dj_int {-1}}}
+           \bool_if_exist:NTF \l__nm_impossible_instruction_bool
+               {\bool_set_false:N \l__nm_impossible_instruction_bool}
+               {\bool_new:N \l__nm_impossible_instruction_bool}
+           \int_zero_new:N  \l__nm_final_i_int
+           \int_zero_new:N  \l__nm_final_j_int
+           \int_set:Nn \l__nm_final_i_int \l__nm_line_int
+           \int_set:Nn \l__nm_final_j_int \l__nm_column_int
+           \bool_if_exist:NTF \l__nm_stop_loop_bool
+                  {\bool_set_false:N \l__nm_stop_loop_bool}
+                  {\bool_new:N \l__nm_stop_loop_bool}
+           \bool_do_until:Nn \l__nm_stop_loop_bool
+              {\int_add:Nn \l__nm_final_i_int \l__nm_di_int
+               \int_add:Nn \l__nm_final_j_int \l__nm_dj_int
+               \bool_if:nTF { \int_compare_p:nNn \l__nm_final_i_int < 1
+                           || \int_compare_p:nNn \l__nm_final_i_int > \g__nm_line_int
+                           || \int_compare_p:nNn \l__nm_final_j_int < 1
+                           || \int_compare_p:nNn \l__nm_final_j_int > \g__nm_nb_column_int}
+                       {\bool_set_true:N \l__nm_impossible_instruction_bool
+                        \bool_set_true:N \l__nm_stop_loop_bool}
+                       {\__nm_if_not_empty_cell:nnT \l__nm_final_i_int \l__nm_final_j_int
+                              {\bool_set_true:N \l__nm_stop_loop_bool}}
+               }
+           \int_zero_new:N  \l__nm_initial_i_int
+           \int_zero_new:N  \l__nm_initial_j_int
+           \int_set:Nn \l__nm_initial_i_int \l__nm_line_int
+           \int_set:Nn \l__nm_initial_j_int \l__nm_column_int
+           \bool_set_eq:NN \l__nm_stop_loop_bool \l__nm_impossible_instruction_bool
+           \bool_do_until:Nn \l__nm_stop_loop_bool
+              {\int_sub:Nn \l__nm_initial_i_int \l__nm_di_int
+               \int_sub:Nn \l__nm_initial_j_int \l__nm_dj_int
+               \bool_if:nTF
+                       {   \int_compare_p:nNn \l__nm_initial_i_int < 1
+                        || \int_compare_p:nNn \l__nm_initial_i_int > \g__nm_line_int
+                        || \int_compare_p:nNn \l__nm_initial_j_int < 1
+                        || \int_compare_p:nNn \l__nm_initial_j_int > \g__nm_nb_column_int}
+                       {\bool_set_true:N \l__nm_impossible_instruction_bool
+                        \bool_set_true:N \l__nm_stop_loop_bool}
+                       {\__nm_if_not_empty_cell:nnT \l__nm_initial_i_int \l__nm_initial_j_int
+                              {\bool_set_true:N \l__nm_stop_loop_bool}}
+               }
+          \bool_if:NTF \l__nm_impossible_instruction_bool
+            {\msg_error:nn {nicematrix} {Impossible~instruction}}
+            {\tl_set:Nx \l_tmpa_tl {\int_use:N \l__nm_initial_i_int-
+                                    \int_use:N \l__nm_initial_j_int-
+                                    \int_use:N \l__nm_final_i_int-
+                                    \int_use:N \l__nm_final_j_int}
+             \seq_if_in:NVF \l__nm_yet_drawn_seq \l_tmpa_tl
+              {\seq_put_left:NV \l__nm_yet_drawn_seq \l_tmpa_tl
+               \dim_zero_new:N \g__nm_x_initial_dim
+               \dim_zero_new:N \g__nm_y_initial_dim
+               \dim_zero_new:N \g__nm_x_final_dim
+               \dim_zero_new:N \g__nm_y_final_dim
+               \int_case:nn \l__nm_type_int
+                {0  \__nm_draw_ldots_line:
+                 1  \__nm_draw_cdots_line:
+                 2  \__nm_draw_vdots_line:
+                 3  \__nm_draw_ddots_line:
+                 4  \__nm_draw_iddots_line:}}}
+            \int_incr:N \l__nm_instruction_int
+         }
+}
+\cs_new_protected:Nn \__nm_retrieve_coords:nn
+     {\tikz[remember~picture]
+       \path let \p1 = (nm-\int_use:N \g__nm_env_int-
+                           \int_use:N \l__nm_initial_i_int-
+                           \int_use:N \l__nm_initial_j_int #1),
+                 \p2 = (nm-\int_use:N \g__nm_env_int-
+                           \int_use:N \l__nm_final_i_int-
+                           \int_use:N \l__nm_final_j_int #2)
+             in \pgfextra {\dim_gset:Nn \g__nm_x_initial_dim {\x1}
+                           \dim_gset:Nn \g__nm_y_initial_dim {\y1}
+                           \dim_gset:Nn \g__nm_x_final_dim {\x2}
+                           \dim_gset:Nn \g__nm_y_final_dim {\y2}} ; }
+\cs_new_protected:Nn \__nm_draw_ldots_line:
+      {\__nm_retrieve_coords:nn {.south~east} {.south~west}
+       \__nm_draw_tikz_line:}
+\cs_new_protected:Nn \__nm_draw_cdots_line:
+      {\__nm_retrieve_coords:nn {.mid~east} {.mid~west}
+       \__nm_draw_tikz_line:}
+\cs_new_protected:Nn \__nm_draw_vdots_line:
+      {\__nm_retrieve_coords:nn {.south} {.north}
+       \__nm_draw_tikz_line:}
+\cs_new_protected:Nn \__nm_draw_ddots_line:
+   {\__nm_retrieve_coords:nn {.south~east} {.north~west}
+    \bool_if:NT \l__nm_parallelize_diags_bool
+       {\int_incr:N \l__nm_ddots_int
+        \int_compare:nNnTF \l__nm_ddots_int = 1
+          {\dim_set:Nn \l__nm_delta_x_one_dim {\g__nm_x_final_dim - \g__nm_x_initial_dim }
+           \dim_set:Nn \l__nm_delta_y_one_dim {\g__nm_y_final_dim - \g__nm_y_initial_dim }}
+          {\dim_gset:Nn \g__nm_y_final_dim
+                  {\g__nm_y_initial_dim +
+                      (\g__nm_x_final_dim - \g__nm_x_initial_dim)
+                      * \dim_ratio:nn \l__nm_delta_y_one_dim \l__nm_delta_x_one_dim }}}
+    \__nm_draw_tikz_line:}
+\cs_new_protected:Nn \__nm_draw_iddots_line:
+   {\__nm_retrieve_coords:nn {.south~west} {.north~east}
+    \bool_if:NT \l__nm_parallelize_diags_bool
+       {\int_incr:N \l__nm_iddots_int
+        \int_compare:nNnTF \l__nm_iddots_int = 1
+          {\dim_set:Nn \l__nm_delta_x_two_dim {\g__nm_x_final_dim - \g__nm_x_initial_dim }
+           \dim_set:Nn \l__nm_delta_y_two_dim {\g__nm_y_final_dim - \g__nm_y_initial_dim }}
+          {\dim_gset:Nn \g__nm_y_final_dim
+                  {\g__nm_y_initial_dim +
+                      (\g__nm_x_final_dim - \g__nm_x_initial_dim)
+                      * \dim_ratio:nn \l__nm_delta_y_two_dim \l__nm_delta_x_two_dim }}}
+    \__nm_draw_tikz_line:}
+
+\cs_new_protected:Nn \__nm_draw_tikz_line:
+                     {\begin{tikzpicture}[overlay]
+                        \tikzmath{
+                           coordinate~\a , \b ;
+                           real~\l, \x, \d ;
+                           integer~\n ;
+                           \a = (\g__nm_x_initial_dim, \g__nm_y_initial_dim) ;
+                           \b = (\g__nm_x_final_dim,  \g__nm_y_final_dim) ;
+                           \l = veclen(\bx-\ax,\by-\ay) ;
+                           \n = (\l - 0.54em)/(0.45em) ;
+                           \x = (\l - \n*0.45em)/(2*\l) ;
+                           \d = 0.45em / \l ;
+                           if~\n>0
+                           then~{ for~\k in~{0,...,\n}
+                                  { {\node at ($(\a)!\x+\k*\d!(\b)$) {.} ; } ; } ;
+                            }  ;
+                           }
+                      \end{tikzpicture}}
+\cs_set_eq:NN \__nm_ldots \ldots
+\cs_set_eq:NN \__nm_cdots \cdots
+\cs_set_eq:NN \__nm_vdots \vdots
+\cs_set_eq:NN \__nm_ddots \ddots
+\cs_set_eq:NN \__nm_iddots \iddots
+\cs_new_protected:Nn \__nm_add_to_empty_cells:
+    {\seq_gput_right:Nx \g__nm_empty_cells_seq
+          {\int_use:N \g__nm_line_int-
+           \int_use:N \g__nm_column_int}}
+\NewDocumentCommand \__nm_Ldots {s}
+    {\IfBooleanF {#1} {\__nm_instruction_of_type:n 0}
+     \bool_if:NF \l__nm_nullify_dots_bool {\phantom \__nm_ldots}
+     \__nm_add_to_empty_cells:}
+\NewDocumentCommand \__nm_Cdots {s}
+    {\IfBooleanF {#1} {\__nm_instruction_of_type:n 1}
+     \bool_if:NF \l__nm_nullify_dots_bool {\phantom \__nm_cdots}
+     \__nm_add_to_empty_cells:}
+\NewDocumentCommand \__nm_Vdots {s}
+    {\IfBooleanF {#1} {\__nm_instruction_of_type:n 2}
+     \bool_if:NF \l__nm_nullify_dots_bool {\phantom \__nm_vdots}
+     \__nm_add_to_empty_cells:}
+\NewDocumentCommand \__nm_Ddots {s}
+    {\IfBooleanF {#1} {\__nm_instruction_of_type:n 3}
+     \bool_if:NF \l__nm_nullify_dots_bool {\phantom \__nm_ddots}
+     \__nm_add_to_empty_cells:}
+\NewDocumentCommand \__nm_Iddots {s}
+    {\IfBooleanF {#1} {\__nm_instruction_of_type:n 4}
+     \bool_if:NF \l__nm_nullify_dots_bool {\phantom \__nm_iddots}
+     \__nm_add_to_empty_cells:}
+\cs_new_protected:Nn \__nm_Hspace:
+  {\__nm_add_to_empty_cells:
+   \hspace}
+\cs_new_protected:Nn \__nm_NiceMatrixEndPoint:
+     {\kern 0.5pt}
+\ProcessKeysOptions {NiceMatrix}
+\msg_new:nnnn {nicematrix}
+              {Impossible~instruction}
+              {It's~not~possible~to~execute~the~instruction~
+               \int_case:nn \l__nm_type_int
+                 {0 {\token_to_str:N \Ldots}
+                  1 {\token_to_str:N \Cdots}
+                  2 {\token_to_str:N \Vdots}
+                  3 {\token_to_str:N \Ddots}}~in~the~line~\int_use:N\l__nm_line_int\
+               ~and~the~column~\int_use:N\l__nm_column_int\space of~the~matrix~
+               because~it's~impossible~to~find~one~of~its~extremities~
+               (both~extremities~must~be~non~empty~cells~of~the~matrix).~
+               If~you~go~on,~the~instruction~will~be~ignored.}
+              {You~can~specify~a~end~of~line~on~a~empty~cell~
+               with~\token_to_str:N \NiceMatrixEndPoint.}
+\msg_new:nnn {nicematrix}
+             {multicolumn~forbidden}
+             {The~command~\token_to_str:N \multicolumn\
+              is~forbidden~in~the~environment~\{NiceMatrix\}~
+              and~its~variants.~The~command~\token_to_str:N \hdotsfor\
+              of~amsmath~is~also~forbidden~since~it~uses~
+              \token_to_str:N \multicolumn.~You~can~go~on~but~your~line~will~
+              probably~be~wrong.}
+\endinput
+%%
+%% End of file `nicematrix.sty'.
diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check
index aa49e705774..568e3984743 100755
--- a/Master/tlpkg/bin/tlpkg-ctan-check
+++ b/Master/tlpkg/bin/tlpkg-ctan-check
@@ -450,7 +450,7 @@ my @TLP_working = qw(
     newcommand newenviron newfile newlfm newpx newsletr newspaper
     newtx newtxsf newtxtt newunicodechar newvbtm
     newverbs nextpage
-    nfssext-cfr nicefilelist niceframe niceframe-type1 nicetext
+    nfssext-cfr nicefilelist niceframe niceframe-type1 nicematrix nicetext
     nih nihbiosketch
     nimbus15 nkarta nlctdoc
     nmbib noconflict nodetree noindentafter noitcrul nolbreaks
diff --git a/Master/tlpkg/tlpsrc/collection-mathscience.tlpsrc b/Master/tlpkg/tlpsrc/collection-mathscience.tlpsrc
index 113c05ae53c..c185ef4cfb2 100644
--- a/Master/tlpkg/tlpsrc/collection-mathscience.tlpsrc
+++ b/Master/tlpkg/tlpsrc/collection-mathscience.tlpsrc
@@ -110,6 +110,7 @@ depend multiobjective
 depend mychemistry
 depend natded
 depend nath
+depend nicematrix
 depend nuc
 depend nucleardata
 depend objectz
diff --git a/Master/tlpkg/tlpsrc/nicematrix.tlpsrc b/Master/tlpkg/tlpsrc/nicematrix.tlpsrc
new file mode 100644
index 00000000000..e69de29bb2d
--- /dev/null
+++ b/Master/tlpkg/tlpsrc/nicematrix.tlpsrc