witharrows (6nov17)

git-svn-id: svn://tug.org/texlive/trunk@45707 c570f23f-e606-0410-a88d-b1316a301751

6 files changed, 2509 insertions, 1217 deletions

diff --git a/Master/texmf-dist/doc/latex/witharrows/README.md b/Master/texmf-dist/doc/latex/witharrows/README.md
index 10ca27cb4f7..7b5f7d31398 100644
--- a/Master/texmf-dist/doc/latex/witharrows/README.md
+++ b/Master/texmf-dist/doc/latex/witharrows/README.md
@@ -1,4 +1,4 @@
-The LaTeX extension witharrows is distributed under the LPPL 1.3 license.
+The LaTeX extension witharrows is distributed under the LPPL 1.3 license.
 
 This extension has been written by F. Pantigny (fpantigny at wanadoo point fr).
 
@@ -6,4 +6,4 @@ This extension is entirely contained in a single file : witharrows.sty
 
 The extension witharrows gives a LaTeX environment {WithArrows} which is similar
 to the environment {aligned} of amsmath but which gives the possibility to draw arrows 
-on the right side of the equations for explanations.
\ No newline at end of file
+on the right side of the equations for explanations.
diff --git a/Master/texmf-dist/doc/latex/witharrows/witharrows.pdf b/Master/texmf-dist/doc/latex/witharrows/witharrows.pdf
index fe3b4175df5..e0d50a7fc31 100644
--- a/Master/texmf-dist/doc/latex/witharrows/witharrows.pdf
+++ b/Master/texmf-dist/doc/latex/witharrows/witharrows.pdf
diff --git a/Master/texmf-dist/doc/latex/witharrows/witharrows.tex b/Master/texmf-dist/doc/latex/witharrows/witharrows.tex
deleted file mode 100644
index 675da4518ee..00000000000
--- a/Master/texmf-dist/doc/latex/witharrows/witharrows.tex
+++ /dev/null
@@ -1,785 +0,0 @@
-% This document is compatible with the following workflows :
-%    pdflatex,
-%    xelatex (with xdvipdfmx),
-%    latex --> dvips --> ps2pdf (or Adobe Distiller).
-\documentclass{article}
-
-\usepackage{ifxetex}
-
-\ifxetex
-  \usepackage{xltxtra}
-\else
-  \usepackage{expl3}
-  \usepackage{xparse}
-  \usepackage[T1]{fontenc}
-\fi
-
-\usepackage{xspace}
-
-
-\usepackage[dvipsnames]{xcolor}
-
-\usepackage{lmodern}
-
-\ifxetex
-   \usepackage[xetex]{geometry}
-\else
-   \usepackage{geometry}
-\fi
-
-\geometry{papersize={16.5cm,24cm},total={12.5cm,21cm},headheight=13.2pt,includeheadfoot,twoside,centering}
-
-
-\usepackage{tikz}
-\usetikzlibrary{calc}
-\usetikzlibrary{arrows.meta}
-\usetikzlibrary{bending}
-\usetikzlibrary{decorations.pathreplacing}
-
-
-\usepackage{footnote}
-
-\usepackage{witharrows}
-
-\usepackage{fancyvrb}
-\usepackage{mathtools}
-
-
-% this following lines only for this document
-
-\usepackage{amsfonts}
-
-\def\interitem{\vskip 7mm plus 2 mm minus 3mm}          
-\def\emphase#1{{\color{RoyalPurple}#1}}
-\fvset{commandchars=\~\#\@,formatcom={\color{gray}}}
-\DeclareMathOperator{\re}{Re}
-\let\group\begingroup
-
-
-\begin{document}
-
-
-\parindent0pt
-
-\title{Extension witharrows, v. 1.0}
-
-\author{Fran\c cois Pantigny}
-
-\date{2017/08/17}
-
-\maketitle
-
-
-
-\begin{abstract}
-The LaTeX package \verb|witharrows| gives an environment \verb|{WithArrows}| which is similar to environment
-\verb|{aligned}| of \verb|amsmath| (and \verb|mathtools|) but gives the possibility to draw arrows on the right
-side of the alignment. These arrows are usually used to give explanations concerning the mathematical calculus presented.
-\end{abstract}
-
-
-\vskip1cm
-
-This package uses Tikz to draw the arrows. It can be used with \verb|xelatex|, \verb|pdflatex| but also by the
-classical workflow \verb|latex|-\verb|dvips|-\verb|ps2pdf| (or Distiller). Two compilations may be necessary.
-
-\medskip
-This package gives an environment \verb|{WithArrows}| to construct alignments of equations with
-arrows for the explanations on the right side :
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 ~emphase#\Arrow{we expand}@ \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{we expand} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-
-
-\medskip
-The arrow has been drawn with the command \verb|\Arrow| on the ligne from which it starts. The command \verb|\Arrow|
-can be used anywhere on the line but the best way is to put it at the end.
-
-
-\medskip
-The ends of the lines of the tabular can be coded by \verb|\\| but also by \verb|\cr| (like in the command
-\verb|\halign| of TeX). In fact, in an environment \verb|{WithArrows}|, the command \verb|\\| has no option for the
-spacing between rows like in many environments of LaTeX.
-
-
-
-
-\section{Options for the shape of the arrows}
-
-The commande \verb|\Arrow| has several options. These options can be put between square brackets, before, or after
-the mandatory argument.
-
-The option \verb|jump| gives the number of lines the arrow must jump (the default value is, of course,~$1$)
-\footnote{It's not possible to give a non-positive value to \texttt{jump}. See below the way to draw an arrow which
-goes backwards.}
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 \Arrow~emphase#[jump=2]@{we expand} \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 \\
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 \Arrow[jump=2]{we expand} \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 \\
-\end{WithArrows}$
-
-
-
-
-\interitem
-It's possible to put several arrows which start from the same line.
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 ~emphase#\Arrow{}\Arrow{}[jump=2]@ \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 \Arrow{}\Arrow{}[jump=2] \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-
-
-\interitem
-The option \verb|xoffset| shift the arrows to the right (we usually don't want the arrows to be stucked
-on the text). The default value of \verb|xoffset| is $3$~mm.
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 
-\Arrow[~emphase#xoffset=1cm@]{with \texttt{xoffset=1cm}} \\
-  & = (a+b)^2 + 2(a+b) +1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 
-\Arrow[xoffset=1cm]{with \texttt{xoffset=1cm}} \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-\end{WithArrows}$
-
-
-
-
-\interitem 
-The arrows are drawn with Tikz. That's why the command \verb|\Arrow| has an option
-\verb|tikz| which can be used to give to the arrow (in fact, the command \verb|\path| of Tikz) the options
-proposed by Tikz for such an arrow. The following example gives an blue thick arrow.
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[~emphase#tikz={blue,thick}@]{we expand} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[tikz={blue,thick}]{we expand} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-
-
-\interitem
-It's also possible to change the arrowheadss. For example, we can draw an arrow which goes backwards 
-with the Tikz option~\verb|<-|.
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow~emphase#[tikz=<-]@{we factorize} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[tikz=<-]{we factorize} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-
-
-\interitem
-It's also possible to suppress both tips of the arrow with the Tikz option \verb|-|.
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[~emphase#tikz=-@]{very classical} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[tikz=-]{very classical} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-
-
-\interitem
-In order to have straight arrows instead of curved ones, we must use the Tikz option ``\verb|bend left = 0|''.
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow~emphase#[tikz={bend left=0}]@{we expand} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[tikz={bend left=0}]{we expand} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-
-
-\interitem
-One of the most useful options is ``\verb|text width|'' to control the with of the text associated to the arrow. 
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 
-\Arrow[jump=2,~emphase#tikz={text width=5.3cm}@]{We have done...} \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = \bigl((a+b)+1\bigr)^2 
-\Arrow[jump=2,tikz={text width=5.3cm}]{We have done a two-stages expansion but it would have been clever
-to expand with the multinomial theorem.} \\
-  & = (a+b)^2 + 2(a+b) +1 \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-
-
-\interitem
-If we want to change the font of the text associated to the arrow, we can, of course, put a command like
-\verb|\bfseries|, \verb|\large| or \verb|\sffamily| at the beginning of the text. But, by default, the texts
-are composed with a combination of \verb|\small| and \verb|\itshape|. When adding \verb|\bfseries| at the beginning
-of the text, we won't suppress the \verb|\small| and the \verb|\itshape| and we will consequently have a text in a
-bold, italic and small font.
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{~emphase#\bfseries@ we expand} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{\bfseries we expand} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-
-\interitem 
-If we put commands \verb|\\| in the text to force newlines, a command of font placed in the beginning of the
-text will have effect only until the first command \verb|\\| (like in a environment \verb|{tabular}|). That's why
-Tikz gives a option \verb|font| to modify the font of the whole text. Nevertheless, if we use the option
-\verb|tikz={font={\bfseries}}|, the default specification of \verb|\small| and \verb|\itshape| will be overwritten.
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[~emphase#tikz={font={\bfseries}}@]{we expand} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow[tikz={font={\bfseries}}]{we expand} \\
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-\medskip
-If we want exactly the same result as previously, we have to give to the option \verb|font| the value 
-\verb|{\itshape\small\bfseries}|.
-
-
-
-
-\interitem 
-Almost all the options can be given directly to the environment \verb|WithArrows| (between square brackets).
-In this case, they apply to all the arrows of the environment.
-%
-\begin{Verbatim}
-$\begin{WithArrows}~emphase#[tikz=blue]@
-A & = \bigl((a+b)+1\bigr)^2 \Arrow{First expansion.} \\
-  & = (a+b)^2 + 2(a+b) +1 \Arrow{Second expansion.} \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}[tikz=blue]
-A & = \bigl((a+b)+1\bigr)^2 \Arrow{First expansion.} \\
-  & = (a+b)^2 + 2(a+b) +1 \Arrow{Second expansion.} \\
-  & = a^2 + 2ab + b^2 + 2a + 2b +1 
-\end{WithArrows}$
-
-
-\interitem
-The environment \verb|{WithArrows}| has an option \verb|displaystyle|. With this option, all the elements are
-composed in \verb|\displaystyle| (like in an environment \verb|{aligned}| of \verb|amsmath|). 
-
-\medskip
-Without the option \verb|displaystyle| :
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-\int_0^1 (x+1)^2 dx 
-& = \int_0^1 (x^2+2x+1) dx
-\Arrow{linearity of integration}     \\
-& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
-& = \frac13 + 2\frac12 + 1 \\
-& = \frac73
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-\int_0^1 (x+1)^2 dx 
-& = \int_0^1 (x^2+2x+1) dx
-\Arrow{linearity of integration}     \\
-& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
-& = \frac13 + 2\frac12 + 1 \\
-& = \frac73
-\end{WithArrows}$
-
-
-\medskip
-The same example with the option \verb|displaystyle| :\par\nobreak
-
-$\begin{WithArrows}[displaystyle]
-\int_0^1 (x+1)^2 dx 
-& = \int_0^1 (x^2+2x+1) dx
-\Arrow{linearity of integration}     \\
-& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
-& = \frac13 + 2\frac12 + 1 \\
-& = \frac73
-\end{WithArrows}$
-
-
-\interitem 
-Almost all the options can also be set at the document level with the command \verb|\WithArrowsOptions|. 
-In this case, the scope of the declarations is the current TeX group (these declarations are ``semi-global'').
-For example, if we want all the environments \verb|{WithArrows}| composed in \verb|\displaystyle| with blue
-arrows, we can write \verb|\WithArrowsOptions{displaystyle,tikz=blue}|.\footnote{It's also possible to give the
-  options directly when loading the package, \emph{i.e.} with the command \texttt{\string\usepackage} in the preamble.}
-%
-\begin{Verbatim}
-~emphase#\WithArrowsOptions{displaystyle,tikz=blue}@
-$\begin{WithArrows}
-\sum_{i=1}^n (x_i+1)^2 
-& = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{by linearity}\\
-& = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n
-\end{WithArrows}$
-\end{Verbatim}
-
-\begin{group}
-\WithArrowsOptions{displaystyle,tikz=blue}
-$\begin{WithArrows}
-\sum_{i=1}^n (x_i+1)^2 
-& = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{by linearity}\\
-& = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n
-\end{WithArrows}$
-\end{group}
-
-
-\interitem
-The command \verb|\Arrow| is recognized only in the environments \verb|{WithArrows}|. If we have a command 
-\verb|\Arrow| previously defined, it's possible to go on using it outside the environments \verb|{WithArrows}|.
-
-However, a previouly defined command \verb|\Arrow| may still be useful in a environment \verb|{WithArrows}|. If we
-want to use it in such an environment, it's possible to change the name of the command \verb|\Arrow| of the package
-\verb|witharrows| : there is an option \verb|CommandName| for this purpose. The new name of the command must be
-given to the option \emph{without} the leading backslash.
-%
-\begin{Verbatim}
-\def\Arrow{\longmapsto}
-$\begin{WithArrows}~emphase#[CommandName=Explanation]@
-f & = \bigl(x \Arrow (x+1)^2\bigr)
-~emphase#\Explanation{we work directly on fonctions}@\\
-& = \bigl(x \Arrow x^2+2x+1\bigr)
-\end{WithArrows}$
-\end{Verbatim}
-%
-\begin{group}
-\def\Arrow{\longmapsto}
-$\begin{WithArrows}[CommandName=Explanation]
-f & = \bigl(x \Arrow (x+1)^2\bigr)
-\Explanation{we work directly on fonctions}\\
-& = \bigl(x \Arrow x^2+2x+1\bigr)
-\end{WithArrows}$
-\end{group}
-
-
-\interitem 
-It's possible to use directly the nodes created by \verb|{WithArrows}| (see below) with explicit Tikz instructions
-(in order, for example, to draw something that can't be drawn with the command \verb|\Arrow|). That's why a style
-for the tips of the arrows has be created : \verb|TipsOfWithArrows|. By using this style, we will have homogeneous
-tips for the arrows of the document.
-
-Therefore, if we want to  modify the tips of the arrows of \verb|{WithArrows}|, we have to modify the style
-\verb|TipsOfWithArrows|. 
-%
-\begin{Verbatim}
-\tikzset{TipsOfWithArrows/.style= { > = {Latex[scale=1.2,bend]}} }
-\end{Verbatim}
-
-
-
-
-\section{Precise positioning of the arrows}
-
-
-The environment \verb|{WithArrows}| defines, during the composition of the array, two series of nodes materialized in
-red in the following example.\footnote{The option \texttt{shownodes} can be used to materialize the nodes.}
-
-\smallskip
-$\begin{WithArrows}[displaystyle,shownodes]
-I
-& = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) \\
-& = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\
-& = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\
-& =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u \\
-& =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\
-& =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\
-& =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u  \\
-& =\frac{\pi}4\ln2-I 
-\end{WithArrows}$
-
-\bigskip
-The nodes of the left are at the end of each line of text. These nodes will be called \emph{left nodes}.
-The nodes of the right side are aligned vertically on the right side of the array. These nodes will be called
-\emph{right nodes}.\footnote{The names of the Tikz nodes created by \texttt{\{WithArrows\}} are \texttt{wa-}$n$\texttt{-l} and
-  \texttt{wa-}$n$\texttt{-r} where $n$~is the number of the line. It's possible to refer to these Tikz nodes after the
-  environment (one should use the options \texttt{remember picture} and \texttt{overlay} and also
-  \texttt{TipsOfWithArrows} and \texttt{->} in order to have the same arrowheads).}
-
-By default, the arrows use the right nodes. We will say that they are in \verb|rr| mode ($r$ for \emph{right}).
-These arrows are \verb|vertical| (we will say that an arrow is \emph{vertical} when its two ends have the
-same abscissa).
-
-
-\smallskip
-However, it's possible to use the left nodes, or a combination of left and right nodes, with one of the options
-\verb|lr|, \verb|rl| and \verb|ll| ($l$ for \emph{left}). Those arrows are, usually, not vertical.
-
-
-Therefore
-$\begin{WithArrows}[displaystyle]
-I
-& = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) 
-\Arrow[lr]{This arrow uses the \texttt{lr} option.}\\
-& = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\
-& = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\
-& =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u 
-\Arrow[ll,jump=2,tikz={text width = 5cm}]{This arrow uses a \texttt{ll} option and a \texttt{jump} equal to $2$}\\
-& =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\
-& =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\
-& =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u  \\
-& =\frac{\pi}4\ln2-I 
-\end{WithArrows}$
-
-
-
-\interitem
-There is also an option called \texttt{i} ($i$ for \emph{intermediate}). With this option, the arrow is vertical
-and at the leftmost position.
-
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-(a+b)(a+ib)(a-b)(a-ib) 
-& = (a+b)(a-b)\cdot(a+ib)(a-ib) \\
-& = (a^2-b^2)(a^2+b^2) \Arrow~emphase#[i]@{because $(x-y)(x+y)=x^2-y^2$}\\
-& = a^4-b^4 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-(a+b)(a+ib)(a-b)(a-ib) 
-& = (a+b)(a-b)\cdot(a+ib)(a-ib) \\
-& = (a^2-b^2)(a^2+b^2) \Arrow[i]{because $(x-y)(x+y)=x^2-y^2$}\\
-& = a^4-b^4 
-\end{WithArrows}$
-
-
-\interitem 
-The environment \verb|{WithArrows}| gives also a \verb|group| option. With this option, \emph{all} the
-arrows of the environment are grouped on a same vertical line and at a leftmost position.
-%
-\begin{Verbatim}[formatcom=\small\color{gray}]
-$\begin{WithArrows}~emphase#[displaystyle,group]@
-2xy'-3y=\sqrt x
-& \Longleftrightarrow 2x(K'y_0+Ky_0')-3Ky_0 = \sqrt x \\
-& \Longleftrightarrow 2xK'y_0 + K(2xy_0'-3y_0) = \sqrt x \\
-& \Longleftrightarrow 2x K'y_0 = \sqrt x \Arrow{...}\\
-...
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}[displaystyle,group]
-2xy'-3y=\sqrt x
-& \Longleftrightarrow 2x(K'y_0+Ky_0')-3Ky_0 = \sqrt x \\
-& \Longleftrightarrow 2xK'y_0 + K(2xy_0'-3y_0) = \sqrt x \\
-& \Longleftrightarrow 2x K'y_0 = \sqrt x \Arrow{We remplace $y_0$ by its value.}\\
-& \Longleftrightarrow 2xK'x^{\frac32} = x^{\frac12} \Arrow{simplification of the $x$}\\
-& \Longleftrightarrow K' = \tfrac1{2x²} \Arrow{antiderivation}\\
-& \Longleftrightarrow K = -\tfrac1{2x} 
-\end{WithArrows}$
-
-
-\bigskip
-If desired, the option \verb|group| can be given to the command \verb|WithArrowsOptions| so that it will become the
-default value.
-
-
-\section{Comparison with the environment \{aligned\}}
-
-
-
-\verb|{WithArrows}| bears similarities with the environment \verb|{aligned}| of the extension
-\verb|amsmath|. These are only similarities because \verb|{WithArrows}| has not been written upon the environment
-\verb|{aligned}|. 
-
-In paticular, the command \verb|\\| of the end of line has no option to change the row spacings. In fact, this
-command \verb|\\| can be replaced, in a environment \verb|{WithArrows}| by a \verb|\cr| of TeX. That's what we will 
-do in the balance of this document.
-
-
-
-
-\interitem
-If desired, it's possible to change the spacing between two given lines by putting a command
-\verb|\vspace| in a \verb|\noalign| (which is a low level command of TeX to insert extraordinary elements between
-the lines of an array).
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{we expand} \cr
-~emphase#\noalign{\vspace{3mm}}@
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{we expand} \cr
-\noalign{\vspace{3mm}}
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-
-\interitem 
-In the  environments of \verb|amsmath|, the spacing between lines is fixed by a parameter called
-\verb|\jot| and that's also the case for the environment \verb|{WithArrows}|. An option \verb|jot| has been given
-to the environment \verb|{WithArrows}| in order to change the value of this parameter \verb|\jot| for an given environment.
-%
-\begin{Verbatim}
-$\begin{WithArrows}[displaystyle,~emphase#jot=2mm@]
-F & = \frac12G     \Arrow{we expand}\cr
-  & = H + \frac12K \Arrow{we go on}\cr
-  & = K 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}[displaystyle,jot=2mm]
-F & = \frac12G     \Arrow{we expand}\cr
-  & = H + \frac12K \Arrow{we go on}\cr
-  & = K 
-\end{WithArrows}$
-
-
-\interitem
-Like the environment \verb|{aligned}|, \verb|{WithArrows}| has an option of placement which can assume the values
-\verb|t|, \verb|c| or \verb|b|. However, the default value is not \verb|c| but \verb|t|. If desired, it's possible
-to have the \verb|c| value as the default with the command \verb|WithArrowsOptions{c}| at the beginning of the document.
-%
-\begin{Verbatim}
-~emphase#Et donc\enskip@
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{we expand} \cr
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-\end{Verbatim}
-
-Et donc\enskip 
-$\begin{WithArrows}
-A & = (a+1)^2 \Arrow{we expand} \cr
-  & = a^2 + 2a + 1 
-\end{WithArrows}$
-
-\bigskip
-The value \verb|c| may be useful, for example, if we want to add curly braces :
-
-\smallskip
-\begin{Verbatim}
-On pose\enskip $~emphase#\left\{@
-\begin{WithArrows}~emphase#[c]@
-f(x) & = 3x^3+2x^2-x+4 
-\Arrow[tikz=-]{both are polynoms}\cr
-g(x) & = 5x^2-5x+6
-\end{WithArrows}
-~emphase#\right.@$
-\end{Verbatim}
-
-
-
-
-On pose\enskip $\left\{
-\begin{WithArrows}[c]
-f(x) & = 3x^3+2x^2-x+4 
-\Arrow[tikz=-]{both are polynoms}\cr
-g(x) & = 5x^2-5x+6
-\end{WithArrows}
-\right.$
-
-
-\interitem
-Unlike \verb|{aligned}|, the environment \verb|{WithArrows}| uses \verb|\textstyle| by default.
-
-Once again, it's possible to change this behaviour with \verb|WithArrowsOptions| :
-
-\quad \verb|WithArrowsOptions{displaystyle}|.
-
-
-\smallskip
-The following example is composed with \verb|{aligned}| :\par\nobreak
-
-\smallskip
-$\left\{
-\begin{aligned}
-\sum_{i=1}^n (x_i+1)^2  
-& = \sum_{i=1}^n (x_i^2 + 2x_i+1) \\
-& = \sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^nx_i + n 
-\end{aligned}
-\right.$%
-
-
-\medskip
-The following is composed with \verb|{WithArrows}[c,displaystyle]|. The results are stricly identical.\par\nobreak
-
-\smallskip
-$\left\{
-\begin{WithArrows}[c,displaystyle]
-\sum_{i=1}^n (x_i+1)^2 
-& = \sum_{i=1}^n (x_i^2 + 2x_i+1) \\
-& = \sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^nx_i + n 
-\end{WithArrows}
-\right.$%
-
-
-
-
-\section{Examples}
-
-It's possible to use the environment \verb|{WithArrows}| with making use of the left column only, or the right
-column only. 
-%
-\begin{Verbatim}
-$\begin{WithArrows}
-&f(x) \ge g(x) \Arrow{by squaring both sides} \cr
-& f(x)^2 \ge g(x)^2 \Arrow{by moving to left side} \cr
-& f(x)^2 - g(x)^2 \ge 0 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}
-&f(x) \ge g(x) \Arrow{by squaring both sides} \cr
-& f(x)^2 \ge g(x)^2 \Arrow{by moving to left side} \cr
-& f(x)^2 - g(x)^2 \ge 0 
-\end{WithArrows}$
-
-
-\interitem
-Here is an example with a loop flow.
-%
-\begin{Verbatim}[formatcom=\small\color{gray}]
-$\begin{WithArrows}[tikz={font={\tiny}}]
-a.\;& f \text{ est continuous on } E 
-\Arrow{(1)}\Arrow[tikz=<-,jump=4,xoffset=1cm]{(5)}\cr
-b.\;& f \text{ est continuous in } 0 
-\Arrow{(2)}\cr
-c.\;& f \text{ is bounded on the unit sphere} 
-\Arrow{(3)}\cr
-d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| 
-\Arrow{(4)}\cr
-e.\;& f \text{ is lipschitzian} 
-\end{WithArrows}$
-\end{Verbatim}
-
-$\begin{WithArrows}[tikz={font={\tiny}}]
-a.\;& f \text{ est continuous on } E 
-\Arrow{(1)}\Arrow[tikz=<-,jump=4,xoffset=1cm]{(5)}\cr
-b.\;& f \text{ est continuous in } 0 
-\Arrow{(2)}\cr
-c.\;& f \text{ is bounded on the unit sphere} 
-\Arrow{(3)}\cr
-d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| 
-\Arrow{(4)}\cr
-e.\;& f \text{ is lipschitzian} 
-\end{WithArrows}$
-
-\interitem
-The option \verb|font| of Tikz contains in fact a list of tokens which will be placed at the beginning of the text.
-
-These tokens can be true commands for a changement of font (like \verb|\bfseries| or \verb|\sffamily|) but can also
-be, in fact, any TeX command.
-
-In the following example, the argument of \verb|font| is the token list \verb|\tiny\counter| where
-\verb|\counter| is a command which increment a counter previously defined and display its new value. Thus, the
-arrows are automatically numbered.
-%
-\begin{Verbatim}[formatcom=\small\color{gray}]
-\newcounter{MyCounter}
-\newcommand{\counter}{\stepcounter{MyCounter}\theMyCounter.}
-$\begin{WithArrows}[tikz={~emphase#font={\tiny\counter}@}]
-A(x) 
-& = B(x) \Arrow{} \cr
-& = C(x) \Arrow{} \cr
-& = C(x) \Arrow{} \cr
-& = E(x) \Arrow{} \cr
-& = F(x) \Arrow{} \cr
-& = G(x)   
-\end{WithArrows}$
-\end{Verbatim}
-
-\begin{group}
-\newcounter{MyCounter}
-\newcommand{\counter}{\stepcounter{MyCounter}\theMyCounter.}
-$\begin{WithArrows}[tikz={font={\tiny\counter}}]
-A(x) 
-& = B(x) \Arrow{} \cr
-& = C(x) \Arrow{} \cr
-& = C(x) \Arrow{} \cr
-& = E(x) \Arrow{} \cr
-& = F(x) \Arrow{} \cr
-& = G(x)   
-\end{WithArrows}$
-\end{group}
-
-
-
-\end{document}
-
-
-
-
-
diff --git a/Master/texmf-dist/source/latex/witharrows/witharrows.dtx b/Master/texmf-dist/source/latex/witharrows/witharrows.dtx
new file mode 100644
index 00000000000..d1806821106
--- /dev/null
+++ b/Master/texmf-dist/source/latex/witharrows/witharrows.dtx
@@ -0,0 +1,2098 @@
+% \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{1.1}
+\def\myfiledate{2017/11/06}
+%<package>\RequirePackage{l3keys2e}
+%<package>\ProvidesExplPackage
+%<package>  {witharrows}
+%<package>  {\myfiledate}
+%<package>  {\myfileversion}
+%<package>  {Draws arrows for explanations on the right}
+%
+%
+%<*batchfile>
+\begingroup
+\input l3docstrip.tex
+\keepsilent
+\usedir{tex/latex/witharrows}
+\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>
+%
+%<@@=wa>
+%<*driver>
+\documentclass{l3doc} % load fancyvrb, amsmath, array, color, etc.
+\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{tikz}
+\usetikzlibrary{calc,arrows.meta,bending}
+\usepackage{footnote}
+\usepackage{witharrows}
+\usepackage{mathtools}
+\usepackage{amsfonts}
+\NewDocumentEnvironment {scope} {} {} {}
+\def\interitem{\vskip 7mm plus 2 mm minus 3mm}          
+\def\emphase#1{{\color{RoyalPurple}#1}}
+\fvset{commandchars=\~\#\@,formatcom={\color{gray}}}
+\DeclareMathOperator{\re}{Re}
+\parindent 0pt
+\DisableCrossrefs
+\begin{document}
+\DocInput{witharrows.dtx}
+\end{document}
+%</driver>
+% \fi 
+% \title{The package \pkg{witharrows}\thanks{This document corresponds to the version~\myfileversion\space of \pkg{witharrows},
+% at the date of~\myfiledate.}} \author{F. Pantigny \\ \texttt{fpantigny@wanadoo.fr}}
+%
+% \maketitle
+%
+% \begin{abstract}
+% The LaTeX package \pkg{witharrows} gives an environment |{WithArrows}| which is similar to environment
+% |{aligned}| of \pkg{amsmath} (and \pkg{mathtools}) but gives the possibility to draw arrows on the right side of
+% the alignment. These arrows are usually used to give explanations concerning the mathematical calculus presented.
+% \end{abstract}
+%
+%
+% \vskip1cm
+% 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{xparse}, \pkg{footnote}\footnote{The package footnote is used to extract the notes
+% from the environments \texttt{\{WithArrows\}}.} and \pkg{tikz}. The following Tikz libraries are also required :
+% \pkg{calc}, \pkg{arrows.meta} and \pkg{bending}.
+%
+% \bigskip
+% This package gives an environment |{WithArrows}| to construct alignments of equations with arrows for the
+% explanations on the right side :
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = (a+1)^2 ~emphase#\Arrow{we expand}@ \\
+%   & = a^2 + 2a + 1  
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow{we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+%
+%
+% \medskip
+% The arrow has been drawn with the command |\Arrow| on the ligne from which it starts. The command |\Arrow| can be
+% used anywhere on the line but the best way is to put it at the end.
+%
+%
+% \section{Options for the shape of the arrows}
+%
+% The commande |\Arrow| has several options. These options can be put between square brackets, before, or after the
+% mandatory argument.
+%
+% The option |jump| gives the number of lines the arrow must jump (the default value is, of course,~$1$)
+% \footnote{It's not possible to give a non-positive value to \texttt{jump}. See below the way to draw an arrow
+% which goes backwards.}
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = \bigl((a+b)+1\bigr)^2 \Arrow[~emphase#jump=2@]{we expand} \\
+%   & = (a+b)^2 + 2(a+b) +1 \\
+%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% 
+%
+% $\begin{WithArrows}
+% A & = \bigl((a+b)+1\bigr)^2 \Arrow[jump=2]{we expand} \\
+%   & = (a+b)^2 + 2(a+b) +1 \\
+%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
+% \end{WithArrows}$
+%
+%
+% \interitem
+% It's possible to put several arrows which start from the same line.
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = \bigl((a+b)+1\bigr)^2 ~emphase#\Arrow{}\Arrow{}[jump=2]@ \\
+%   & = (a+b)^2 + 2(a+b) +1 \\
+%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = \bigl((a+b)+1\bigr)^2 \Arrow{}\Arrow{}[jump=2] \\
+%   & = (a+b)^2 + 2(a+b) +1 \\
+%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
+% \end{WithArrows}$
+%
+% \interitem
+% The option |xoffset| shift the arrows to the right (we usually don't want the arrows to be stucked on the text).
+% The default value of |xoffset| is $3$~mm.
+% 
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = \bigl((a+b)+1\bigr)^2 
+% \Arrow[~emphase#xoffset=1cm@]{with \texttt{xoffset=1cm}} \\
+%   & = (a+b)^2 + 2(a+b) +1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = \bigl((a+b)+1\bigr)^2 
+% \Arrow[xoffset=1cm]{with \texttt{xoffset=1cm}} \\
+%   & = (a+b)^2 + 2(a+b) +1 
+% \end{WithArrows}$
+%
+%
+% \interitem 
+% The arrows are drawn with Tikz. That's why the command |\Arrow| has an option |tikz| which can be used to give to
+% the arrow (in fact, the command |\path| of Tikz) the options proposed by Tikz for such an arrow. The following
+% example gives an blue thick arrow.
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow[~emphase#tikz={blue,thick}@]{we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow[tikz={blue,thick}]{we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+%
+% \interitem
+% It's also possible to change the arrowheads. For example, we can draw an arrow which goes backwards with the Tikz
+% option~|<-|.
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow~emphase#[tikz=<-]@{we factorize} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow[tikz=<-]{we factorize} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+%
+% \interitem
+% It's also possible to suppress both tips of the arrow with the Tikz option |-|.
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow[~emphase#tikz=-@]{very classical} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow[tikz=-]{very classical} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+%
+% \interitem
+% In order to have straight arrows instead of curved ones, we must use the Tikz option ``|bend left = 0|''.
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow~emphase#[tikz={bend left=0}]@{we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow[tikz={bend left=0}]{we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+%
+% \interitem
+% One of the most useful options is ``|text width|'' to control the with of the text associated to the arrow. 
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = \bigl((a+b)+1\bigr)^2 
+% \Arrow[jump=2,~emphase#tikz={text width=5.3cm}@]{We have done...} \\
+%   & = (a+b)^2 + 2(a+b) +1 \\
+%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = \bigl((a+b)+1\bigr)^2 
+% \Arrow[jump=2,tikz={text width=5.3cm}]{We have done a two-stages expansion but it would have been clever
+% to expand with the multinomial theorem.} \\
+%   & = (a+b)^2 + 2(a+b) +1 \\
+%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
+% \end{WithArrows}$
+%
+% \interitem
+% If we want to change the font of the text associated to the arrow, we can, of course, put a command like
+% |\bfseries|, |\large| or |\sffamily| at the beginning of the text. But, by default, the texts are composed with a
+% combination of |\small| and |\itshape|. When adding |\bfseries| at the beginning of the text, we won't suppress
+% the |\small| and the |\itshape| and we will consequently have a text in a bold, italic and small font.
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow{~emphase#\bfseries@ we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow{\bfseries we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+%
+% \interitem 
+% If we put commands |\\| in the text to force newlines, a command of font placed in the beginning of the text will
+% have effect only until the first command |\\| (like in a environment |{tabular}|). That's why Tikz gives a option
+% |font| to modify the font of the whole text. Nevertheless, if we use the option |tikz={font={\bfseries}}|, the
+% default specification of |\small| and |\itshape| will be overwritten.
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow[~emphase#tikz={font={\bfseries}}@]{we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow[tikz={font={\bfseries}}]{we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+%
+% \medskip
+% If we want exactly the same result as previously, we have to give to the option |font| the value
+% |{\itshape\small\bfseries}|.
+%
+%
+% \interitem 
+% Almost all the options can be given directly to the environment |{WithArrows}| (between square brackets). In this
+% case, they apply to all the arrows of the environment.\footnote{They applies also to the nested environments
+% \texttt{\{WithArrows\}} with the notable exception of \texttt{interline}.}
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}[~emphase#tikz=blue@]
+% A & = \bigl((a+b)+1\bigr)^2 \Arrow{First expansion.} \\
+%   & = (a+b)^2 + 2(a+b) +1 \Arrow{Second expansion.} \\
+%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}[tikz=blue]
+% A & = \bigl((a+b)+1\bigr)^2 \Arrow{First expansion.} \\
+%   & = (a+b)^2 + 2(a+b) +1 \Arrow{Second expansion.} \\
+%   & = a^2 + 2ab + b^2 + 2a + 2b +1 
+% \end{WithArrows}$
+%
+%
+% \interitem
+% The environment |{WithArrows}| has an option |displaystyle|. With this option, all the elements are composed in
+% |\displaystyle| (like in an environment |{aligned}| of \pkg{amsmath}).
+%
+% \medskip
+% Without the option |displaystyle| :
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% \int_0^1 (x+1)^2 dx 
+% & = \int_0^1 (x^2+2x+1) dx
+% \Arrow{linearity of integration}     \\
+% & = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
+% & = \frac13 + 2\frac12 + 1 \\
+% & = \frac73
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% \int_0^1 (x+1)^2 dx 
+% & = \int_0^1 (x^2+2x+1) dx
+% \Arrow{linearity of integration}     \\
+% & = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
+% & = \frac13 + 2\frac12 + 1 \\
+% & = \frac73
+% \end{WithArrows}$
+%
+%
+% \medskip
+% The same example with the option |displaystyle| :\par\nobreak
+%
+% $\begin{WithArrows}[displaystyle]
+% \int_0^1 (x+1)^2 dx 
+% & = \int_0^1 (x^2+2x+1) dx
+% \Arrow{linearity of integration}     \\
+% & = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\
+% & = \frac13 + 2\frac12 + 1 \\
+% & = \frac73
+% \end{WithArrows}$
+%
+%
+% \interitem 
+% Almost all the options can also be set at the document level with the command |\WithArrowsOptions|. In this case,
+% the scope of the declarations is the current TeX group (these declarations are ``semi-global''). For example, if
+% we want all the environments |{WithArrows}| composed in |\displaystyle| with blue arrows, we can write
+% |\WithArrowsOptions{displaystyle,tikz=blue}|.\footnote{It's also possible to give the options directly when
+% loading the package, \emph{i.e.} with the command \texttt{\string\usepackage} in the preamble.}
+% %
+% \begin{Verbatim}
+% ~emphase#\WithArrowsOptions{displaystyle,tikz=blue}@
+% $\begin{WithArrows}
+% \sum_{i=1}^n (x_i+1)^2 
+% & = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{by linearity}\\
+% & = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% \begin{scope}
+% \WithArrowsOptions{displaystyle,tikz=blue}
+% $\begin{WithArrows}
+% \sum_{i=1}^n (x_i+1)^2 
+% & = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{by linearity}\\
+% & = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n
+% \end{WithArrows}$
+% \end{scope}
+%
+%
+% \interitem
+% The command |\Arrow| is recognized only in the environments |{WithArrows}|. If we have a command |\Arrow|
+% previously defined, it's possible to go on using it outside the environments |{WithArrows}|.
+%
+% However, a previouly defined command |\Arrow| may still be useful in an environment |{WithArrows}|. If we want to
+% use it in such an environment, it's possible to change the name of the command |\Arrow| of the package
+% \pkg{witharrows} : there is an option |CommandName| for this purpose. The new name of the command must be given to
+% the option \emph{without} the leading backslash.
+% %
+% \begin{Verbatim}
+% \def\Arrow{\longmapsto}
+% $\begin{WithArrows}[~emphase#CommandName=Explanation@]
+% f & = \bigl(x \Arrow (x+1)^2\bigr)
+% ~emphase#\Explanation{we work directly on fonctions}@\\
+% & = \bigl(x \Arrow x^2+2x+1\bigr)
+% \end{WithArrows}$
+% \end{Verbatim}
+% %
+% \begin{scope}
+% \def\Arrow{\longmapsto}
+% $\begin{WithArrows}[CommandName=Explanation]
+% f & = \bigl(x \Arrow (x+1)^2\bigr)
+% \Explanation{we work directly on fonctions}\\
+% & = \bigl(x \Arrow x^2+2x+1\bigr)
+% \end{WithArrows}$
+% \end{scope}
+%
+%
+% \interitem 
+% It's possible to use directly the nodes created by |{WithArrows}| with explicit Tikz instructions (in order, for
+% example, to draw something that can't be drawn with the command |\Arrow|). That's why a style for the tips of the
+% arrows has be created : |TipsOfWithArrows|. By using this style, we will have homogeneous tips for the arrows of
+% the document.
+%
+% Therefore, if we want to modify the tips of the arrows of |{WithArrows}|, we have to modify the style
+% |TipsOfWithArrows|.
+% %
+% \begin{Verbatim}
+% \tikzset{TipsOfWithArrows/.style= { > = {Latex[scale=1.2,bend]}} }
+% \end{Verbatim}
+%
+% The names of the Tikz nodes created by \pkg{witharrows} in the whole document are explained below.
+%
+%
+% \section{Precise positioning of the arrows}
+%
+%
+% The environment |{WithArrows}| defines, during the composition of the array, two series of nodes materialized in
+% red in the following example.\footnote{The option \texttt{shownodes} can be used to materialize the nodes.}
+%
+% \smallskip
+% $\begin{WithArrows}[displaystyle,shownodes]
+% I
+% & = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) \\
+% & = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\
+% & = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\
+% & =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u \\
+% & =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\
+% & =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\
+% & =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u  \\
+% & =\frac{\pi}4\ln2-I 
+% \end{WithArrows}$
+%
+% \bigskip
+% The nodes of the left are at the end of each line of text. These nodes will be called \emph{left nodes}. The
+% nodes of the right side are aligned vertically on the right side of the array. These nodes will be called
+% \emph{right nodes}.
+%
+% % The names of the Tikz nodes created by \texttt{\{WithArrows\}} are \texttt{wa-}$n$\texttt{-l} and
+% % \texttt{wa-}$n$\texttt{-r} where $n$~is the number of the line. It's possible to refer to these Tikz nodes after
+% % the environment (one should use the options \texttt{remember picture} and \texttt{overlay} and also
+% % \texttt{TipsOfWithArrows} and \texttt{->} in order to have the same arrowheads).
+%
+% By default, the arrows use the right nodes. We will say that they are in |rr| mode ($r$ for \emph{right}). These
+% arrows are |vertical| (we will say that an arrow is \emph{vertical} when its two ends have the same abscissa).
+%
+%
+% \smallskip
+% However, it's possible to use the left nodes, or a combination of left and right nodes, with one of the options
+% |lr|, |rl| and |ll| ($l$ for \emph{left}). Those arrows are, usually, not vertical.
+%
+%
+% Therefore
+% $\begin{WithArrows}[displaystyle]
+% I
+% & = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) 
+% \Arrow[lr]{This arrow uses the \texttt{lr} option.}\\
+% & = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\
+% & = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\
+% & =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u 
+% \Arrow[ll,jump=2,tikz={text width = 5cm}]{This arrow uses a \texttt{ll} option and a \texttt{jump} equal to $2$}\\
+% & =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\
+% & =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\
+% & =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u  \\
+% & =\frac{\pi}4\ln2-I 
+% \end{WithArrows}$
+%
+%
+%
+% \interitem
+% There is also an option called \texttt{i} ($i$ for \emph{intermediate}). With this option, the arrow is vertical
+% and at the leftmost position.
+%
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% (a+b)(a+ib)(a-b)(a-ib) 
+% & = (a+b)(a-b)\cdot(a+ib)(a-ib) \\
+% & = (a^2-b^2)(a^2+b^2) \Arrow~emphase#[i]@{because $(x-y)(x+y)=x^2-y^2$}\\
+% & = a^4-b^4 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% (a+b)(a+ib)(a-b)(a-ib) 
+% & = (a+b)(a-b)\cdot(a+ib)(a-ib) \\
+% & = (a^2-b^2)(a^2+b^2) \Arrow[i]{because $(x-y)(x+y)=x^2-y^2$}\\
+% & = a^4-b^4 
+% \end{WithArrows}$
+%
+%
+% \interitem 
+% The environment |{WithArrows}| gives also a |group| option. With this option, \emph{all} the arrows of the
+% environment are grouped on a same vertical line and at a leftmost position.
+% %
+% \begin{Verbatim}[formatcom=\small\color{gray}]
+% $\begin{WithArrows}[~emphase#displaystyle,group@]
+% 2xy'-3y=\sqrt x
+% & \Longleftrightarrow 2x(K'y_0+Ky_0')-3Ky_0 = \sqrt x \\
+% & \Longleftrightarrow 2xK'y_0 + K(2xy_0'-3y_0) = \sqrt x \\
+% & \Longleftrightarrow 2x K'y_0 = \sqrt x \Arrow{...}\\
+% ...
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}[displaystyle,group]
+% 2xy'-3y=\sqrt x
+% & \Longleftrightarrow 2x(K'y_0+Ky_0')-3Ky_0 = \sqrt x \\
+% & \Longleftrightarrow 2xK'y_0 + K(2xy_0'-3y_0) = \sqrt x \\
+% & \Longleftrightarrow 2x K'y_0 = \sqrt x \Arrow{We replace $y_0$ by its value.}\\
+% & \Longleftrightarrow 2xK'x^{\frac32} = x^{\frac12} \Arrow{simplification of the $x$}\\
+% & \Longleftrightarrow K' = \tfrac1{2x^2} \Arrow{antiderivation}\\
+% & \Longleftrightarrow K = -\tfrac1{2x} 
+% \end{WithArrows}$
+%
+%
+% \bigskip
+% If desired, the option |group| can be given to the command |\WithArrowsOptions| so that it will become the default
+% value.
+%
+%
+% \section{Comparison with the environment \{aligned\}}
+%
+%
+%
+% |{WithArrows}| bears similarities with the environment |{aligned}| of the extension \pkg{amsmath}. These are only
+% similarities because |{WithArrows}| has not been written upon the environment |{aligned}|.\footnote{In fact, it's
+% possible to use the package \pkg{witharrows} without the environment \pkg{amsmath}.}
+%
+% \interitem
+% As in the environments of \pkg{amsmath}, it's possible to change the spacing between two given lines with the
+% option of the command |\\| of end of line (it's also possible to use |\\*| but is has exactly the same effect as
+% |\\| since an environment |{WithArrows}| is always unbreakable).
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow{we expand} ~emphase#\\[2ex]@
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow{we expand} \\*[2ex]
+% \noalign{\vspace{3mm}}
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+%
+%
+% \interitem 
+% In the environments of \pkg{amsmath} (or \pkg{mathtools}), the spacing between lines is fixed by a parameter
+% called |\jot| (it's a dimension and not a skip). That's also the case for the environment |{WithArrows}|. An
+% option |jot| has been given to the environment |{WithArrows}| in order to change the value of this parameter
+% |\jot| for an given environment.\footnote{It's also possible to change \texttt{\string\jot} with the environment
+% \texttt{\{spreadlines\}} of \pkg{mathtools}.}
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}[displaystyle,~emphase#jot=2ex@]
+% F & = \frac12G     \Arrow{we expand}\\
+%   & = H + \frac12K \Arrow{we go on}\\
+%   & = K 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}[displaystyle,jot=2ex]
+% F & = \frac12G     \Arrow{we expand}\\
+%   & = H + \frac12K \Arrow{we go on}\\
+%   & = K 
+% \end{WithArrows}$
+%
+% \bigskip
+% However, this new value of |\jot| will also be used in other alignments included in the
+% environment~|{WithArrows}| :
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}[jot=2ex]
+% \varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
+% \Arrow{$x$ and $y$ are real}\\
+% & \Leftrightarrow \left\{
+% \begin{aligned}
+% x+y & = 0 \\
+% x+2y & = 0 \\
+% \end{aligned}
+% \right.
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+%
+% $\begin{WithArrows}[jot=2ex]
+% \varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
+% \Arrow{$x$ and $y$ are real}\\
+% & \Leftrightarrow \left\{
+% \begin{aligned}
+% x+y & = 0 \\
+% x+2y & = 0 \\
+% \end{aligned}
+% \right.
+% \end{WithArrows}$
+%
+% \bigskip
+% Maybe this doesn't correspond to the desired outcome. That's why an option |interline| is proposed. It's possible
+% to use a skip (=glue) for this option.
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}[~emphase#interline=2ex@]
+% \varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
+% \Arrow{$x$ and $y$ are real}\\
+% & \Leftrightarrow \left\{
+% \begin{aligned}
+% x+y & = 0 \\
+% x+2y & = 0 \\
+% \end{aligned}
+% \right.
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+%
+% $\begin{WithArrows}[interline=2ex]
+% \varphi(x,y) = 0  & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 
+% \Arrow{$x$ and $y$ are real}\\
+% & \Leftrightarrow \left\{
+% \begin{aligned}
+% x+y & = 0 \\
+% x+2y & = 0 \\
+% \end{aligned}
+% \right.
+% \end{WithArrows}$
+%
+%
+% \interitem
+% Like the environment |{aligned}|, |{WithArrows}| has an option of placement which can assume the values |t|, |c|
+% or |b|. However, the default value is not |c| but |t|. If desired, it's possible to have the |c| value as the
+% default with the command |\WithArrowsOptions{c}| at the beginning of the document.
+% %
+% \begin{Verbatim}
+% ~emphase#Et donc\enskip@
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow{we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% So\enskip 
+% $\begin{WithArrows}
+% A & = (a+1)^2 \Arrow{we expand} \\
+%   & = a^2 + 2a + 1 
+% \end{WithArrows}$
+%
+% \bigskip
+% The value |c| may be useful, for example, if we want to add curly braces :
+%
+% \smallskip
+% \begin{Verbatim}
+% On pose\enskip $~emphase#\left\{@
+% \begin{WithArrows}[~emphase#c@]
+% f(x) & = 3x^3+2x^2-x+4 
+% \Arrow[tikz=-]{both are polynoms}\\
+% g(x) & = 5x^2-5x+6
+% \end{WithArrows}
+% ~emphase#\right.@$
+% \end{Verbatim}
+%
+%
+% On pose\enskip $\left\{
+% \begin{WithArrows}[c]
+% f(x) & = 3x^3+2x^2-x+4 
+% \Arrow[tikz=-]{both are polynoms}\\
+% g(x) & = 5x^2-5x+6
+% \end{WithArrows}
+% \right.$
+%
+%
+% \interitem
+% Unlike |{aligned}|, the environment |{WithArrows}| uses |\textstyle| by default.
+%
+% Once again, it's possible to change this behaviour with |\WithArrowsOptions| :
+%
+% \quad |\WithArrowsOptions{displaystyle}|.
+%
+%
+% \smallskip
+% The following example is composed with |{aligned}| :\par\nobreak
+%
+% \smallskip
+% $\left\{
+% \begin{aligned}
+% \sum_{i=1}^n (x_i+1)^2  
+% & = \sum_{i=1}^n (x_i^2 + 2x_i+1) \\
+% & = \sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^nx_i + n 
+% \end{aligned}
+% \right.$
+%
+%
+% \medskip 
+% The following is composed with |{WithArrows}[c,displaystyle]|. The results are stricly identical.\footnote{In
+% versions of \texttt{amsmath} older than the 5~nov.~2016, an thin space was added on the left of an environment
+% \texttt{\{aligned\}}. The new versions do not add this space and neither do \texttt{\{WithArrows\}}.}\par\nobreak
+%
+% \smallskip
+% $\left\{
+% \begin{WithArrows}[c,displaystyle]
+% \sum_{i=1}^n (x_i+1)^2 
+% & = \sum_{i=1}^n (x_i^2 + 2x_i+1) \\
+% & = \sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^nx_i + n 
+% \end{WithArrows}
+% \right.$
+%
+%
+%
+%
+% \section{Examples}
+%
+% \subsection{With only one column}
+%
+% It's possible to use the environment |{WithArrows}| with making use of the left column only, or the right column
+% only.
+% %
+% \begin{Verbatim}
+% $\begin{WithArrows}
+% &f(x) \ge g(x) \Arrow{by squaring both sides} \\
+% & f(x)^2 \ge g(x)^2 \Arrow{by moving to left side} \\
+% & f(x)^2 - g(x)^2 \ge 0 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}
+% &f(x) \ge g(x) \Arrow{by squaring both sides} \\
+% & f(x)^2 \ge g(x)^2 \Arrow{by moving to left side} \\
+% & f(x)^2 - g(x)^2 \ge 0 
+% \end{WithArrows}$
+%
+%
+% \subsection{MoveEqLeft}
+%
+% It's possible to use |\MoveEqLeft| of \pkg{mathtools} (if we don't want ampersand on the firt line) :
+% %
+% \begin{Verbatim}[formatcom=\small\color{gray}]
+% $\begin{WithArrows}[jot=2mm]
+% ~emphase#\MoveEqLeft@ \arccos(x) = \arcsin \frac45 + \arcsin \frac5{13} 
+% \Arrow{because both are in $[-\frac{\pi}2,\frac{\pi}2]$} \\
+% & \Leftrightarrow x = \sin\left(\arcsin\frac45 + \arcsin\frac5{13}\right) \\
+% & \Leftrightarrow x = \frac45\cos\arcsin\frac5{13} + \frac5{13} \cos\arcsin\frac45 
+% \Arrow{$\forall x \in [-1,1], \cos(\arcsin x) = \sqrt{1-x^2}$} \\
+% & \Leftrightarrow x = \frac45\sqrt{1-\bigl(\frac5{13}\bigr)^2}
+% + \frac5{13}\sqrt{1-\bigl(\frac45\bigr)^2} \\
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+%
+% \medskip
+% $\begin{WithArrows}[jot=2mm]
+% \MoveEqLeft \arccos(x) = \arcsin \frac45 + \arcsin \frac5{13} 
+% \Arrow{because both are in $[-\frac{\pi}2,\frac{\pi}2]$} \\
+% & \Leftrightarrow x = \sin\left(\arcsin\frac45 + \arcsin\frac5{13}\right) \\
+% & \Leftrightarrow x = \frac45\cos\arcsin\frac5{13} + \frac5{13} \cos\arcsin\frac45 
+% \Arrow{$\forall x \in [-1,1], \cos(\arcsin x) = \sqrt{1-x^2}$} \\
+% & \Leftrightarrow x = \frac45\sqrt{1-\bigl(\frac5{13}\bigr)^2}
+% + \frac5{13}\sqrt{1-\bigl(\frac45\bigr)^2} \\
+% \end{WithArrows}$
+%
+%
+%
+% \subsection{Nested environments}
+%
+%
+% The environments |{WithArrows}| can be nested. In this case, the options given to the encompassing environment
+% applies also to the inner ones (with the notable exception of |interline|).
+% %
+% \begin{Verbatim}[formatcom=\small\color{gray}]
+% $~emphase#\begin{WithArrows}@[tikz=blue]
+% \varphi(x,y)=0
+%   & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \Arrow{the numbers are real}\\
+%   & \Leftrightarrow
+%   \left\{~emphase#\begin{WithArrows}@[c]
+%   x+2y & = 0 \\
+%   2x+4y & = 0 
+%   ~emphase#\end{WithArrows}@\right. \\
+%   & \Leftrightarrow
+%   \left\{~emphase#\begin{WithArrows}@[c]
+%   x+2y & = 0 \Arrow[tikz=-]{the same équation}\\
+%   x+2y & = 0 
+%   ~emphase#\end{WithArrows}@\right. \\
+%   & \Leftrightarrow x+2y=0 
+% ~emphase#\end{WithArrows}@$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}[tikz=blue]
+% \varphi(x,y)=0
+%   & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \Arrow{the numbers are real}\\
+%   & \Leftrightarrow
+%   \left\{\begin{WithArrows}[c]
+%   x+2y & = 0 \\
+%   2x+4y & = 0 
+%   \end{WithArrows}\right. \\
+%   & \Leftrightarrow
+%   \left\{\begin{WithArrows}[c]
+%   x+2y & = 0 \Arrow[tikz=-]{the same equation}\\
+%   x+2y & = 0 
+%   \end{WithArrows}\right. \\
+%   & \Leftrightarrow x+2y=0 
+% \end{WithArrows}$
+%
+%
+%
+% \subsection{A loop flow}
+%
+% Here is an example with a loop flow.\par\nobreak
+% %
+% \begin{Verbatim}[formatcom=\small\color{gray}]
+% $\begin{WithArrows}[tikz={font={\tiny}}]
+% a.\;& f \text{ est continuous on } E 
+% \Arrow{(1)}\Arrow[tikz=<-,jump=4,xoffset=1cm]{(5)}\\
+% b.\;& f \text{ est continuous in } 0 
+% \Arrow{(2)}\\
+% c.\;& f \text{ is bounded on the unit sphere} 
+% \Arrow{(3)}\\
+% d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| 
+% \Arrow{(4)}\\
+% e.\;& f \text{ is lipschitzian} 
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% $\begin{WithArrows}[tikz={font={\tiny}}]
+% a.\;& f \text{ est continuous on } E 
+% \Arrow{(1)}\Arrow[tikz=<-,jump=4,xoffset=1cm]{(5)}\\
+% b.\;& f \text{ est continuous in } 0 
+% \Arrow{(2)}\\
+% c.\;& f \text{ is bounded on the unit sphere} 
+% \Arrow{(3)}\\
+% d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| 
+% \Arrow{(4)}\\
+% e.\;& f \text{ is lipschitzian} 
+% \end{WithArrows}$
+%
+%
+% \subsection{Automatic numerotation}
+%
+% The option |font| of Tikz contains in fact a list of tokens which will be placed at the beginning of the text.
+%
+% These tokens can be true commands for a change of font (like |\bfseries| or |\sffamily|) but can also be, in
+% fact, any TeX command.
+%
+% In the following example, the argument of |font| is the token list |\tiny\counter| where |\counter| is a command
+% which increment a counter previously defined and display its new value. Thus, the arrows are automatically
+% numbered.
+% %
+% \begin{Verbatim}[formatcom=\small\color{gray}]
+% \newcounter{MyCounter}
+% \newcommand{\counter}{\stepcounter{MyCounter}\theMyCounter.}
+% $\begin{WithArrows}[tikz={~emphase#font={\tiny\counter}@}]
+% A(x) 
+% & = B(x) \Arrow{} \\
+% & = C(x) \Arrow{} \\
+% & = C(x) \Arrow{} \\
+% & = E(x) \Arrow{} \\
+% & = F(x) \Arrow{} \\
+% & = G(x)   
+% \end{WithArrows}$
+% \end{Verbatim}
+%
+% \begin{scope}
+% \newcounter{MyCounter}
+% \newcommand{\counter}{\stepcounter{MyCounter}\theMyCounter.}
+% $\begin{WithArrows}[tikz={font={\tiny\counter}}]
+% A(x) 
+% & = B(x) \Arrow{} \\
+% & = C(x) \Arrow{} \\
+% & = C(x) \Arrow{} \\
+% & = E(x) \Arrow{} \\
+% & = F(x) \Arrow{} \\
+% & = G(x)   
+% \end{WithArrows}$
+% \end{scope}
+%
+%
+% \section{An technical remark about the names of the nodes}
+%
+% Environments |{WithArrows}| can be nested, and, therefore, we have a ``nesting tree'' for the environments
+% |{WithArrows}| of the whole document. This nesting tree is used to give a unique name to each node in the
+% document.
+%
+% \smallskip 
+% The Tikz name of a node created by \pkg{witharrows} is prefixed by |wa-|. Then, we have a list of numbers with
+% give the position in the nesting tree and the number of the line in the environment. At the end, we have the
+% suffixe |l| for a ``left node'' and |r| for a ``right node''.
+% 
+% \smallskip
+% For illustrative purposes, we give an example of nested environments |{WithArrows}|, and, for each ``right
+% node'', the name of that node.\footnote{There is an option \texttt{shownodenames} to show the names of these nodes.}
+% 
+% \medskip
+% \[\begin{WithArrows}[shownodes,shownodenames]
+% A & \vartriangleleft B+B+B+B+B+B+B+B+B+B+B+B+B \\
+% & \vartriangleleft \left\{
+% \begin{WithArrows}[c]
+% C & \vartriangleleft D \\
+% E & \vartriangleleft F 
+% \end{WithArrows}
+% \right. \\
+%  & \vartriangleleft 
+% \left\{
+% \begin{WithArrows}[c]
+% G & \vartriangleleft H+H+H+H+H+H+H \\
+% I & \vartriangleleft 
+% \left\{
+% \begin{WithArrows}
+% J &\vartriangleleft K \\
+% L &\vartriangleleft M 
+% \end{WithArrows}
+% \right.
+% \end{WithArrows}
+% \right. \\
+%  & \vartriangleleft 
+% \left\{
+% \begin{WithArrows}[c]
+% N & \vartriangleleft O \\
+% P & \vartriangleleft Q 
+% \end{WithArrows}
+% \right.
+% \end{WithArrows}\]
+%
+% \bigskip
+% The command |\WithArrowsLastEnv| gives the number of the last environment of level~$0$. For example, we can draw
+% an arrow from the node \texttt{wa-\WithArrowsLastEnv-1} to the node \texttt{wa-\WithArrowsLastEnv-2-1} with the
+% following Tikz command.\footnote{The command \texttt{\string\WithArrowsLastEnv} is \emph{fully expandable} and
+% thus, can be used directly in the name of a Tikz node.}
+%
+% \begin{Verbatim}
+% \begin{tikzpicture}[remember picture,overlay,->,TipsOfWithArrows]
+% \draw (wa-\WithArrowsLastEnv-1-r) to (wa-\WithArrowsLastEnv-2-1-r) ;
+% \end{tikzpicture}
+% \end{Verbatim}
+%
+% \section{Implementation}
+%
+% \subsection{Some extensions are loaded}
+%
+% This package is written in \pkg{expl3}.
+%    \begin{macrocode}
+\RequirePackage{expl3}
+%    \end{macrocode}
+%
+% \bigskip
+% The package \pkg{xparse} will be used to define the environment |{WithArrows}| and the document-level commands
+% (|\Arrow|, |\WithArrowsOptions| ans |\WithArrowsLastEnv|).
+%    \begin{macrocode}
+\RequirePackage{xparse}
+%    \end{macrocode}
+%
+% \bigskip
+% The arrows are drawn with Tikz and that's why \pkg{tikz} is required with some libraries.
+%    \begin{macrocode}
+\RequirePackage{tikz}
+\usetikzlibrary{calc,arrows.meta,bending}
+%    \end{macrocode}
+%
+% \bigskip
+% The package \pkg{footnote} will be used to extract footnotes.
+%    \begin{macrocode}
+\RequirePackage{footnote}
+%    \end{macrocode}
+%
+% \subsection{Some technical definitions}
+%
+% We define a Tikz style |wa_node_style| for the nodes that will be created in the |\halign|.
+%    \begin{macrocode}
+\tikzstyle{@@_node_style}=[rectangle,
+                           inner~sep = 0 pt,
+                           minimum~height = 3 pt,
+                           minimum~width = 0pt,
+                           red,
+                           \bool_if:NT \l_@@_shownodes_bool {draw}]
+%    \end{macrocode}
+% The color of the nodes is red, but in fact, the nodes will be drawn only when the option |shownodes| is used
+% (this option is useful for debugging).
+%
+% \bigskip
+% We also define a style for the tips of arrow. The final user of the extension \pkg{WithArrows} will use this
+% style if he wants to draw an arrow directly with a Tikz command in his document (probably using the Tikz nodes
+% created by |{WithArrows}| in the |\halign|).
+%    \begin{macrocode}
+\tikzset{TipsOfWithArrows/.style= { > = {Straight~Barb[scale=1.2,bend]}} }
+%    \end{macrocode}
+%
+% \bigskip
+% In order to increase the interline in the environments |{WithArrows}|, we will use the command |\spread@equation|
+% of \pkg{amsmath}. When used, this command becomes no-op (in the current TeX group). Therefore, it will be
+% possible to use the environments of \pkg{amsmath} (\emph{e.g.} |{aligned}|) in an environment |{WithArrows}|.
+% 
+% Nevertheless, we want the extension \pkg{witharrows} available without \pkg{amsmath}. That's why we give a
+% definition of |\spread@equation| (this definition will be loaded only if \pkg{amsmath} --- or \pkg{mathtools} --- has
+% not been loaded yet).
+%    \begin{macrocode}
+\cs_if_free:NT \spread@equation
+    {\cs_set:Npn \spread@equation{\openup\jot   
+                                  \cs_set_eq:NN \spread@equation \prg_do_nothing}}
+%    \end{macrocode}
+%
+%
+% \subsection{Variables}
+%
+% \bigskip
+% The following sequence is the position of the last environment |{WithArrows}| in the tree of the imbricated
+% environments |{WithArrows}|. 
+%    \begin{macrocode}
+\seq_new:N \g_@@_position_in_the_tree_seq
+\seq_gput_right:Nn \g_@@_position_in_the_tree_seq 1
+%    \end{macrocode}
+%
+% \bigskip
+% The following counter will give the number of the last environment |{WithArrows}| of level~$0$. This
+% counter will be used only in the definition of |\WithArrowsLastEnv|.
+%    \begin{macrocode}
+\int_new:N \g_@@_last_env_int
+%    \end{macrocode}
+%
+% \bigskip
+% The following skip (=glue) is the vertical space inserted between two lines of the |\halign|.
+%    \begin{macrocode}
+\skip_new:N \l_@@_interline_skip
+%    \end{macrocode}
+%
+% \bigskip
+% If the following flag is raised, then the user can use more than two columns.
+%    \begin{macrocode}
+\bool_new:N \l_@@_MoreColumns_bool
+%    \end{macrocode}
+%
+% \bigskip
+% The following integer indicates the position of the box that will be created : 0 (=|t|=|\vtop|), 1~(=|c|=|\vcenter|) or 2 (=|b|=|\vbox|).
+%    \begin{macrocode}
+\int_new:N \l_@@_pos_int 
+%    \end{macrocode}
+% \bigskip
+% The following flag indicates if the beginning of the arrow use a |r| option (if not, it's a |l| option).
+%    \begin{macrocode}
+\bool_new:N \l_@@_initial_r_bool
+\bool_set_true:N \l_@@_initial_r_bool
+%    \end{macrocode}
+%
+% \bigskip
+% The following flag indicates if the end of the arrow use a |r| option (if not, it's a |l| option).
+%    \begin{macrocode}
+\bool_new:N \l_@@_final_r_bool
+\bool_set_true:N \l_@@_final_r_bool
+%    \end{macrocode}
+%
+% \bigskip
+% The following flag indicates if the arrow use a |i| option (in this case, the options |l| and |r| for the
+% ends are meaningless).
+%    \begin{macrocode}
+\bool_new:N \l_@@_i_bool
+%    \end{macrocode}
+%
+% \bigskip
+% The following dimension is the value of the translation of the whole arrow to the right (of course, it's a
+% dimension and not a skip).
+%    \begin{macrocode}
+\dim_new:N \l_@@_xoffset_dim 
+\dim_set:Nn \l_@@_xoffset_dim {3mm}
+%    \end{macrocode}
+%
+% \bigskip
+% If the following flag is raised, the nodes will be drawn in red (useful for debugging).
+%    \begin{macrocode}
+\bool_new:N \l_@@_shownodes_bool
+%    \end{macrocode}
+%
+% \bigskip
+% If the following flag is raised, the name of the ``right nodes'' will be shown in the document (useful for
+% debugging). 
+%    \begin{macrocode}
+\bool_new:N \l_@@_shownodenames_bool
+%    \end{macrocode}
+% 
+% \bigskip
+% If the following flag is raised, the elements of the |\halign| will be composed with |\displaystyle| :
+%    \begin{macrocode}
+\bool_new:N \l_@@_displaystyle_bool
+%    \end{macrocode}
+%
+% \bigskip
+% The following token list variable will contains the \pkg{Tikz} options used to draw the arrows.
+%    \begin{macrocode}
+\tl_clear_new:N \l_@@_options_tikz_tl
+%    \end{macrocode}
+%
+% At each possible level for the options (\emph{global}, \emph{env} or \emph{local} : see below), the new values
+% will be appended on the right of this token list.
+%
+% \bigskip
+% The following flag will be raised when a key controling position of the arrow has been set in the same list of
+% keys (this is useful in order to raise an error if two incompatibles keys are specified at the same level).
+%    \begin{macrocode}
+\bool_new:N \l_@@_position_key_already_set_bool
+%    \end{macrocode}
+% This flag is set to |false| each time we have to process a list of options.
+%
+% \bigskip
+% In the |\halign| of an environment |{WithArrows}|, we will have to use three counters :
+% \begin{itemize}
+% \item |\g_@@_arrow_int| to count the arrows created in the environment ;
+% \item |\g_@@_line_int| to count the lines of the |\halign| ;
+% \item |\g_@@_line_bis_int| to count the lines of the |\halign| which have a second column.\footnote{This counter
+% is used in order to raise an error if there is a line without the second column (such an situation could raise a
+% \textsc{pgf} error for an undefined node).}
+% \end{itemize}
+%
+% These three counters will be incremented in a cell of the |\halign| and, therefore, the incrementation must be
+% global. However, we want to be able to include a |{WithArrows}| in another |{WithArrows}|. To do so, we must
+% restore the previous value of these counters at the end of an environment |{WithArrows}| and we decide to manage
+% a stack for each of these counters.
+%    \begin{macrocode}
+\seq_new:N \g_@@_stack_counter_arrows_seq
+\int_new:N \g_@@_arrow_int
+\seq_new:N \g_@@_stack_counter_lines_seq
+\int_new:N \g_@@_line_int
+\seq_new:N \g_@@_stack_counter_lines_bis_seq
+\int_new:N \g_@@_line_bis_int
+%    \end{macrocode}
+
+%
+% \subsection{The definition of the options}
+% There are three levels where options can be set :
+% \begin{itemize}
+% \item with |\WithArrowsOptions{...}| : this level will be called \emph{global} level;
+% \item with |\begin{WithArrows}[...]| : this level will be called \emph{env} level;
+% \item with |\Arrow[...]| : this level will be called \emph{local} level.
+% \end{itemize}
+%
+% That's why there is three groups of keys named |global|, |env| and |local|.
+%
+% \bigskip 
+% Before each |\keys_set_groups:nnn|, we execute a |\keys_set_filter:nnn| with group |secondary|. Thus, an
+% unknown key will raise an error. Furthermore, the \emph{primary} keys (those which are not in the group
+% |secondary|) will be set first : it's useful to raise an error if, for example, keys |i| and
+% |group| are set at the same level (which is incoherent).
+%
+% \bigskip
+%    \begin{macrocode}
+\keys_define:nn {WithArrows} 
+%    \end{macrocode}
+%
+% \medskip
+% The  key |jump| indicates the number of lines jumped by the arrow (1 by default). This key will be extracted
+% when the command |\Arrow| will be executed. That's why this key is the only key of a dedicated group also named
+% |jump|.
+%    \begin{macrocode}
+    { jump  .groups:n   = {jump,secondary},
+      jump  .code:n     = {\int_set:Nn \l_@@_jump_int {#1}
+                           \int_compare:nNnF \l_@@_jump_int > 0
+                               {\msg_error:nn {witharrows} 
+                                              {The~option~"jump"~must~be~non~negative}}},
+      jump  .value_required:n  = true,
+%    \end{macrocode}
+%
+% \bigskip
+% The options |t|, |c| and |b| indicate if we will create a |\vtop|, a |\vcenter| of a |\vbox|. This information is
+% stored in the variable |\l_@@_pos_int|.
+%    \begin{macrocode}
+      t   .groups:n          = {global,env,secondary},
+      t   .code:n            = {\int_set:Nn \l_@@_pos_int 0},
+      t   .value_forbidden:n = true,
+      c   .groups:n          = {global,env,secondary},
+      c   .code:n            = {\int_set:Nn \l_@@_pos_int 1},
+      c   .value_forbidden:n = true,
+      b   .groups:n          = {global,env,secondary},
+      b   .code:n            = {\int_set:Nn \l_@@_pos_int 2},
+      b   .value_forbidden:n = true,
+%    \end{macrocode}
+%
+% \bigskip
+% Usually, the number of columns in a |{WithArrows}| environment is limited to 2. Nevertheless, it's possible to
+% have more columns with the option |MoreColumns|.
+%    \begin{macrocode}
+      MoreColumns .groups:n          = {global,env,secondary},
+      MoreColumns .bool_set:N        = \l_@@_MoreColumns_bool,
+      MoreColumns .default:n         = true,
+      MoreColumns .value_forbidden:n = true,
+%    \end{macrocode}
+%
+% \bigskip
+% If the user wants to give a new name to the |\Arrow| command (and the name |\Arrow| remains free).
+%    \begin{macrocode}
+      CommandName .groups:n         = {global,env,secondary},
+      CommandName .tl_set:N         = \l_@@_CommandName_tl,
+      CommandName .initial:n        = {Arrow},
+      CommandName .value_required:n = true,
+%    \end{macrocode}
+%
+% \bigskip
+% With the option |displaystyle|, all the elements of the environment will be composed in |\displaystyle|.
+%    \begin{macrocode}
+      displaystyle .groups:n          = {global,env,secondary},
+      displaystyle .bool_set:N        = \l_@@_displaystyle_bool,
+%    \end{macrocode}
+      %
+% \bigskip
+% With the option |shownodes|, the nodes will be drawn in red (useful only for debugging).
+%    \begin{macrocode}
+      shownodes .groups:n          = {global,env,secondary},
+      shownodes .bool_set:N        = \l_@@_shownodes_bool,
+      shownodes .default:n         = true,
+%    \end{macrocode}
+% 
+% \bigskip
+% With the option |shownodenames|, the name of the ``right nodes'' will be written in the document (useful only
+% for debugging). 
+%    \begin{macrocode}
+      shownodenames .groups:n          = {global,env,secondary},
+      shownodenames .bool_set:N        = \l_@@_shownodenames_bool,
+      shownodenames .default:n         = true,
+%    \end{macrocode}
+%
+% \bigskip
+% The option |jot| can be used to change the value of the LaTeX parameter |\jot|. If we put this option in the
+% |global| group, the use of this option in |\WithArrowsOptions| will change |\jot| for the whole document (at
+% least the current TeX group) and not only for the |{WithArrows}| environments. This is certainly not what the
+% user wants. That's why the option |jot| is not in the group |global|. It's interesting to note that |\jot| is a
+% dimension and not a skip (=glue).
+% 
+%    \begin{macrocode}
+      jot       .groups:n          = {env,secondary}, 
+      jot       .dim_set:N         = \jot, 
+      jot       .value_required:n  = true,
+%    \end{macrocode}
+%
+% \bigskip
+% The option |interline| gives the vertical skip (=glue) inserted between two lines (independently of |\jot|). By
+% design, this option has a particular behaviour : it applies only to an environment and doesn't apply to the
+% nested environments.
+%    \begin{macrocode}
+      interline   .groups:n         = {env,secondary},
+      interline   .skip_set:N       = \l_@@_interline_skip,
+      interline   .initial:n        = \c_zero_skip,
+      interline   .value_required:n = true,
+%    \end{macrocode}
+%
+% \bigskip
+% The option |xoffset| change the $x$-offset of the arrows (towards the right). It's a dimension and not a skip.
+%    \begin{macrocode}
+      xoffset  .groups:n          = {global,env,local,secondary},
+      xoffset  .dim_set:N         = \l_@@_xoffset_dim,
+      xoffset  .value_required:n  = true,           
+%    \end{macrocode}
+%
+% \bigskip
+% The option |tikz| gives Tikz parameters that will be given to the arrow when it is drawn (more precisely, the
+% parameters will be given to the command |\path| of Tikz).
+%    \begin{macrocode}
+      tikz     .groups:n          = {global,env,local,secondary},
+      tikz     .code:n            = {\tl_put_right:Nn \l_@@_options_tikz_tl {,#1}},
+      tikz     .value_required:n  = true,
+%    \end{macrocode}
+%
+% \bigskip
+% The following options can be used to specify the position of the arrows. We control that a previous specification
+% of position has not been set at the same level of option. This is done with the help of the flag 
+% |\l_@@_position_key_already_set_bool|.
+%    \begin{macrocode}
+      ll       .groups:n          = {global,env,local,secondary},
+      ll       .value_forbidden:n = true, 
+      ll       .default:n         = true,
+      ll       .code:n            = {\bool_if:NT \l_@@_position_key_already_set_bool
+                                       {\msg_error:nn {witharrows} 
+                                                      {Two~options~are~incompatible}}
+                                     \bool_if:NT \l_@@_group_bool
+                                       {\msg_error:nn {witharrows} 
+                                                      {Option~incompatible~with~group}}
+                                     \bool_set_true:N \l_@@_position_key_already_set_bool
+                                     \bool_set_false:N \l_@@_initial_r_bool
+                                     \bool_set_false:N \l_@@_final_r_bool
+                                     \bool_set_false:N \l_@@_i_bool },
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+      lr       .groups:n          = {global,env,local,secondary},
+      lr       .value_forbidden:n = true,
+      lr       .default:n         = true, 
+      lr       .code:n            = {\bool_if:NT \l_@@_position_key_already_set_bool
+                                       {\msg_error:nn {witharrows} 
+                                                      {Two~options~are~incompatible}}
+                                     \bool_if:NT \l_@@_group_bool
+                                       {\msg_error:nn {witharrows} 
+                                                      {Option~incompatible~with~group}}
+                                     \bool_set_true:N \l_@@_position_key_already_set_bool
+                                     \bool_set_false:N \l_@@_initial_r_bool
+                                     \bool_set_true:N  \l_@@_final_r_bool
+                                     \bool_set_false:N \l_@@_i_bool},
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+      rl       .groups:n          = {global,env,local,secondary},
+      rl       .value_forbidden:n = true,
+      rl       .default:n         = true, 
+      rl       .code:n            = {\bool_if:NT \l_@@_position_key_already_set_bool
+                                       {\msg_error:nn {witharrows} 
+                                                      {Two~options~are~incompatible}}
+                                     \bool_if:NT \l_@@_group_bool
+                                       {\msg_error:nn {witharrows} 
+                                                      {Option~incompatible~with~group}}
+                                     \bool_set_true:N \l_@@_position_key_already_set_bool
+                                     \bool_set_true:N  \l_@@_initial_r_bool
+                                     \bool_set_false:N \l_@@_final_r_bool
+                                     \bool_set_false:N \l_@@_i_bool},
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+      rr       .groups:n          = {global,env,local,secondary},
+      rr       .value_forbidden:n = true,
+      rr       .default:n         = true, 
+      rr       .code:n            = {\bool_if:NT \l_@@_position_key_already_set_bool
+                                       {\msg_error:nn {witharrows} 
+                                                      {Two~options~are~incompatible}}
+                                     \bool_if:NT \l_@@_group_bool
+                                       {\msg_error:nn {witharrows} 
+                                                      {Option~incompatible~with~group}}
+                                     \bool_set_true:N \l_@@_position_key_already_set_bool
+                                     \bool_set_true:N  \l_@@_initial_r_bool
+                                     \bool_set_true:N  \l_@@_final_r_bool
+                                     \bool_set_false:N  \l_@@_i_bool},
+%    \end{macrocode}
+%
+% \bigskip
+% With option |i| (for \emph{intermediate}), the arrow will be drawn on the leftmost position compatible with all
+% the lines between the starting line and the final line of the arrow.
+%    \begin{macrocode}
+      i        .groups:n          = {global,env,local,secondary},
+      i        .code:n            = {\bool_if:NT \l_@@_position_key_already_set_bool
+                                       {\msg_error:nn {witharrows} 
+                                                      {Two~options~are~incompatible}}
+                                     \bool_if:NT \l_@@_group_bool
+                                       {\msg_error:nn {witharrows} 
+                                                      {Option~incompatible~with~group}}
+                                     \bool_set_true:N \l_@@_position_key_already_set_bool
+                                     \bool_set_true:N \l_@@_i_bool},
+      i        .value_forbidden:n = true,
+      i        .default:n         = true,
+%    \end{macrocode}
+%
+% \bigskip 
+% With the option |group|, \emph{all} the arrows of the environment are grouped on a same vertical line and at a
+% leftmost position. Of course, this option is not available at the local level.
+% 
+% This key is not in the |secondary| group. Thus, it will be set first during the |\keys_set_filter:nnn| and an
+% incompatibility like, for example, |[i,group]| will be detected (with a non fatal error).
+%    \begin{macrocode}
+      group        .groups:n          = {global,env},   
+      group        .bool_set:N        = \l_@@_group_bool,
+      group        .value_forbidden:n = true
+}
+%    \end{macrocode}
+%
+% \bigskip
+% We process the options when the package is loaded (with |\usepackage|) but we recommend to use |\WithArrowOptions| instead.
+%    \begin{macrocode}
+\ProcessKeysOptions {WithArrows}
+%    \end{macrocode}
+%
+% \bigskip
+% |\WithArrowsOptions| is the command of the \pkg{witharrows} package to fix options at the document level.
+%    \begin{macrocode}
+\NewDocumentCommand \WithArrowsOptions {m}
+    {\bool_set_false:N \l_@@_position_key_already_set_bool
+     \keys_set_filter:nnn {WithArrows} {secondary} {#1}  
+     \keys_set_groups:nnn {WithArrows} {global} {#1}}
+%    \end{macrocode}
+%
+% 
+% \subsection{The command Arrow}
+%
+% In fact, the internal command is not named |\Arrow| but |\@@_Arrow|. Usually, at the beginning of an environment
+% |{WithArrows}|, |\Arrow| is set to be equivalent to |\@@_Arrow|. However, the user can change the name with the
+% option |CommandName| and the user command for |\@@_Arrow| will be different. This mechanism can be useful when
+% the user has already a command named |\Arrow| he wants to still be able to use in the environment |{WithArrows}|.
+%
+% \medskip
+%    \begin{macrocode}
+\NewDocumentCommand \@@_Arrow {O{} m O{}}
+         {\tl_if_eq:noF {WithArrows} {\@currenvir} 
+                  {\msg_error:nn {witharrows} {Arrow~used~outside~{WithArrows}~environment}}
+%    \end{macrocode}
+%
+% The counter |\g_@@_arrow_int| counts the arrows in the environment. The incrementation must be global (|gincr|)
+% because the command |\Arrow| will be used in the cell of a |\halign|. It's recalled that we manage a stack for
+% this counter.
+%    \begin{macrocode}
+          \int_gincr:N \g_@@_arrow_int
+%    \end{macrocode}
+%
+% We decide to extract immediatly the key |jump| in order to compute the end line. That's the reason why there is a
+% group |jump| with only one key (the key |jump|).
+%    \begin{macrocode}
+          \int_zero_new:N \l_@@_jump_int
+          \int_set:Nn \l_@@_jump_int 1
+          \keys_set_groups:nnn {WithArrows} {jump} {#1,#3} 
+%    \end{macrocode}
+%
+% \medskip
+% We will construct a global property list to store the informations of the considered arrow. The four fields of
+% this property list are ``initial'', ``final'', ``options'' and ``label''.
+%
+% \smallskip
+% \begin{enumerate}
+% \item First, the line from which the arrow starts :
+%    \begin{macrocode}
+          \prop_put:NnV \l_tmpa_prop {initial} \g_@@_line_int
+%    \end{macrocode}
+%
+% \item The line where the arrow ends (that's why it was necessary to extract the key |jump|) :
+%    \begin{macrocode}
+          \int_set:Nn \l_tmpa_int {\g_@@_line_int + \l_@@_jump_int}
+          \prop_put:NnV \l_tmpa_prop {final} \l_tmpa_int
+%    \end{macrocode}
+%
+% \item All the options of the arrow (it's a token list) :
+%    \begin{macrocode}
+          \prop_put:Nnn \l_tmpa_prop {options} {#1,#3}
+%    \end{macrocode}
+%
+% \item The label of the arrow (it's also a token list) :
+%    \begin{macrocode}
+          \prop_put:Nnn \l_tmpa_prop {label} {#2}
+%    \end{macrocode}
+% \end{enumerate}
+%
+% The property list has been created in a local variable for convenience. Now, it will be stored in a global
+% variable indicating both the position-in-the-tree and the number of the arrow. 
+% 
+%    \begin{macrocode}
+          \prop_gclear_new:c 
+                {g_@@_arrow_\l_@@_prefix_tl _\int_use:N\g_@@_arrow_int _prop}
+          \prop_gset_eq:cN 
+                {g_@@_arrow_\l_@@_prefix_tl _\int_use:N\g_@@_arrow_int _prop} 
+                \l_tmpa_prop
+          }       
+%    \end{macrocode}
+%
+%
+% \subsection{The environnement \{WithArrows\}}
+%
+%
+% The environment |{WithArrows}| starts with the initialisation of the three counters |\g_@@_arrow_int|,
+% |\g_@@_line_int| dans |\g_@@_line_bis_int|. However, we have to save their previous values with the three stacks
+% created for this end.
+%    \begin{macrocode}
+\NewDocumentEnvironment {WithArrows} {O{}}
+         { \seq_gput_right:NV \g_@@_stack_counter_arrows_seq \g_@@_arrow_int
+           \int_gzero:N \g_@@_arrow_int 
+           \seq_gput_right:NV \g_@@_stack_counter_lines_seq \g_@@_line_int
+           \int_gzero:N \g_@@_line_int 
+           \seq_gput_right:NV \g_@@_stack_counter_lines_bis_seq \g_@@_line_bis_int
+           \int_gzero:N \g_@@_line_bis_int 
+%    \end{macrocode}
+% 
+% \bigskip
+% We also have to update the position on the nesting tree.
+%    \begin{macrocode}
+           \seq_gput_right:Nn \g_@@_position_in_the_tree_seq 1
+%    \end{macrocode}
+%
+% The nesting tree is used to create a prefix which will be used in the names of the Tikz nodes and in the names of
+% the arrows (each arrow is a property list of four fields). If we are in the second environment |{WithArrows}|
+% nested in the third environment |{WithArrows}| of the document, the prefix will be |3-2| (although the position
+% in the tree is $[3,2,1]$ since such a position always ends with a~$1$). First, we do a copy of the
+% position-in-the-tree and then we pop the last element of this copy (in order to drop the last~$1$).
+%    \begin{macrocode}
+           \seq_set_eq:NN \l_tmpa_seq \g_@@_position_in_the_tree_seq
+           \seq_pop_right:NN \l_tmpa_seq \l_tmpa_tl
+           \tl_clear_new:N \l_@@_prefix_tl
+           \tl_set:Nx \l_@@_prefix_tl {\seq_use:Nnnn \l_tmpa_seq {-} {-} {-}}
+%    \end{macrocode}
+%
+%
+
+% 
+% \bigskip
+% The environment |{WithArrows}| must be used in math mode.
+%    \begin{macrocode}
+           \reverse_if:N \if_mode_math:
+                             \msg_error:nn {witharrows} {{WithArrows}~used~outside~math~mode}
+                         \fi
+%    \end{macrocode}
+%
+% \bigskip
+% We extract the footnotes of the environments |{WithArrows}| with the pair |\savenotes-\spewnotes| of the
+% extension \pkg{footnote} (of course, we have put a |\spewnotes| at the end of the environment).
+%    \begin{macrocode}
+           \savenotes
+%    \end{macrocode}
+%
+% \bigskip
+% We define the command |\\| to be the command |\@@_cr:| (defined below). 
+%    \begin{macrocode}
+           \cs_set_eq:NN \\ \@@_cr:
+           \mathsurround = \c_zero_dim
+%    \end{macrocode}
+%
+% \bigskip
+% These three counters will be used later as variables.
+%    \begin{macrocode}
+           \int_zero_new:N \l_@@_initial_int
+           \int_zero_new:N \l_@@_final_int
+           \int_zero_new:N \l_@@_arrow_int
+%    \end{macrocode}
+%
+% \bigskip
+% The flag |\l_@@_position_key_already_set_bool| is set to false before the treatment of the options of the
+% environment. It will be raised if a key indicating the position of the arrows is found. Thus, we can detect
+% incompatible keys.
+%    \begin{macrocode}
+           \bool_set_false:N \l_@@_position_key_already_set_bool
+%    \end{macrocode}
+%
+% \bigskip
+% The value corresponding to the key |interline| is put to zero before the treatment of the options of the
+% environment.\footnote{It's recalled that, by design, the option \texttt{interline} of a environment doesn't apply
+% in the nested environments.}
+%    \begin{macrocode}
+           \skip_zero:N \l_@@_interline_skip
+%    \end{macrocode}
+%
+% \bigskip
+% The following code in order to raise an error if a key is unknown.
+%    \begin{macrocode}
+           \keys_set_filter:nnn {WithArrows} {secondary} {#1} 
+%    \end{macrocode}
+%
+% \bigskip
+% We process the options given at the \emph{env} level, that is to say in the option of the |{WithArrows}| environment.
+%    \begin{macrocode}
+           \keys_set_groups:nnn {WithArrows} {env} {#1}
+%    \end{macrocode}
+%
+% \bigskip
+% If the user has given a value for the option |CommandName| (at the global or at the \emph{env} level), a command
+% with this name is defined locally in the environment with meaning |\@@_Arrow|. The default value of the option
+% |CommandName| is ``|Arrow|'' and thus, by default, the name of the command will be |\Arrow|.
+%    \begin{macrocode}
+           \cs_set_eq:cN \l_@@_CommandName_tl \@@_Arrow
+%    \end{macrocode}
+%
+% \bigskip
+% The environment begins with a |\vtop|, a |\vcenter| or a |\vbox|\footnote{Notice that the use of
+% \texttt{\string\vtop} seems color-safe here...} depending of the value of |\l_@@_pos_int| (usually fixed by the
+% options |t|, |c| or |b|). The environment |{WithArrows}| must be used in math mode\footnote{An error is raised if
+% the environment is used outside math mode.} and therefore, we can use |\vcenter|.
+%    \begin{macrocode}
+           \int_case:nn \l_@@_pos_int 
+                   {0 {\vtop}
+                    1 {\vcenter}
+                    2 {\vbox}}
+           \bgroup
+%    \end{macrocode}
+%
+% \bigskip
+% The command |\spread@equation| is the command used by \pkg{amsmath} in the beginning of an alignment to fix the
+% interline. When used, it becomes no-op. However, it's possible to use \pkg{witharrows} without \pkg{amsmath}
+% since we have redefined |\spread@equation| (if it is not defined yet). 
+%    \begin{macrocode}
+           \spread@equation
+%    \end{macrocode}
+%
+% \bigskip
+% We begin the |\halign| and the preamble.
+%    \begin{macrocode}
+           \ialign\bgroup
+%    \end{macrocode}
+%
+% \bigskip 
+% We increment the counter |\g_@@_line_int| which will be used in the names of the Tikz nodes created in the array.
+% This incrementation must be global (|gincr|) because we are in the cell of a |\halign|. It's recalled that we
+% manage a stack for this counter.
+%    \begin{macrocode}
+           \int_gincr:N \g_@@_line_int 
+           \strut\hfil
+           $\bool_if:NT \l_@@_displaystyle_bool \displaystyle {##}$
+           & 
+%    \end{macrocode}
+% 
+% \bigskip
+% In the second column, we increment the counter |\g_@@_line_bis_int| because we want to count the lines with a
+% second column and raise an error if there is lines without a second column. Once again, the incrementation must
+% be global and it's recalled that we manage a stack for this counter too.
+%    \begin{macrocode}
+           \int_gincr:N \g_@@_line_bis_int 
+           $\bool_if:NT \l_@@_displaystyle_bool \displaystyle {{}##}$
+%    \end{macrocode}
+%
+% \bigskip
+% We create the ``left node'' of the line (when using macros in Tikz node names, the macros have to be fully
+% expandable : here, |\tl_use:N| and |\int_use:N| are fully expandable).
+%    \begin{macrocode}
+           \tikz[remember~picture] 
+                  \node [@@_node_style] 
+                  (wa-\tl_use:N\l_@@_prefix_tl-\int_use:N\g_@@_line_int-l) {} ;
+           \hfil
+%    \end{macrocode}
+%
+% \bigskip
+% Now, after the |\hfil|, we create the ``right node'' and, if the option |shownodenames| is raised, the name of
+% the node is written in the document (useful for debugging).
+%    \begin{macrocode}
+           \tikz[remember~picture,label~position=right] 
+                  \node [@@_node_style] 
+                  (wa-\tl_use:N\l_@@_prefix_tl-\int_use:N\g_@@_line_int-r) {} ;
+           \bool_if:NT \l_@@_shownodenames_bool
+                {\hbox_overlap_right:n {\small wa-\tl_use:N\l_@@_prefix_tl
+                                                 -\int_use:N\g_@@_line_int}}
+%    \end{macrocode}
+% 
+% \bigskip
+% Usually, the |\halign| of an environment |{WithArrows}| will have exactly two columns. Nevertheless, if the user
+% wants to use more columns (without arrows) it's possible with the option |MoreColumns|.
+%    \begin{macrocode}
+           && \bool_if:NF \l_@@_MoreColumns_bool
+                {\msg_error:nn {witharrows} {Third~column~in~a~{WithArrows}~environment}}
+           $\bool_if:NT \l_@@_displaystyle_bool \displaystyle {##}$
+           \cr
+          }
+%    \end{macrocode}
+%
+% \bigskip
+% We begin the second part of the environment |{WithArrows}|. We have two |\egroup| : one for the |\halign| and
+% one for the |\vtop| (or |\vcenter| or |\vbox|).
+%    \begin{macrocode}
+          {\crcr
+           \egroup 
+           \egroup
+%    \end{macrocode}
+%
+% \bigskip
+% If there is a line without the second column, we raise an error (a line without the second column could generate
+% an \textsc{pgf} error for an unknown node since the nodes are created in the second column).
+%    \begin{macrocode}
+           \int_compare:nNnT \g_@@_line_bis_int < \g_@@_line_int
+                  {\msg_error:nn {witharrows} {All~lines~must~have~an~ampersand}}
+%    \end{macrocode}
+%
+% \bigskip 
+% It there is really arrows in the environment, we draw the arrows with |\@@_draw_arrows:| (a special macro has
+% been written for lisibility of the code). 
+%    \begin{macrocode}
+            \int_compare:nNnT \g_@@_arrow_int > 0 
+                    \@@_draw_arrows:             
+%    \end{macrocode}
+%
+% \bigskip
+% We use |\spewnotes| of \pkg{footnote} to spew the footnotes of the environment (a |\savenotes| has been put at
+% the beginning of the environment).
+%    \begin{macrocode}
+           \spewnotes
+%    \end{macrocode}
+%
+% \bigskip
+% We update the position-in-the-tree. First, we drop the last component and then we increment the last element.
+%    \begin{macrocode}
+           \seq_gpop_right:NN \g_@@_position_in_the_tree_seq \l_tmpa_tl
+           \seq_gpop_right:NN \g_@@_position_in_the_tree_seq \l_tmpa_tl
+           \seq_gput_right:Nx \g_@@_position_in_the_tree_seq {\int_eval:n {\l_tmpa_tl + 1}}
+%    \end{macrocode}
+%
+% \bigskip
+% We update the value of the counter |\g_@@_last_env_int|. This counter is used only by the fonction |\WithArrowsLastEnv|.
+%    \begin{macrocode}
+           \int_compare:nNnT {\seq_count:N \g_@@_position_in_the_tree_seq} = 1
+                      {\int_gincr:N \g_@@_last_env_int}
+%    \end{macrocode}
+%
+% \bigskip
+% Finally, we restore the previous values of the three counters |\g_@@_arrow_int|, |\g_@@_line_int| and
+% |\g_@@_line_bis_int|. It is recalled that we manage three stacks in order to be able to do such a restoration.
+%    \begin{macrocode}
+           \seq_gpop_right:NN \g_@@_stack_counter_arrows_seq {\l_tmpa_tl}
+           \int_gset:Nn \g_@@_arrow_int {\l_tmpa_tl}
+           \seq_gpop_right:NN \g_@@_stack_counter_lines_seq \l_tmpa_tl
+           \int_gset:Nn \g_@@_line_int {\l_tmpa_tl}
+           \seq_gpop_right:NN \g_@@_stack_counter_lines_bis_seq \l_tmpa_tl
+           \int_gset:Nn \g_@@_line_bis_int {\l_tmpa_tl}
+           }
+%    \end{macrocode}
+% That's the end of the environment |{WithArrows}|.
+%
+% \bigskip
+% We give now the definition of |\@@_cr:| which is the definition of |\\| in an environment |{WithArrows}|. The two
+% \pkg{expl3} commands |\group_align_safe_begin:| and |\group_align_safe_end:| are specifically designed for this
+% purpose : test the token that follows in a |\halign| structure.
+%
+% First, we remove an eventual token |*| since the commands |\\| and |\\*| are equivalent in an environment
+% |{WithArrows}| (an environment |{WithArrows}|, like an environment |{aligned}| of \pkg{amsmath} is always unbreakable).
+%    \begin{macrocode}
+\cs_set_protected:Nn \@@_cr:
+      {\scan_stop:
+       \group_align_safe_begin:
+       \peek_meaning_remove:NTF * \@@_cr_i: \@@_cr_i:}
+%    \end{macrocode}
+%
+% \medskip
+% Then, we peek the next token to see if it's a |[|. In this case, the command |\\| has an optional argument which
+% is the vertical skip (=glue) to put.
+%    \begin{macrocode}
+\cs_set_protected:Nn \@@_cr_i:
+      {\peek_meaning:NTF [ {\@@_cr_ii:} {\@@_cr_ii:[\c_zero_dim]} }
+\cs_new_protected:Npn \@@_cr_ii:[#1]
+      {\group_align_safe_end:
+       \cr\noalign{\skip_vertical:n {#1 + \l_@@_interline_skip}
+       \scan_stop:}}
+%    \end{macrocode}
+% According of the documentation of \pkg{expl3}, the previous addition in ``|#1 + \l_@@_interline_skip|'' is really
+% an addition of skips (=glues).
+%
+% \subsection{We draw the arrows}
+%
+% The following code is necessary because we will have to expand an argument exactly 3 times.
+%    \begin{macrocode}
+\cs_generate_variant:Nn \keys_set_groups:nnn {nno}
+\cs_new_protected:Nn \keys_set_groups_WithArrows_local: 
+                     {\keys_set_groups:nno {WithArrows} {local}}
+%    \end{macrocode}
+%
+% \bigskip
+%    \begin{macrocode}
+\cs_generate_variant:Nn \keys_set_filter:nnn {nno}
+\cs_new_protected:Nn \keys_set_filter_WithArrows_secondary: 
+           {\keys_set_filter:nno {WithArrows} {secondary}}
+%    \end{macrocode}
+%
+% \bigskip
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_draw_arrows:
+  { 
+%    \end{macrocode}
+%
+% \medskip
+% If the option |group| is used (for the whole document --- with |\WithArrowsOptions| --- or for the current environment), 
+% we have to compute the $x$-value common to all the arrows. This work is done by the command 
+% |\@@_x_computation_for_option_group:| and the computed $x$-value is store in |\g_@@_x_dim| (we use a global
+% variable for technical reasons).
+%    \begin{macrocode}
+   \bool_if:NT \l_@@_group_bool
+        \@@_x_computation_for_option_group: 
+%    \end{macrocode}
+%
+% \bigskip
+% We begin a loop over the arrows of the environment. The variable |\l_@@_arrow_int| (local in the environment
+% |{WithArrows}|) will be used as index for the loop. The number of arrows in the environment is |\g_@@_arrow_int|.
+% This variable was a counter incremented when an arrows is encountered during the construction of the |\halign|.
+% After the end of the |\halign|, |g_@@_arrow_int| is the number of arrows in the environment.
+%    \begin{macrocode}
+   \int_set:Nn \l_@@_arrow_int 1
+   \int_until_do:nNnn \l_@@_arrow_int > \g_@@_arrow_int 
+     {
+%    \end{macrocode}
+%
+% \bigskip 
+% We extract from the property list of the current arrow the fields ``initial'' and ``final'' and we store these
+% values in |\l_@@_initial_int| and |\l_@@_final_int|. However, we have to do a conversion because the components
+% of a property list are token lists.
+% 
+% \smallskip
+% If the arrow ends after the last line of the environment, we raise an error.
+%    \begin{macrocode}
+      \prop_get:cnN {g_@@_arrow_\l_@@_prefix_tl _\int_use:N\l_@@_arrow_int _prop} 
+                    {initial} \l_tmpa_tl
+      \int_set:Nn \l_@@_initial_int {\l_tmpa_tl}
+      \prop_get:cnN {g_@@_arrow_\l_@@_prefix_tl _\int_use:N\l_@@_arrow_int _prop} 
+                    {final} \l_tmpa_tl
+      \int_set:Nn \l_@@_final_int {\l_tmpa_tl}
+      \int_compare:nNnT \l_@@_final_int > \g_@@_line_int
+             {\msg_error:nn {witharrows} {Too~few~lines~for~an~arrow}}
+%    \end{macrocode}
+%
+% \bigskip
+% We begin an TeX group which will contains the options local to the current arrow. We declare ``undefined'' the
+% key |group| because it's not possible to have a |group| key for an individual arrow.
+%    \begin{macrocode}
+           \group_begin:
+           \keys_define:nn {WithArrows} {group .undefine:}
+           \bool_set_false:N \l_@@_position_key_already_set_bool
+%    \end{macrocode}
+%
+% \bigskip
+% We process the options of the current arrow. The third argument de |\keys_set_groups:nnn| must be expanded exactly
+% three times. An x-expansion is not possible because there can be tokens like |\bfseries| in the option |font| of
+% the option |tikz|. This expansion is a bit tricky.
+%    \begin{macrocode}
+           \prop_get:cnN {g_@@_arrow_\l_@@_prefix_tl 
+                             _\int_use:N\l_@@_arrow_int _prop} {options} \l_tmpa_tl
+           \exp_args:NNo \exp_args:No \keys_set_filter_WithArrows_secondary: {\l_tmpa_tl}
+           \exp_args:NNo \exp_args:No \keys_set_groups_WithArrows_local: {\l_tmpa_tl}
+%    \end{macrocode}
+%
+% \bigskip
+% In case of option |i|, we have to compute the $x$-value of the arrow (which is vertical). This work is done by
+% the command |\@@_x_computation_for_option_i:| and the computed $x$-value is stored in |g_@@_x_dim| (the same
+% variable used when the option |group| is used).
+%    \begin{macrocode}
+           \bool_if:NT \l_@@_i_bool
+               \@@_x_computation_for_option_i: 
+%    \end{macrocode}
+%
+% \bigskip
+% |\l_@@_initial_tl| contains the name of the Tikz node from which the arrow starts (in normal cases...
+% because with option |group| or option |i|, the point will perhaps have an other $x$-value --- but always the
+% same |y|-value). Idem for |\l_@@_final_tl|.
+%    \begin{macrocode}
+           \tl_set:Nx \l_@@_initial_tl 
+                   {wa-\tl_use:N\l_@@_prefix_tl-\int_use:N\l_@@_initial_int-
+                            \bool_if:NTF\l_@@_initial_r_bool rl} 
+           \tl_set:Nx \l_@@_final_tl 
+                   {wa-\tl_use:N\l_@@_prefix_tl-\int_use:N\l_@@_final_int-
+                            \bool_if:NTF\l_@@_final_r_bool rl . north}
+%    \end{macrocode}
+% We use ``|. north|'' because we want a small gap between two consecutive arrows (and the Tikz nodes created have
+% the shape of small vertical segments : use option |shownodes| to visualize the nodes).
+%
+% \bigskip
+% We can now draw the arrow in a |{tikzpicture}| :
+%    \begin{macrocode}
+           \begin{tikzpicture}[remember~picture,
+                               overlay,
+                               align=left,
+                               auto=left,
+                               font = {\small\itshape},
+                               TipsOfWithArrows,
+                               ->,
+                               looseness=1,
+                               bend~left=45]
+%    \end{macrocode}
+%
+% Of course, the arrow is drawn with the command |\draw| of Tikz. The syntax for this command is :
+%
+% \qquad |\draw| $(x_1,y_1)$ |to node| (\textsl{name}) |{|\textsl{contents}|}| $(x_2,y_2)$
+% 
+% The surprising aspect of this syntax is the position of \textsl{contents} which is the label of the arrow.
+%
+% We give a name to the node (\textsl{name} in the previous syntax) but, in fact, we don't use it in the extension
+% |witharrows|.
+%
+% |\p1| and |\p2| are the two ends of the arrow (in fact, if the option |i| or the option |group| is used, it's not
+% exactly the two ends of the arrow because, in this case, this abscissa used is the value previously calculated in
+% |g_@@_x_dim|).
+%
+% The ability to define |\p1| and |\p2| is given by the library |calc| of Tikz. When |\p1| and |\p2| are defined,
+% the $x$-value and $y$-value of these two points can be read in |\x1|, |\x2|, |\y1| and |\y2|. This is the way to
+% have the coordinates of a node defined in Tikz.
+%    \begin{macrocode}
+           \prop_get:cnN {g_@@_arrow_\l_@@_prefix_tl _\int_use:N\l_@@_arrow_int _prop} 
+                         {label} \l_tmpa_tl
+           \draw \exp_after:wN [\l_@@_options_tikz_tl]
+                 let \p1 = (\tl_use:N \l_@@_initial_tl),
+                     \p2 = (\tl_use:N \l_@@_final_tl) in 
+                   (\bool_if:nTF {\l_@@_group_bool || \l_@@_i_bool}
+                     {\dim_use:N \g_@@_x_dim + \dim_use:N \l_@@_xoffset_dim, \y1}
+                     {\x1 + \dim_use:N \l_@@_xoffset_dim, \y1} )
+%    \end{macrocode}
+% There are two ways to give the content of the node : the classical way, with curly braces, and the option ``node
+% contents''. However, both are not strictly equivalent : when |\usetikzlibrary{babel}| is used, the tokens of the
+% contents are rescanned in the first way but not in the second. We don't want the tokens to be rescanned (because
+% this would lead to an error due of the characters |_| and |:| of the \pkg{expl3} syntax) and that's why we use
+% the second method. \footnote{cf. :
+% |tex.stackexchange.com/questions/298177/how-to-get-around-a-problem-with-usetikzlibrarybabel|}
+%    \begin{macrocode}
+                   to node [node~contents = {\tl_use:N \l_tmpa_tl}] {}
+                   (\bool_if:nTF {\l_@@_group_bool || \l_@@_i_bool}
+                     {\dim_use:N \g_@@_x_dim + \dim_use:N \l_@@_xoffset_dim, \y2}
+                     {\x2 + \dim_use:N \l_@@_xoffset_dim, \y2} ) ; 
+           \end{tikzpicture}
+%    \end{macrocode}
+%
+% \smallskip
+% We close the TeX group opened for the options given to |\Arrow[...]| (local level of the options).
+%    \begin{macrocode}
+       \group_end: 
+       \int_incr:N \l_@@_arrow_int
+      } 
+     }
+%    \end{macrocode}
+%
+% \bigskip
+% We want to compute the $x$-value for the current arrow which has option |i| (and therefore is vertical).
+% This value will be computed in |\g_@@_x_dim| (which is global for technical reasons : we have to do assignments in
+% a Tikz command). 
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_x_computation_for_option_i:
+  {\dim_gzero_new:N \g_@@_x_dim
+%    \end{macrocode}
+% 
+% \medskip
+% First, we calculate the initial value for |\g_@@_x_dim|. In this loop, we use a Tikz command, but, in fact,
+% nothing is drawn. We use this Tikz command only to read the abscissa of a Tikz node.
+%    \begin{macrocode}
+   \tikz[remember~picture]
+      \path let \p1 = (wa-\tl_use:N\l_@@_prefix_tl-\int_use:N\l_@@_initial_int-l)
+            in \pgfextra {\dim_gset:Nn \g_@@_x_dim {\x1}} ;
+%    \end{macrocode}
+% A global assignment is necessary because of Tikz.
+%
+% Then, we will loop to determine the maximal length of all the lines between the lines |\l_@@_initial_int| and
+% |\l_@@_final_int|... but we have written a command dedicated to this work because it will also be used in 
+% |\@@_x_computation_for_option_group:|
+%    \begin{macrocode}
+   \@@_x_computation_analyze_lines_between:
+   }
+%    \end{macrocode}
+%
+%
+% \bigskip
+% The command |\@@_x_computation_analyze_lines_between:| will analyse the lines between between |\l_@@_initial_int|
+% and |\l_@@_final_int| in order to modify |\g_@@_x_dim| in consequence. More precisely, we will increase
+% |\g_@@_x_dim| if we find a line longer than the current value of |\g_@@_x_dim|.
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_x_computation_analyze_lines_between:
+    {\int_compare:nNnT \l_@@_final_int > \g_@@_line_int
+             {\msg_error:nn {witharrows} {Too~few~lines~for~an~arrow}}
+%    \end{macrocode}
+%
+% We begin a loop with |\l_tmpa_int| as index. In this loop, we use a Tikz command, but, in fact, nothing is drawn.
+% We use this Tikz command only to read the abscissa of a Tikz node.
+%    \begin{macrocode}
+     \int_set:Nn \l_tmpa_int \l_@@_initial_int
+     \int_until_do:nNnn \l_tmpa_int > \l_@@_final_int
+         {\tikz[remember~picture]
+             \path let \p1 = (wa-\tl_use:N\l_@@_prefix_tl-\int_use:N\l_tmpa_int-l) 
+                   in \pgfextra {\dim_gset:Nn \g_@@_x_dim {\dim_max:nn \g_@@_x_dim {\x1}}} ;
+          \int_incr:N \l_tmpa_int
+         }
+    }   
+%    \end{macrocode}
+%
+%
+% \bigskip
+% We want to compute the $x$-value for the current environment which has option |group| (and therefore all arrows are
+% vertical at the same abscissa). Once again, the value will be computed in |\g_@@_x_dim|.
+%
+%    \begin{macrocode}
+\cs_new_protected:Nn \@@_x_computation_for_option_group:
+  {\dim_gzero_new:N \g_@@_x_dim
+%    \end{macrocode}
+% 
+% \medskip
+% First, we calculate the initial value for |\g_@@_x_dim|. In this loop, we use a Tikz command, but, once again,
+% nothing is drawn. We use this Tikz command only to read the abscissa of a Tikz node.
+%    \begin{macrocode}
+   \prop_get:cnN {g_@@_arrow_\l_@@_prefix_tl _1_prop} {initial} \l_tmpa_tl
+   \tikz[remember~picture]
+      \path let \p1 = (wa-\tl_use:N\l_@@_prefix_tl-\tl_use:N\l_tmpa_tl-l)   
+            in \pgfextra {\dim_gset:Nn \g_@@_x_dim {\x1}} ; 
+%    \end{macrocode}
+% A global assignment is necessary because of Tikz.
+%
+% Then, we loop to determine the maximal length of all the lines concerned by the arrows of the environment.
+%    \begin{macrocode}
+   \int_set:Nn \l_@@_arrow_int 1
+   \int_until_do:nNnn \l_@@_arrow_int > \g_@@_arrow_int
+      { 
+%    \end{macrocode}
+% \smallskip
+% |\l_@@_initial_int| is the line number from which the arrow starts and |\l_@@_final_int| is the line number to which
+% the arrow ends.
+%    \begin{macrocode}
+        \prop_get:cnN {g_@@_arrow_\l_@@_prefix_tl _\int_use:N\l_@@_arrow_int _prop} 
+                      {initial} \l_tmpa_tl
+        \int_set:Nn \l_@@_initial_int {\l_tmpa_tl}
+        \prop_get:cnN {g_@@_arrow_\l_@@_prefix_tl _\int_use:N\l_@@_arrow_int _prop} 
+                      {final} \l_tmpa_tl
+        \int_set:Nn \l_@@_final_int {\l_tmpa_tl}
+%    \end{macrocode}
+% 
+% \smallskip
+% |\@@_x_computation_analyze_lines_between:| will compute between lines |\l_@@_initial_int| and |\l_@@_final_int|.
+%    \begin{macrocode}
+        \@@_x_computation_analyze_lines_between:
+        \int_incr:N \l_@@_arrow_int
+      }
+   }   
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\cs_generate_variant:Nn \int_compare:nNnT {cNnT}
+\cs_generate_variant:Nn \tl_if_eq:nnF {noF}
+%    \end{macrocode}
+%
+%
+\bigskip
+% The command |\WithArrowsLastEnv| is not used by the package \pkg{witharrows}. It's only a facility given to the
+% final user. It gives the number of the last environment |{WithArrows}| at level~$0$. This macro is fully
+% expandable and, thus, can be used directly in the name of a Tikz node.
+%    \begin{macrocode}
+\NewDocumentCommand \WithArrowsLastEnv {}
+     {\int_use:N \g_@@_last_env_int}
+%    \end{macrocode}
+%
+% \subsection{The error messages of the package}
+%    \begin{macrocode}          
+\msg_new:nnn {witharrows}
+             {Third~column~in~a~{WithArrows}~environment}
+             {By~default,~a~\{WithArrows\}~environment~can~only~have~two~columns.~
+              Maybe~you~have~forgotten~a~newline~symbol.~If~you~really~want~
+              more~than~two~columns,~you~should~use~the~option~"MoreColumns"~at~
+              a~global~level~or~for~an~environment.~However,~you~can~go~one~for~this~time.}
+%    \end{macrocode}
+%             
+%    \begin{macrocode}          
+\msg_new:nnn {witharrows}
+             {Arrow~used~outside~{WithArrows}~environment}
+             {The~command~\string\Arrow\space~should~be~used~only~directly~
+              in~\{WithArrows\}~environment~and~not~in~a~subenvironment.~However,~you~
+              can~go~on.}
+%    \end{macrocode}
+%
+%    \begin{macrocode}          
+\msg_new:nnn {witharrows}
+             {The~option~"jump"~must~be~non~negative}
+             {You~can't~use~a~strictly~negative~value~for~the~option~"jump"~of~command~
+              \string\Arrow.~ You~can~create~an~arrow~going~backwards~with~
+              the~option~"<-"~of~Tikz.}
+%    \end{macrocode}
+%
+%    \begin{macrocode}          
+\msg_new:nnn {witharrows}          
+             {Too~few~lines~for~an~arrow}
+             {There~is~at~least~an~arrow~that~can't~be~drawn~because~it~arrives~after~the~
+              last~line~of~the~environment.}
+%    \end{macrocode}
+%
+%    \begin{macrocode}          
+\msg_new:nnn {witharrows}
+             {{WithArrows}~used~outside~math~mode}
+             {The~environment~\{WithArrows\}~should~be~used~only~in~math~mode.~
+              Nevertheless,~you~can~go~on.}
+%    \end{macrocode}
+%
+%    \begin{macrocode}          
+\msg_new:nnn {witharrows}
+             {Option~incompatible~with~group}
+             {You~try~to~use~the~option~"\tl_use:N\l_keys_key_tl"~while~
+              you~are~using~the~option~"group".~It's~incompatible.~You~can~go~on~ignoring~
+              this~option~"\tl_use:N\l_keys_key_tl"~and~"group"~will~be~used.}
+%    \end{macrocode}
+%
+%    \begin{macrocode}          
+\msg_new:nnn {witharrows}
+             {Two~options~are~incompatible}
+             {You~try~to~use~the~option~"\tl_use:N\l_keys_key_tl"~but~
+             this~option~is~incompatible~with~an~option~previously~set.~
+             If~you~go~on,~I~will~overwrite~the~previous~option.}
+%    \end{macrocode}
+%
+%    \begin{macrocode}          
+\msg_new:nnnn {witharrows}
+              {All~lines~must~have~an~ampersand}
+              {All~lines~of~an~environment~\{WithArrows\}~must~have~an~second~column~
+               (because~the~nodes~are~created~in~the~second~column).~You~can~go~on~but~maybe~
+               you~will~have~an~pgf~error~for~an~undefined~shape.}
+              {The~ampersand~can~be~implicit~
+               (e.g.~if~you~use~\string\MoveEqLeft\space~of~mathtools).}
+%    \end{macrocode}
+%
+%
+% \section{History}
+%
+% \subsection{Changes between versions 1.0 and 1.1}
+% 
+% Option for the command |\\| and option |interline|
+% 
+% Compatibility with |\usetikzlibrary{babel}|
+%
+% Possibility of nested environments |{WithArrows}|
+% 
+% Better error messages 
+% 
+% Creation of a \textsc{dtx} file
+% \endinput
+%
+% Local Variables:
+% TeX-fold-mode: nil
+% End:
diff --git a/Master/texmf-dist/source/latex/witharrows/witharrows.ins b/Master/texmf-dist/source/latex/witharrows/witharrows.ins
new file mode 100644
index 00000000000..8e3a891c4dc
--- /dev/null
+++ b/Master/texmf-dist/source/latex/witharrows/witharrows.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/witharrows}
+\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{witharrows.sty}{\from{witharrows.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 witharrows.sty}
+\Msg{*}
+\Msg{* To produce the documentation run the file witharrows.dtx}
+\Msg{* through XeLaTeX.}
+\Msg{*}
+\Msg{* Happy TeXing!}
+\Msg{*********************************************************}
+\endbatchfile
+
diff --git a/Master/texmf-dist/tex/latex/witharrows/witharrows.sty b/Master/texmf-dist/tex/latex/witharrows/witharrows.sty
index c3bd9a31d67..5f9619ed32c 100644
--- a/Master/texmf-dist/tex/latex/witharrows/witharrows.sty
+++ b/Master/texmf-dist/tex/latex/witharrows/witharrows.sty
@@ -1,341 +1,328 @@
-% This work may be distributed and 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://mirrors.ctan.org/help/Catalogue/licenses.lppl.html
-% and version 1.3 or later is part of all distributions of LaTeX
-% version 2005/12/01 or later.
-
-
-% The author of this work is F. Pantigny (fpantigny at wanadoo point fr)
-
-\NeedsTeXFormat{LaTeX2e}[1994/06/01]
-
-
+%%
+%% This is file `witharrows.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% witharrows.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{1.1}
+\def\myfiledate{2017/11/06}
 \RequirePackage{l3keys2e}
-
 \ProvidesExplPackage
-  {WithArrows}
-  {2017/08/09}
-  {1.0}
-  {Draws arrows for explanations on the right side of a alignment.} 
-
-
+  {witharrows}
+  {\myfiledate}
+  {\myfileversion}
+  {Draws arrows for explanations on the right}
 \RequirePackage{expl3}
 \RequirePackage{xparse}
-
 \RequirePackage{tikz}
-\usetikzlibrary{calc}
-\usetikzlibrary{arrows.meta}
-\usetikzlibrary{bending}
-
-
-
+\usetikzlibrary{calc,arrows.meta,bending}
 \RequirePackage{footnote}
-
-
-
-% There is a style for the tips of arrow because someone will use this style
-% if he wants draw an arrow directly with a Tikz command in his document (probably using the Tikz nodes created by
-% {WithArrows} in the \halign.
-\tikzset{TipsOfWithArrows/.style= { > = {Straight~Barb[scale=1.2,bend]}} }
-
-
-% The following variables are for the options ; these options can be set at 3 levels : see the groups of keys defined in
-% the \keys_define:nn comand below.
-
-% if the beginning of the arrow use a "r" option (if not, it's a "l" option)
-\bool_new:N \l_wa_initial_r_bool
-\bool_set_true:N \l_wa_initial_r_bool
-
-% if the end of the arrow use a "r" option (if not, it's à "l" option)
-\bool_new:N \l_wa_final_r_bool
-\bool_set_true:N \l_wa_final_r_bool
-
-% if the arrow use a "i" option (in this case the options "l" and "r" for the ends are meaningless)
-\bool_new:N \l_wa_i_bool
-\bool_set_false:N \l_wa_i_bool
-
-% to translate the whole arrow to the right
-\dim_new:N \l_wa_xoffset_dim 
-\dim_set:Nn \l_wa_xoffset_dim {3mm}
-
-% to indicate if the nodes will be drawn (in red) ; useful only for debugging
-\bool_new:N \l_wa_shownodes_bool
-\bool_set_false:N \l_wa_shownodes_bool
-
-% to indiate if the elements of the \halign will be composed with \displaystyle
-\bool_new:N \l_wa_displaystyle_bool
-\bool_set_false:N \l_wa_displaystyle_bool
-
-% will contains the Tikz options used to draw the arrow
-\tl_clear_new:N \l_wa_options_tikz_tl
-% At each possible level for the options ("global", "env" or "local : see below), the new values will be appended
-% on the right of the token list \l_wa_options_tikz_tl
-
-% will be raised when a key controling position of the arrow has been set in the same list of key
-% useful in order to raise an error if 2 incompatibles keys are specified at the same level
-\bool_new:N \l_wa_position_key_already_set_bool
-\bool_set_false:N \l_wa_position_key_already_set_bool
-
-% This Tikz style is for the nodes created automatically in the \halign.
-\tikzstyle{wa_node_style}=[rectangle,
+\tikzstyle{__wa_node_style}=[rectangle,
                            inner~sep = 0 pt,
                            minimum~height = 3 pt,
                            minimum~width = 0pt,
-                           red,  % red... but will be drawn only if shownodes=true
-                           \bool_if:NT \l_wa_shownodes_bool {draw}]
-
-
-
-% There are 3 levels where keys can be set :
-% with \WithArrowsOptions{...} : this level will be called "global" level ;
-% with \begin{WithArrows}[...] : this level will be called "env" level ;
-% with \Arrow[...] : this level will be called "local" level.
-
-% That's why there is 3 groups of keys named "global", "env" and "local".
-
-% Before each \keys_set_groups:nnn, we execute a \keys_set_filter:nnn with group "secondary"
-% Thus, an unknown key will raise an error. Furthermore, the "primary" keys (those which are not in the 
-% group "secondary") will be set first : it's useful to raise an error if, for example, keys "i" and "group"
-% are set at the same level (which is incoherent).
-
-% There is also the group named "jump" (with only one key : "jump") for technical reasons.
-\keys_define:nn {WithArrows} 
-    { % the key named "jump" will be extracted in the \Arrow command 
-      jump     .groups:n          = {jump,secondary},
-      jump     .code:n            = {\int_set:Nn \l_jump_int {#1}
-                                     \int_compare:nNnF \l_jump_int > 0
-                                         {\msg_error:nn {WithArrows} {The~option~"jump"~must~be~non~negative}}},
-      jump     .value_required:n  = true,
-      %
-      % 0 = t = \vtop , 1 = c = \vcenter, 2 = b = \vbox
-      pos         .groups:n         = {global,env,secondary},
-      pos         .int_set:N        = \l_wa_pos_int,
-      pos         .initial:n        = 0,
-      pos         .value_required:n = true,
-      %
-      t           .groups:n         = {global,env,kown},
-      t           .meta:n           = {pos=0},
-      c           .groups:n         = {global,env,kown},
-      c           .meta:n           = {pos=1},
-      b           .groups:n         = {global,env,kown},
-      b           .meta:n           = {pos=2},
-      %
-      % if the user wants to give a new name to the \Arrow command (and the name \Arrow remains free)
+                           red,
+                           \bool_if:NT \l__wa_shownodes_bool {draw}]
+\tikzset{TipsOfWithArrows/.style= { > = {Straight~Barb[scale=1.2,bend]}} }
+\cs_if_free:NT \spread@equation
+    {\cs_set:Npn \spread@equation{\openup\jot
+                                  \cs_set_eq:NN \spread@equation \prg_do_nothing}}
+\seq_new:N \g__wa_position_in_the_tree_seq
+\seq_gput_right:Nn \g__wa_position_in_the_tree_seq 1
+\int_new:N \g__wa_last_env_int
+\skip_new:N \l__wa_interline_skip
+\bool_new:N \l__wa_MoreColumns_bool
+\int_new:N \l__wa_pos_int
+\bool_new:N \l__wa_initial_r_bool
+\bool_set_true:N \l__wa_initial_r_bool
+\bool_new:N \l__wa_final_r_bool
+\bool_set_true:N \l__wa_final_r_bool
+\bool_new:N \l__wa_i_bool
+\dim_new:N \l__wa_xoffset_dim
+\dim_set:Nn \l__wa_xoffset_dim {3mm}
+\bool_new:N \l__wa_shownodes_bool
+\bool_new:N \l__wa_shownodenames_bool
+\bool_new:N \l__wa_displaystyle_bool
+\tl_clear_new:N \l__wa_options_tikz_tl
+\bool_new:N \l__wa_position_key_already_set_bool
+\seq_new:N \g__wa_stack_counter_arrows_seq
+\int_new:N \g__wa_arrow_int
+\seq_new:N \g__wa_stack_counter_lines_seq
+\int_new:N \g__wa_line_int
+\seq_new:N \g__wa_stack_counter_lines_bis_seq
+\int_new:N \g__wa_line_bis_int
+
+\keys_define:nn {WithArrows}
+    { jump  .groups:n   = {jump,secondary},
+      jump  .code:n     = {\int_set:Nn \l__wa_jump_int {#1}
+                           \int_compare:nNnF \l__wa_jump_int > 0
+                               {\msg_error:nn {witharrows}
+                                              {The~option~"jump"~must~be~non~negative}}},
+      jump  .value_required:n  = true,
+      t   .groups:n          = {global,env,secondary},
+      t   .code:n            = {\int_set:Nn \l__wa_pos_int 0},
+      t   .value_forbidden:n = true,
+      c   .groups:n          = {global,env,secondary},
+      c   .code:n            = {\int_set:Nn \l__wa_pos_int 1},
+      c   .value_forbidden:n = true,
+      b   .groups:n          = {global,env,secondary},
+      b   .code:n            = {\int_set:Nn \l__wa_pos_int 2},
+      b   .value_forbidden:n = true,
+      MoreColumns .groups:n          = {global,env,secondary},
+      MoreColumns .bool_set:N        = \l__wa_MoreColumns_bool,
+      MoreColumns .default:n         = true,
+      MoreColumns .value_forbidden:n = true,
       CommandName .groups:n         = {global,env,secondary},
-      CommandName .tl_set:N         = \l_wa_CommandName_tl,
+      CommandName .tl_set:N         = \l__wa_CommandName_tl,
       CommandName .initial:n        = {Arrow},
       CommandName .value_required:n = true,
-      %
       displaystyle .groups:n          = {global,env,secondary},
-      displaystyle .bool_set:N        = \l_wa_displaystyle_bool,
-      displaystyle .value_forbidden:n = true,
-      %
+      displaystyle .bool_set:N        = \l__wa_displaystyle_bool,
       %
       shownodes .groups:n          = {global,env,secondary},
-      shownodes .bool_set:N        = \l_wa_shownodes_bool,
+      shownodes .bool_set:N        = \l__wa_shownodes_bool,
       shownodes .default:n         = true,
-      shownodes .value_forbidden:n = true, 
-      %
-      jot       .groups:n          = {env,secondary},  % don't put "global"
-      jot       .dim_set:N         = \jot, % \jot is a LaTeX parameter for the distance between 2 lines in displaymath
+      shownodenames .groups:n          = {global,env,secondary},
+      shownodenames .bool_set:N        = \l__wa_shownodenames_bool,
+      shownodenames .default:n         = true,
+      jot       .groups:n          = {env,secondary},
+      jot       .dim_set:N         = \jot,
       jot       .value_required:n  = true,
-      %
+      interline   .groups:n         = {env,secondary},
+      interline   .skip_set:N       = \l__wa_interline_skip,
+      interline   .initial:n        = \c_zero_skip,
+      interline   .value_required:n = true,
       xoffset  .groups:n          = {global,env,local,secondary},
-      xoffset  .dim_set:N         = \l_wa_xoffset_dim,
-      xoffset  .value_required:n  = true,           
-      %
+      xoffset  .dim_set:N         = \l__wa_xoffset_dim,
+      xoffset  .value_required:n  = true,
       tikz     .groups:n          = {global,env,local,secondary},
-      tikz     .code:n            = {\tl_put_right:Nn \l_wa_options_tikz_tl {,#1}},
+      tikz     .code:n            = {\tl_put_right:Nn \l__wa_options_tikz_tl {,#1}},
       tikz     .value_required:n  = true,
-      %
       ll       .groups:n          = {global,env,local,secondary},
-      ll       .value_forbidden:n = true, 
+      ll       .value_forbidden:n = true,
       ll       .default:n         = true,
-      ll       .code:n            = {\bool_if:NT \l_wa_position_key_already_set_bool
-                                       {\msg_error:nn {WithArrows} {Two~options~are~incompatible}}
-                                     \bool_if:NT \l_wa_group_bool
-                                       {\msg_error:nn {WithArrows} {Option~incompatible~with~group}}
-                                     \bool_set_true:N \l_wa_position_key_already_set_bool
-                                     \bool_set_false:N \l_wa_initial_r_bool
-                                     \bool_set_false:N \l_wa_final_r_bool
-                                     \bool_set_false:N \l_wa_i_bool },
-      %
+      ll       .code:n            = {\bool_if:NT \l__wa_position_key_already_set_bool
+                                       {\msg_error:nn {witharrows}
+                                                      {Two~options~are~incompatible}}
+                                     \bool_if:NT \l__wa_group_bool
+                                       {\msg_error:nn {witharrows}
+                                                      {Option~incompatible~with~group}}
+                                     \bool_set_true:N \l__wa_position_key_already_set_bool
+                                     \bool_set_false:N \l__wa_initial_r_bool
+                                     \bool_set_false:N \l__wa_final_r_bool
+                                     \bool_set_false:N \l__wa_i_bool },
       lr       .groups:n          = {global,env,local,secondary},
       lr       .value_forbidden:n = true,
-      lr       .default:n         = true, 
-      lr       .code:n            = {\bool_if:NT \l_wa_position_key_already_set_bool
-                                       {\msg_error:nn {WithArrows} {Two~options~are~incompatible}}
-                                     \bool_if:NT \l_wa_group_bool
-                                       {\msg_error:nn {WithArrows} {Option~incompatible~with~group}}
-                                     \bool_set_true:N \l_wa_position_key_already_set_bool
-                                     \bool_set_false:N \l_wa_initial_r_bool
-                                     \bool_set_true:N  \l_wa_final_r_bool
-                                     \bool_set_false:N \l_wa_i_bool},
-      %
+      lr       .default:n         = true,
+      lr       .code:n            = {\bool_if:NT \l__wa_position_key_already_set_bool
+                                       {\msg_error:nn {witharrows}
+                                                      {Two~options~are~incompatible}}
+                                     \bool_if:NT \l__wa_group_bool
+                                       {\msg_error:nn {witharrows}
+                                                      {Option~incompatible~with~group}}
+                                     \bool_set_true:N \l__wa_position_key_already_set_bool
+                                     \bool_set_false:N \l__wa_initial_r_bool
+                                     \bool_set_true:N  \l__wa_final_r_bool
+                                     \bool_set_false:N \l__wa_i_bool},
       rl       .groups:n          = {global,env,local,secondary},
       rl       .value_forbidden:n = true,
-      rl       .default:n         = true, 
-      rl       .code:n            = {\bool_if:NT \l_wa_position_key_already_set_bool
-                                       {\msg_error:nn {WithArrows} {Two~options~are~incompatible}}
-                                     \bool_if:NT \l_wa_group_bool
-                                       {\msg_error:nn {WithArrows} {Option~incompatible~with~group}}
-                                     \bool_set_true:N \l_wa_position_key_already_set_bool
-                                     \bool_set_true:N  \l_wa_initial_r_bool
-                                     \bool_set_false:N \l_wa_final_r_bool
-                                     \bool_set_false:N \l_wa_i_bool},
-      %
+      rl       .default:n         = true,
+      rl       .code:n            = {\bool_if:NT \l__wa_position_key_already_set_bool
+                                       {\msg_error:nn {witharrows}
+                                                      {Two~options~are~incompatible}}
+                                     \bool_if:NT \l__wa_group_bool
+                                       {\msg_error:nn {witharrows}
+                                                      {Option~incompatible~with~group}}
+                                     \bool_set_true:N \l__wa_position_key_already_set_bool
+                                     \bool_set_true:N  \l__wa_initial_r_bool
+                                     \bool_set_false:N \l__wa_final_r_bool
+                                     \bool_set_false:N \l__wa_i_bool},
       rr       .groups:n          = {global,env,local,secondary},
       rr       .value_forbidden:n = true,
-      rr       .default:n         = true, 
-      rr       .code:n            = {\bool_if:NT \l_wa_position_key_already_set_bool
-                                       {\msg_error:nn {WithArrows} {Two~options~are~incompatible}}
-                                     \bool_if:NT \l_wa_group_bool
-                                       {\msg_error:nn {WithArrows} {Option~incompatible~with~group}}
-                                     \bool_set_true:N \l_wa_position_key_already_set_bool
-                                     \bool_set_true:N  \l_wa_initial_r_bool
-                                     \bool_set_true:N  \l_wa_final_r_bool
-                                     \bool_set_false:N  \l_wa_i_bool},
-      %
+      rr       .default:n         = true,
+      rr       .code:n            = {\bool_if:NT \l__wa_position_key_already_set_bool
+                                       {\msg_error:nn {witharrows}
+                                                      {Two~options~are~incompatible}}
+                                     \bool_if:NT \l__wa_group_bool
+                                       {\msg_error:nn {witharrows}
+                                                      {Option~incompatible~with~group}}
+                                     \bool_set_true:N \l__wa_position_key_already_set_bool
+                                     \bool_set_true:N  \l__wa_initial_r_bool
+                                     \bool_set_true:N  \l__wa_final_r_bool
+                                     \bool_set_false:N  \l__wa_i_bool},
       i        .groups:n          = {global,env,local,secondary},
-      i        .code:n            = {\bool_if:NT \l_wa_position_key_already_set_bool
-                                       {\msg_error:nn {WithArrows} {Two~options~are~incompatible}}
-                                     \bool_if:NT \l_wa_group_bool
-                                       {\msg_error:nn {WithArrows} {Option~incompatible~with~group}}
-                                     \bool_set_true:N \l_wa_position_key_already_set_bool
-                                     \bool_set_true:N \l_wa_i_bool},
+      i        .code:n            = {\bool_if:NT \l__wa_position_key_already_set_bool
+                                       {\msg_error:nn {witharrows}
+                                                      {Two~options~are~incompatible}}
+                                     \bool_if:NT \l__wa_group_bool
+                                       {\msg_error:nn {witharrows}
+                                                      {Option~incompatible~with~group}}
+                                     \bool_set_true:N \l__wa_position_key_already_set_bool
+                                     \bool_set_true:N \l__wa_i_bool},
       i        .value_forbidden:n = true,
       i        .default:n         = true,
-      %
-      % indicate if all the arrows of an environment are grouped
-      % volontary not in "secondary" group : thus, if will be set first during the \keys_set_filter:nnn
-      group        .groups:n          = {global,env},   
-      group        .bool_set:N        = \l_wa_group_bool,
+      group        .groups:n          = {global,env},
+      group        .bool_set:N        = \l__wa_group_bool,
       group        .value_forbidden:n = true
 }
-
-
-
-
-
 \ProcessKeysOptions {WithArrows}
-
-
-% \WithArrowsOptions is the command of the WithArrows package to fix options at the document level
 \NewDocumentCommand \WithArrowsOptions {m}
-    {\bool_set_false:N \l_wa_position_key_already_set_bool
-     \keys_set_filter:nnn {WithArrows} {secondary} {#1}   % in order to raise an error if a key is unknown
+    {\bool_set_false:N \l__wa_position_key_already_set_bool
+     \keys_set_filter:nnn {WithArrows} {secondary} {#1}
      \keys_set_groups:nnn {WithArrows} {global} {#1}}
-
-
-
+\NewDocumentCommand \__wa_Arrow {O{} m O{}}
+         {\tl_if_eq:noF {WithArrows} {\@currenvir}
+                  {\msg_error:nn {witharrows} {Arrow~used~outside~{WithArrows}~environment}}
+          \int_gincr:N \g__wa_arrow_int
+          \int_zero_new:N \l__wa_jump_int
+          \int_set:Nn \l__wa_jump_int 1
+          \keys_set_groups:nnn {WithArrows} {jump} {#1,#3}
+          \prop_put:NnV \l_tmpa_prop {initial} \g__wa_line_int
+          \int_set:Nn \l_tmpa_int {\g__wa_line_int + \l__wa_jump_int}
+          \prop_put:NnV \l_tmpa_prop {final} \l_tmpa_int
+          \prop_put:Nnn \l_tmpa_prop {options} {#1,#3}
+          \prop_put:Nnn \l_tmpa_prop {label} {#2}
+          \prop_gclear_new:c
+                {g__wa_arrow_\l__wa_prefix_tl _\int_use:N\g__wa_arrow_int _prop}
+          \prop_gset_eq:cN
+                {g__wa_arrow_\l__wa_prefix_tl _\int_use:N\g__wa_arrow_int _prop}
+                \l_tmpa_prop
+          }
 \NewDocumentEnvironment {WithArrows} {O{}}
-          {\reverse_if:N \if_mode_math:
-                             \msg_error:nn {WithArrows} {WithArrows~used~outside~math~mode}
+         { \seq_gput_right:NV \g__wa_stack_counter_arrows_seq \g__wa_arrow_int
+           \int_gzero:N \g__wa_arrow_int
+           \seq_gput_right:NV \g__wa_stack_counter_lines_seq \g__wa_line_int
+           \int_gzero:N \g__wa_line_int
+           \seq_gput_right:NV \g__wa_stack_counter_lines_bis_seq \g__wa_line_bis_int
+           \int_gzero:N \g__wa_line_bis_int
+           \seq_gput_right:Nn \g__wa_position_in_the_tree_seq 1
+           \seq_set_eq:NN \l_tmpa_seq \g__wa_position_in_the_tree_seq
+           \seq_pop_right:NN \l_tmpa_seq \l_tmpa_tl
+           \tl_clear_new:N \l__wa_prefix_tl
+           \tl_set:Nx \l__wa_prefix_tl {\seq_use:Nnnn \l_tmpa_seq {-} {-} {-}}
+
+           \reverse_if:N \if_mode_math:
+                             \msg_error:nn {witharrows} {{WithArrows}~used~outside~math~mode}
                          \fi
-           \savenotes % to extract the footnotes of the environment {WithArrows}
-           \m@th                
-           \def\\{\cr}
-           %
-           \int_gzero_new:N \g_wa_line_int  % to count the lines in the \halign 
-           %
-           % to count the arrows created in the environment
-           \int_gzero_new:N \g_wa_arrow_int 
-           %
-           % these 3 counters will be used later as variables
-           \int_zero_new:N \l_initial_int
-           \int_zero_new:N \l_final_int
-           \int_zero_new:N \l_arrow_int
-           % 
-           \bool_set_false:N \l_wa_position_key_already_set_bool
-           \keys_set_filter:nnn {WithArrows} {secondary} {#1} % in order to raise an error if a key is unknown
+           \savenotes
+           \cs_set_eq:NN \\ \__wa_cr:
+           \mathsurround = \c_zero_dim
+           \int_zero_new:N \l__wa_initial_int
+           \int_zero_new:N \l__wa_final_int
+           \int_zero_new:N \l__wa_arrow_int
+           \bool_set_false:N \l__wa_position_key_already_set_bool
+           \skip_zero:N \l__wa_interline_skip
+           \keys_set_filter:nnn {WithArrows} {secondary} {#1}
            \keys_set_groups:nnn {WithArrows} {env} {#1}
-           %
-           \cs_set:cpn \l_wa_CommandName_tl {\wa_Arrow} % new name for \Arrow command in {WithArrows} environments
-           %
-           \int_case:nnF \l_wa_pos_int % is fixed via the options t, c or b
+           \cs_set_eq:cN \l__wa_CommandName_tl \__wa_Arrow
+           \int_case:nn \l__wa_pos_int
                    {0 {\vtop}
                     1 {\vcenter}
                     2 {\vbox}}
-                   {\msg_error:nn {WithArrows} {Bad~value~for~option~pos}}
            \bgroup
-           \openup\jot
+           \spread@equation
            \ialign\bgroup
-           \int_gincr:N \g_wa_line_int % will be used for the names of the 2 nodes of the line
+           \int_gincr:N \g__wa_line_int
            \strut\hfil
-           $\bool_if:NT \l_wa_displaystyle_bool \displaystyle {##}$
-           & 
-           $\bool_if:NT \l_wa_displaystyle_bool \displaystyle {{}##}$
-           %
-           % we create a first node (the "left node" of the line)
-           \tikz[remember~picture] 
-                  \node [wa_node_style] (wa-\int_use:N\g_wa_line_int-l) {} ;
+           $\bool_if:NT \l__wa_displaystyle_bool \displaystyle {##}$
+           &
+           \int_gincr:N \g__wa_line_bis_int
+           $\bool_if:NT \l__wa_displaystyle_bool \displaystyle {{}##}$
+           \tikz[remember~picture]
+                  \node [__wa_node_style]
+                  (wa-\tl_use:N\l__wa_prefix_tl-\int_use:N\g__wa_line_int-l) {} ;
            \hfil
-           % we create a second node (the "right node" of the line)
-           \tikz[remember~picture] 
-                  \node [wa_node_style] (wa-\int_use:N\g_wa_line_int-r) {} ;
+           \tikz[remember~picture,label~position=right]
+                  \node [__wa_node_style]
+                  (wa-\tl_use:N\l__wa_prefix_tl-\int_use:N\g__wa_line_int-r) {} ;
+           \bool_if:NT \l__wa_shownodenames_bool
+                {\hbox_overlap_right:n {\small wa-\tl_use:N\l__wa_prefix_tl
+                                                 -\int_use:N\g__wa_line_int}}
+           && \bool_if:NF \l__wa_MoreColumns_bool
+                {\msg_error:nn {witharrows} {Third~column~in~a~{WithArrows}~environment}}
+           $\bool_if:NT \l__wa_displaystyle_bool \displaystyle {##}$
            \cr
           }
-          {\crcr % 
-           \egroup% end of halign
-           \egroup% end of vtop (or \vcenter or \vbox)
-           %
-           \int_compare:nNnT \g_wa_arrow_int > 0   % If there is really arrows...
-                    \wa_draw_arrows:               % ...we draw these arrows.
+          {\crcr
+           \egroup
+           \egroup
+           \int_compare:nNnT \g__wa_line_bis_int < \g__wa_line_int
+                  {\msg_error:nn {witharrows} {All~lines~must~have~an~ampersand}}
+            \int_compare:nNnT \g__wa_arrow_int > 0
+                    \__wa_draw_arrows:
            \spewnotes
+           \seq_gpop_right:NN \g__wa_position_in_the_tree_seq \l_tmpa_tl
+           \seq_gpop_right:NN \g__wa_position_in_the_tree_seq \l_tmpa_tl
+           \seq_gput_right:Nx \g__wa_position_in_the_tree_seq {\int_eval:n {\l_tmpa_tl + 1}}
+           \int_compare:nNnT {\seq_count:N \g__wa_position_in_the_tree_seq} = 1
+                      {\int_gincr:N \g__wa_last_env_int}
+           \seq_gpop_right:NN \g__wa_stack_counter_arrows_seq {\l_tmpa_tl}
+           \int_gset:Nn \g__wa_arrow_int {\l_tmpa_tl}
+           \seq_gpop_right:NN \g__wa_stack_counter_lines_seq \l_tmpa_tl
+           \int_gset:Nn \g__wa_line_int {\l_tmpa_tl}
+           \seq_gpop_right:NN \g__wa_stack_counter_lines_bis_seq \l_tmpa_tl
+           \int_gset:Nn \g__wa_line_bis_int {\l_tmpa_tl}
            }
-
-
-
-% le following code is necessary because we whill have to expand un argument exactly 3 times
+\cs_set_protected:Nn \__wa_cr:
+      {\scan_stop:
+       \group_align_safe_begin:
+       \peek_meaning_remove:NTF * \__wa_cr_i: \__wa_cr_i:}
+\cs_set_protected:Nn \__wa_cr_i:
+      {\peek_meaning:NTF [ {\__wa_cr_ii:} {\__wa_cr_ii:[\c_zero_dim]} }
+\cs_new_protected:Npn \__wa_cr_ii:[#1]
+      {\group_align_safe_end:
+       \cr\noalign{\skip_vertical:n {#1 + \l__wa_interline_skip}
+       \scan_stop:}}
 \cs_generate_variant:Nn \keys_set_groups:nnn {nno}
-\cs_new:Nn \keys_set_groups_WithArrows_local: {\keys_set_groups:nno {WithArrows} {local}}
-
+\cs_new_protected:Nn \keys_set_groups_WithArrows_local:
+                     {\keys_set_groups:nno {WithArrows} {local}}
 \cs_generate_variant:Nn \keys_set_filter:nnn {nno}
-\cs_new:Nn \keys_set_filter_WithArrows_secondary: {\keys_set_filter:nno {WithArrows} {secondary}}
-
-\cs_new:Nn \wa_draw_arrows:
-  {%
-   % if the option "group" is used in the current environment
-   \bool_if:NT \l_wa_group_bool
-        \wa_x_computation_for_option_group:   % will compute \g_wa_x_dim which is the abscissa of all the arrows 
-   %
-   % loop over the arrows created in the environment : the arrows will be drawn
-   \int_set:Nn \l_arrow_int 1
-   \int_until_do:nNnn \l_arrow_int > \g_wa_arrow_int   % g_wa_arrow_int is the total number of arrows
+\cs_new_protected:Nn \keys_set_filter_WithArrows_secondary:
+           {\keys_set_filter:nno {WithArrows} {secondary}}
+\cs_new_protected:Nn \__wa_draw_arrows:
+  {
+   \bool_if:NT \l__wa_group_bool
+        \__wa_x_computation_for_option_group:
+   \int_set:Nn \l__wa_arrow_int 1
+   \int_until_do:nNnn \l__wa_arrow_int > \g__wa_arrow_int
      {
-      % \l_initial_int is the line number from which the arrow starts
-      \int_set:Nn \l_initial_int {\int_use:c {wa_initial\int_use:N\l_arrow_int}}
-      %
-      % \l_final_int is the line number to which the arrow ends
-      \int_set:Nn \l_final_int {\int_use:c {wa_final\int_use:N\l_arrow_int}}
-      %
-      \int_compare:nNnT \l_final_int > \g_wa_line_int
-             {\msg_error:nn {WithArrows} {Too~few~lines~for~an~arrow}}
-      %
-      \group_begin: % for the options given in \Arrow[...] ("local level" of the options)
+      \prop_get:cnN {g__wa_arrow_\l__wa_prefix_tl _\int_use:N\l__wa_arrow_int _prop}
+                    {initial} \l_tmpa_tl
+      \int_set:Nn \l__wa_initial_int {\l_tmpa_tl}
+      \prop_get:cnN {g__wa_arrow_\l__wa_prefix_tl _\int_use:N\l__wa_arrow_int _prop}
+                    {final} \l_tmpa_tl
+      \int_set:Nn \l__wa_final_int {\l_tmpa_tl}
+      \int_compare:nNnT \l__wa_final_int > \g__wa_line_int
+             {\msg_error:nn {witharrows} {Too~few~lines~for~an~arrow}}
+           \group_begin:
            \keys_define:nn {WithArrows} {group .undefine:}
-           \bool_set_false:N \l_wa_position_key_already_set_bool
-           % the third argument de \keys_set_groups:nnn must be expanded exactly three times
-           % a x-expansion is not possible because there can be tokens like \bfseries in the option "font"
-           \exp_args:NNo \exp_args:No \keys_set_filter_WithArrows_secondary: {\use:c {wa_options\int_use:N\l_arrow_int}}
-           \exp_args:NNo \exp_args:No \keys_set_groups_WithArrows_local: {\use:c {wa_options\int_use:N\l_arrow_int}}
-           %
-           % In case of option "i", we have to compute the abscissa of the arrow (which is vertical).
-           \bool_if:NT \l_wa_i_bool
-               \wa_x_computation_for_option_i: % the abscissa is computed in \g_wa_x_dim
-           %
-           % \l_initial_tl contains the name of the Tikz node from which the arrow starts (in normal cases...
-           % because with option "group" or option "i", the point will perhaps have an other x-value --- but always the
-           % same y-value). 
-           \tl_set:Nx \l_initial_tl {wa-\int_use:N\l_initial_int-\bool_if:NTF\l_wa_initial_r_bool rl} 
-           %
-           % \l_final_tl contains the name of the Tikz node to which the arrow ends (in normal cases : with option
-           % "group" or option "i", the point will perhaps have an other x-value but always the same y-value)
-           \tl_set:Nx \l_final_tl {wa-\int_use:N\l_final_int-\bool_if:NTF\l_wa_final_r_bool rl . north}
-           % ". north" because we want a small gap between two consecutive arrows
-           % 
+           \bool_set_false:N \l__wa_position_key_already_set_bool
+           \prop_get:cnN {g__wa_arrow_\l__wa_prefix_tl
+                             _\int_use:N\l__wa_arrow_int _prop} {options} \l_tmpa_tl
+           \exp_args:NNo \exp_args:No \keys_set_filter_WithArrows_secondary: {\l_tmpa_tl}
+           \exp_args:NNo \exp_args:No \keys_set_groups_WithArrows_local: {\l_tmpa_tl}
+           \bool_if:NT \l__wa_i_bool
+               \__wa_x_computation_for_option_i:
+           \tl_set:Nx \l__wa_initial_tl
+                   {wa-\tl_use:N\l__wa_prefix_tl-\int_use:N\l__wa_initial_int-
+                            \bool_if:NTF\l__wa_initial_r_bool rl}
+           \tl_set:Nx \l__wa_final_tl
+                   {wa-\tl_use:N\l__wa_prefix_tl-\int_use:N\l__wa_final_int-
+                            \bool_if:NTF\l__wa_final_r_bool rl . north}
            \begin{tikzpicture}[remember~picture,
                                overlay,
                                align=left,
@@ -345,161 +332,106 @@
                                ->,
                                looseness=1,
                                bend~left=45]
-           \draw \exp_after:wN [\l_wa_options_tikz_tl]
-                 % \p1 and \p2 are the two ends of the arrow (in fact, not exactly in case of options "group" or "i")
-                 let \p1 = (\tl_use:N \l_initial_tl),
-                     \p2 = (\tl_use:N \l_final_tl) in 
-                   (\bool_if:nTF {\l_wa_group_bool || \l_wa_i_bool}
-                     {\dim_use:N \g_wa_x_dim + \dim_use:N \l_wa_xoffset_dim, \y1}
-                     {\x1 + \dim_use:N \l_wa_xoffset_dim, \y1} )
-                   to node (wa-a-\int_use:N\l_arrow_int) % in fact, this name will not be used by WithArrows
-                           {\tl_use:c {wa_label\int_use:N\l_arrow_int}}
-                   (\bool_if:nTF {\l_wa_group_bool || \l_wa_i_bool}
-                     {\dim_use:N \g_wa_x_dim + \dim_use:N \l_wa_xoffset_dim, \y2}
-                     {\x2 + \dim_use:N \l_wa_xoffset_dim, \y2} ) ; 
+           \prop_get:cnN {g__wa_arrow_\l__wa_prefix_tl _\int_use:N\l__wa_arrow_int _prop}
+                         {label} \l_tmpa_tl
+           \draw \exp_after:wN [\l__wa_options_tikz_tl]
+                 let \p1 = (\tl_use:N \l__wa_initial_tl),
+                     \p2 = (\tl_use:N \l__wa_final_tl) in
+                   (\bool_if:nTF {\l__wa_group_bool || \l__wa_i_bool}
+                     {\dim_use:N \g__wa_x_dim + \dim_use:N \l__wa_xoffset_dim, \y1}
+                     {\x1 + \dim_use:N \l__wa_xoffset_dim, \y1} )
+                   to node [node~contents = {\tl_use:N \l_tmpa_tl}] {}
+                   (\bool_if:nTF {\l__wa_group_bool || \l__wa_i_bool}
+                     {\dim_use:N \g__wa_x_dim + \dim_use:N \l__wa_xoffset_dim, \y2}
+                     {\x2 + \dim_use:N \l__wa_xoffset_dim, \y2} ) ;
            \end{tikzpicture}
-       \group_end: % for the options given to \Arrow[...] ("local level" of the options)
-       \int_incr:N \l_arrow_int
-      } % end of the loop over the arrows : all arrows are drawn
+       \group_end:
+       \int_incr:N \l__wa_arrow_int
+      }
      }
-
-
-% We want to compute the x-value for the current environment which has option "group" (and therefore all arrows are
-% vertical at the same abscissa). This value will be computed in \g_wa_x_dim (which is global for technical reasons :
-% we have to do assignments in a \tikz command).
-\cs_new:Nn \wa_x_computation_for_option_group:
-  {\dim_gzero_new:N \g_wa_x_dim
-   %
-   % first, we calculate the initial value for \g_wa_x_dim
-   % in this \tikz command, nothing is drawn : we only want to read the abscissa of a Tikz node
-   \tikz[remember~picture]
-      \path let \p1 = (wa-\int_use:c{wa_initial1}-l)      % "let" is given by the Tikz library "calc"
-            in \pgfextra {\dim_gset:Nn \g_wa_x_dim {\x1}} ;  % a global assignment is necessary because of \tikz
-   %
-   % Then, we loop to determine the maximal length of all the lines concerned by the arrows of the environment.
-   \int_set:Nn \l_arrow_int 1
-   \int_until_do:nNnn \l_arrow_int > \g_wa_arrow_int   % g_wa_arrow_int is the total number of arrows
-      { % \l_initial_int is the line number from which the arrow starts
-        \int_set:Nn \l_initial_int {\int_use:c {wa_initial\int_use:N\l_arrow_int}}
-        %
-        % \l_final_int is the line number to which the arrow ends
-        \int_set:Nn \l_final_int {\int_use:c {wa_final\int_use:N\l_arrow_int}}
-        %
-        \wa_x_computation_analyze_lines_between: %... between lines \l_initial_int and \l_final_int
-        %
-        \int_incr:N \l_arrow_int
-      } % end of the loop over the arrows of the environment
-   }   
-
-
-% We want to compute the x-value for the current arrow which has option "i" (and therefore is vertical).
-% This value will be computed in \g_wa_x_dim (which is global for technical reasons : we have to do assignments in
-% a \tikz command). 
-\cs_new:Nn \wa_x_computation_for_option_i:
-  {\dim_gzero_new:N \g_wa_x_dim
-   % First, we calculate the initial value for \g_wa_x_dim.
-   % In the next \tikz command, nothing is drawn : we only want to read a abscissa of a Tikz node.
+\cs_new_protected:Nn \__wa_x_computation_for_option_i:
+  {\dim_gzero_new:N \g__wa_x_dim
    \tikz[remember~picture]
-      \path let \p1 = (wa-\int_use:N\l_initial_int-l) % "let" is given by the Tikz library "calc"
-            in \pgfextra {\dim_gset:Nn \g_wa_x_dim {\x1}} ;  % a global assignment is necessary because of \tikz
-   %
-   \wa_x_computation_analyze_lines_between:  %... between lines \l_initial_int and \l_final_int
+      \path let \p1 = (wa-\tl_use:N\l__wa_prefix_tl-\int_use:N\l__wa_initial_int-l)
+            in \pgfextra {\dim_gset:Nn \g__wa_x_dim {\x1}} ;
+   \__wa_x_computation_analyze_lines_between:
    }
-
-
-
-        
-% We analyse lines between \l_initial_int and \l_final_int in order to modify \g_wa_x_dim in consequence.
-% More precisely, we will increase \g_wa_x_dim if we find a line longer than the current value of \g_wa_x_dim.
-\cs_new:Nn \wa_x_computation_analyze_lines_between:
-    {\int_compare:nNnT \l_final_int > \g_wa_line_int
-             {\msg_error:nn {WithArrows} {Too~few~lines~for~an~arrow}}
-     %
-     % \l_tmpa_int will be the index of the loop
-     \int_set:Nn \l_tmpa_int \l_initial_int
-     \int_until_do:nNnn \l_tmpa_int > \l_final_int
-         {% in the next \tikz command, nothing is drawn : we only want to read the abscissa of a Tikz node
-          \tikz[remember~picture]
-             \path let \p1 = (wa-\int_use:N\l_tmpa_int-l) 
-                   in \pgfextra {\dim_gset:Nn \g_wa_x_dim {\dim_max:nn \g_wa_x_dim {\x1}}} ; % \gset because of \tikz
+\cs_new_protected:Nn \__wa_x_computation_analyze_lines_between:
+    {\int_compare:nNnT \l__wa_final_int > \g__wa_line_int
+             {\msg_error:nn {witharrows} {Too~few~lines~for~an~arrow}}
+     \int_set:Nn \l_tmpa_int \l__wa_initial_int
+     \int_until_do:nNnn \l_tmpa_int > \l__wa_final_int
+         {\tikz[remember~picture]
+             \path let \p1 = (wa-\tl_use:N\l__wa_prefix_tl-\int_use:N\l_tmpa_int-l)
+                   in \pgfextra {\dim_gset:Nn \g__wa_x_dim {\dim_max:nn \g__wa_x_dim {\x1}}} ;
           \int_incr:N \l_tmpa_int
-         } % loop on the lines between \l_initial_int et \l_final_int
-    }   
-
-
-
+         }
+    }
+\cs_new_protected:Nn \__wa_x_computation_for_option_group:
+  {\dim_gzero_new:N \g__wa_x_dim
+   \prop_get:cnN {g__wa_arrow_\l__wa_prefix_tl _1_prop} {initial} \l_tmpa_tl
+   \tikz[remember~picture]
+      \path let \p1 = (wa-\tl_use:N\l__wa_prefix_tl-\tl_use:N\l_tmpa_tl-l)
+            in \pgfextra {\dim_gset:Nn \g__wa_x_dim {\x1}} ;
+   \int_set:Nn \l__wa_arrow_int 1
+   \int_until_do:nNnn \l__wa_arrow_int > \g__wa_arrow_int
+      {
+        \prop_get:cnN {g__wa_arrow_\l__wa_prefix_tl _\int_use:N\l__wa_arrow_int _prop}
+                      {initial} \l_tmpa_tl
+        \int_set:Nn \l__wa_initial_int {\l_tmpa_tl}
+        \prop_get:cnN {g__wa_arrow_\l__wa_prefix_tl _\int_use:N\l__wa_arrow_int _prop}
+                      {final} \l_tmpa_tl
+        \int_set:Nn \l__wa_final_int {\l_tmpa_tl}
+        \__wa_x_computation_analyze_lines_between:
+        \int_incr:N \l__wa_arrow_int
+      }
+   }
 \cs_generate_variant:Nn \int_compare:nNnT {cNnT}
-
-\cs_generate_variant:Nn \tl_if_eq:nnF {onF}
-
-
-% The next command has a strange name, but, in fact, usually, we will have \let\Arrow\wa_Arrow ;
-% The user can use the CommandName option if he wants an other name for the command called \Arrow by default.
-% It's useful if the user already has a command named "\Arrow" he still wants to use.
-\NewDocumentCommand \wa_Arrow {O{} m O{}}
-         {\tl_if_eq:onF {\@currenvir} {WithArrows}
-                  {\msg_fatal:nn {WithArrows} {Arrow~used~outside~{WithArrows}~environment}}
-          %
-          % \g_wa_arrow_int counts the arrows in the environment
-          \int_gincr:N \g_wa_arrow_int
-          %
-          % we decide to extract immediatly the key "jump" in ordre to compute the end line ;
-          \int_zero_new:N \l_jump_int
-          \int_set:Nn \l_jump_int 1
-          \keys_set_groups:nnn {WithArrows} {jump} {#1,#3} % "jump" is the only key of the group "jump"
-          % 
-          % to stock the informations of the considered arrow (in four variables) ;
-          % these informations will be used when the arrow will be really drawn
-          \int_gzero_new:c {wa_initial\int_use:N\g_wa_arrow_int}
-          \int_gset_eq:cN  {wa_initial\int_use:N\g_wa_arrow_int} \g_wa_line_int
-          %
-          \int_gzero_new:c {wa_final\int_use:N\g_wa_arrow_int}
-          \int_gset:cn     {wa_final\int_use:N\g_wa_arrow_int} {\g_wa_line_int + \l_jump_int}
-          %
-          \tl_gclear_new:c {wa_options\int_use:N\g_wa_arrow_int}
-          \tl_gset:cn      {wa_options\int_use:N\g_wa_arrow_int} {#1,#3}
-          %
-          \tl_gclear_new:c {wa_label\int_use:N\g_wa_arrow_int}
-          \tl_gset:cn      {wa_label\int_use:N\g_wa_arrow_int} {#2}
-          %
-          }
-
-
-
-\msg_new:nnn {WithArrows}
+\cs_generate_variant:Nn \tl_if_eq:nnF {noF}
+\bigskip
+\NewDocumentCommand \WithArrowsLastEnv {}
+     {\int_use:N \g__wa_last_env_int}
+\msg_new:nnn {witharrows}
+             {Third~column~in~a~{WithArrows}~environment}
+             {By~default,~a~\{WithArrows\}~environment~can~only~have~two~columns.~
+              Maybe~you~have~forgotten~a~newline~symbol.~If~you~really~want~
+              more~than~two~columns,~you~should~use~the~option~"MoreColumns"~at~
+              a~global~level~or~for~an~environment.~However,~you~can~go~one~for~this~time.}
+\msg_new:nnn {witharrows}
              {Arrow~used~outside~{WithArrows}~environment}
-             {Arrow~command~should~be~used~only~directly~in~\{WithArrows\}~environment\\
-              and~not~in~a~subenvironment.}
-
-\msg_new:nnn {WithArrows}
+             {The~command~\string\Arrow\space~should~be~used~only~directly~
+              in~\{WithArrows\}~environment~and~not~in~a~subenvironment.~However,~you~
+              can~go~on.}
+\msg_new:nnn {witharrows}
              {The~option~"jump"~must~be~non~negative}
-             {You~can't~use~a~stricly~negative~value~for~the~option~"jump"~of~command~Arrow\\
-              You~can~create~an~arrow~going~backwards~with~the~option~"<-"~of~Tikz.}
-
-\msg_new:nnn {WithArrows}          
+             {You~can't~use~a~strictly~negative~value~for~the~option~"jump"~of~command~
+              \string\Arrow.~ You~can~create~an~arrow~going~backwards~with~
+              the~option~"<-"~of~Tikz.}
+\msg_new:nnn {witharrows}
              {Too~few~lines~for~an~arrow}
-             {There~is~at~least~an~arrow~that~can't~be~drawn~because~it~arrives~after~the\\
+             {There~is~at~least~an~arrow~that~can't~be~drawn~because~it~arrives~after~the~
               last~line~of~the~environment.}
-
-\msg_new:nnn {WithArrows}
-             {Bad~value~for~option~pos}
-             {The~option~"pos"~of~the~environment~\{WithArrows\}~must~be~equal~to\\        
-              0,~1,~or~2.}
-
-\msg_new:nnn {WithArrows}
-             {WithArrows~used~outside~math~mode}
-             {The~environment~WithArrows~must~be~used~only~in~math~mode.}
-
-\msg_new:nnn {WithArrows}
+\msg_new:nnn {witharrows}
+             {{WithArrows}~used~outside~math~mode}
+             {The~environment~\{WithArrows\}~should~be~used~only~in~math~mode.~
+              Nevertheless,~you~can~go~on.}
+\msg_new:nnn {witharrows}
              {Option~incompatible~with~group}
-             {You~try~to~use~the~option~"\tl_use:N\l_keys_key_tl"~while~you~are~using~the~option~"group".\\
-              It's~incompatible.~You~can~go~on~ignoring~this~option~"\tl_use:N\l_keys_key_tl"~and~"group"~will~be~used.}
-
-
-\msg_new:nnn {WithArrows}
+             {You~try~to~use~the~option~"\tl_use:N\l_keys_key_tl"~while~
+              you~are~using~the~option~"group".~It's~incompatible.~You~can~go~on~ignoring~
+              this~option~"\tl_use:N\l_keys_key_tl"~and~"group"~will~be~used.}
+\msg_new:nnn {witharrows}
              {Two~options~are~incompatible}
-             {You~try~to~use~the~option~"\tl_use:N\l_keys_key_tl"~but~this~option~is~incompatible\\
-              with~an~option~previously~set.~If~you~go~on,~it~will~overwrite~the~previous~option.}
-
-
-\endinput
\ No newline at end of file
+             {You~try~to~use~the~option~"\tl_use:N\l_keys_key_tl"~but~
+             this~option~is~incompatible~with~an~option~previously~set.~
+             If~you~go~on,~I~will~overwrite~the~previous~option.}
+\msg_new:nnnn {witharrows}
+              {All~lines~must~have~an~ampersand}
+              {All~lines~of~an~environment~\{WithArrows\}~must~have~an~second~column~
+               (because~the~nodes~are~created~in~the~second~column).~You~can~go~on~but~maybe~
+               you~will~have~an~pgf~error~for~an~undefined~shape.}
+              {The~ampersand~can~be~implicit~
+               (e.g.~if~you~use~\string\MoveEqLeft\space~of~mathtools).}
+\endinput
+%%
+%% End of file `witharrows.sty'.