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-rw-r--r--Master/texmf-dist/doc/latex/witharrows/README.md4
-rw-r--r--Master/texmf-dist/doc/latex/witharrows/witharrows.pdfbin124003 -> 209455 bytes
-rw-r--r--Master/texmf-dist/doc/latex/witharrows/witharrows.tex785
3 files changed, 2 insertions, 787 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
Binary files differ
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}
-
-
-
-
-
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