From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Mon, 2 Sep 2019 13:46:59 +0900 Subject: Initial commit --- macros/generic/witharrows/README.md | 32 + macros/generic/witharrows/witharrows-french.pdf | Bin 0 -> 253675 bytes macros/generic/witharrows/witharrows-french.tex | 2275 ++++++++ macros/generic/witharrows/witharrows.dtx | 6977 +++++++++++++++++++++++ macros/generic/witharrows/witharrows.ins | 48 + macros/generic/witharrows/witharrows.pdf | Bin 0 -> 577204 bytes 6 files changed, 9332 insertions(+) create mode 100644 macros/generic/witharrows/README.md create mode 100644 macros/generic/witharrows/witharrows-french.pdf create mode 100644 macros/generic/witharrows/witharrows-french.tex create mode 100644 macros/generic/witharrows/witharrows.dtx create mode 100644 macros/generic/witharrows/witharrows.ins create mode 100644 macros/generic/witharrows/witharrows.pdf (limited to 'macros/generic/witharrows') diff --git a/macros/generic/witharrows/README.md b/macros/generic/witharrows/README.md new file mode 100644 index 0000000000..fa5444c5e1 --- /dev/null +++ b/macros/generic/witharrows/README.md @@ -0,0 +1,32 @@ +# Readme for the package witharrows + +Author : F. Pantigny (`fpantigny@wanadoo.fr`). + +CTAN page : `https://ctan.org/pkg/witharrows` + +## License +The extension `witharrows` for TeX and LaTeX is distributed under the LPPL 1.3 license. + +## Presentation + +The LaTeX package `witharrows` provides environments `{WithArrows}` and `{DispWithArrows}` +similar to the environments `{aligned}` and `{align}` of `amsmath` but with 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. + +The extension `witharrows` can also be used with plain-TeX. + + + +## Installation + +The package `witharrows` is present in the distributions MiKTeX, TeXLive and MacTeX. + +For a manual installation: + +* put the files `witharrows.ins` dans `witharrows.dtx` in the same directory; +* run `latex witharrows.ins`. + +The files `witharrows.sty` and `witharrows.tex` will be generated. + +The file `witharrows.sty` is the only file necessary to use the extension `witharrows` with LaTeX (with `\usepakage{witharrows}`). + +The file `witharrows.tex` is the only file necessary to use the extension `witharrows` with plain-TeX (with `\input{witharrows.tex}`). diff --git a/macros/generic/witharrows/witharrows-french.pdf b/macros/generic/witharrows/witharrows-french.pdf new file mode 100644 index 0000000000..dfc63d2609 Binary files /dev/null and b/macros/generic/witharrows/witharrows-french.pdf differ diff --git a/macros/generic/witharrows/witharrows-french.tex b/macros/generic/witharrows/witharrows-french.tex new file mode 100644 index 0000000000..9d3f57b5b4 --- /dev/null +++ b/macros/generic/witharrows/witharrows-french.tex @@ -0,0 +1,2275 @@ +% -*- coding: utf-8 ; -*- +\documentclass[dvipsnames]{article}% dvipsnames est pour xcolor (chargé par Tikz) +\usepackage{xltxtra} +\usepackage[french]{babel} + +\usepackage[xetex]{geometry} +\geometry{left=2.8cm,right=2.8cm,top=2.5cm,bottom=2.5cm,papersize={21cm,29.7cm}} + +\usepackage{amsmath} +\usepackage{color} +\usepackage{verbatim} +\usepackage{mathtools} +\usepackage[footnotehyper]{witharrows} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{varwidth} +\usetikzlibrary{calc} +\usepackage[only,llbracket,rrbracket]{stmaryrd} + +\usepackage{fancyvrb} +\fvset{commandchars=\~\#\@,formatcom={\color{gray}}} + +\usepackage{titlesec} +\titlespacing*{\section}{0pt}{6.5ex plus 1ex minus .2ex}{4.3ex plus .2ex} +\titlespacing*{\subsection}{0pt}{4.5ex plus 1ex minus .2ex}{2ex plus .2ex} + + +\def\interitem{\vskip 7mm plus 2 mm minus 3mm} +\def\emphase{\bgroup\color{RoyalPurple}\let\next=} + +\skip \footins = 2 \bigskipamount + +\usepackage[hyperfootnotes = false]{hyperref} + +\hypersetup{ + pdfinfo = { + Title = { L’extension witharrows }, + Subject = { Une extension pour plain-TeX et LaTeX } , + Author = { F. Pantigny } + } +} + +\NewDocumentEnvironment {scope} {} {} {} + +\NewDocumentCommand {\pkg} {m} {\textsf{#1}} +\NewDocumentCommand {\cls} {m} {\textsf{#1}} + +\setlength{\parindent}{0pt} + + +\begin{document} + +\VerbatimFootnotes + +\title{L'extension \pkg{witharrows} pour plain-TeX et LaTeX\thanks{Ce document correspond à la +version~\myfileversion\space de \pkg{witharrows}, à la date du~\myfiledate.}} +\author{F. Pantigny \\ \texttt{fpantigny@wanadoo.fr}} + +\maketitle + +\begin{abstract} +L'extension \pkg{witharrows} fournit des environments \verb|{WithArrows}| et +\verb|{DispWithArrows}| similaires aux environnements \verb|{aligned}| et \verb|{align}| de +l'\pkg{amsmath} mais avec la possibilité de dessiner des flèches sur le côté droit. +Ces flèches sont habituellement utilisées pour donner des explications concernant +le calcul mathématique présenté. +\end{abstract} + + +\vspace{1cm} +Dans la suite, on décrira l'extension LaTeX \pkg{witharrows} (néanmoins \pkg{witharrows} peut aussi être utilisé en +plain-TeX : voir à ce sujet p.~\pageref{plain-TeX}). Cette extension peut être utilisée avec \verb|xelatex|, +\verb|lualatex|, \verb|pdflatex| mais aussi avec le cheminement classique \verb|latex|-\verb|dvips|-\verb|ps2pdf| +(ou Adobe Distiller). L'extension \pkg{witharrows} charge les extensions \pkg{expl3}, \pkg{xparse}, \pkg{tikz} +ainsi que les extensions Tikz \pkg{arrows.meta} et \pkg{bending}. Les flèches sont tracées avec Tikz et donc +plusieurs compilations peuvent être nécessaires. + +\bigskip +Cette extension fournit un environnement \verb|{WithArrows}| pour construire des alignements d'équations +avec des flèches pour les explications sur le côté droit. + +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 ~emphase#\Arrow{on développe}@ \\ + & = a^2 + 2a + 1 % ne pas mettre de \\ ici +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + + + +\medskip +La flèche a été tracée avec la commande \verb|\Arrow| dans la rangée dont la flèche part. La commande \verb|\Arrow| +doit être utilisée dans la seconde colonne (le mieux est de la mettre à la fin de la ligne comme dans l'exemple +précédent). + + +\medskip +Comme on le voit, l'environnement \verb|{WithArrows}| est proche de l'environnement +\verb|{aligned}| de l'\pkg{amsmath}. L'extension \pkg{witharrows} +propose aussi un environnement \verb|{DispWithArrows}| qui est similaire à l'environnement \verb|{align}| de +l'\pkg{amsmath}: cf. p. \pageref{DispWithArrows}. + + +\section{Options pour la forme des flèches} + +La commande \verb|\Arrow| a plusieurs options. Ces options peuvent être placées entre crochets, avant, ou après, +l'argument obligatoire. + +L'option \verb|jump| indique le nombre\footnote{Il n'est pas possible de donner une valeur négative à \verb|jump|. +Voir plus loin (p.~\pageref{Backwards}) la manière de tracer une flèche qui remonte.} de rangées que la flèche doit sauter (la valeur par défaut est, bien +entendu,~$1$). + + +\begin{Verbatim} +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 \Arrow[~emphase#jump=2@]{on développe} \\ + & = (a+b)^2 + 2(a+b) +1 \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 \Arrow[jump=1+1]{on développe} \\ + & = (a+b)^2 + 2(a+b) +1 \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ + +\interitem +Il est possible de faire partir plusieurs flèches d'une même rangée. +\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 +L'option \verb|xoffset| décale la flèche vers la droite (habituellement, on ne souhaite pas que les flèches soient +collées au texte). La valeur par défaut de \verb|xoffset| est de $3$~mm. +\begin{Verbatim} +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 +\Arrow[~emphase#xoffset=1cm@]{avec \texttt{xoffset=1cm}} \\ + & = (a+b)^2 + 2(a+b) +1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 +\Arrow[xoffset=1cm]{avec \texttt{xoffset=1cm}} \\ + & = (a+b)^2 + 2(a+b) +1 +\end{WithArrows}$ + + +\interitem +Les flèches sont tracées avec Tikz. C'est pourquoi la commande \verb|\Arrow| a une option +\verb|tikz| qui peut être utilisée pour donner à la flèche (en fait, à la commande \verb|\path| de +Tikz) les options proposées par Tikz pour une telle flèche. L'exemple suivant fournit une flèche en trait épais. +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[~emphase#tikz=thick@]{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[tikz=thick]{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + +\interitem +Il est également possible de changer les pointes de flèche. Par exemple, nous pouvons tracer une flèche +qui remonte vers le haut avec l'option Tikz~\verb|<-|.\label{Backwards} + +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow~emphase#[tikz=<-]@{on factorise} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[tikz=<-]{on factorise} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + +\interitem +Il est aussi possible de supprimer les deux pointes de flèche avec l'option Tikz «\verb|-|». +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[~emphase#tikz=-@]{très classique} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[tikz=-]{très classique} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + +\interitem +Pour avoir des flèches droites et non incurvées, il convient d'utiliser l'option Tikz +«\verb|bend left = 0|». +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow~emphase#[tikz={bend left=0}]@{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[tikz={bend left=0}]{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + +\smallskip +En fait, il est possible de modifier de manière plus drastique la forme des flèches avec l'option +\verb|tikz-code| (présentée p.~\pageref{tikz-code}). + +\interitem +Il est possible d'utiliser l'option «\verb|text width|» pour contrôler la largeur du texte associé à la +flèche.\footnote{Il est possible d'éviter les coupures de mots dans ces étiquettes +avec l'option «\verb|align = flush left|» de Tikz.} +% +\begin{Verbatim} +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 +\Arrow[jump=2,~emphase#tikz={text width=5.3cm}@]{Nous avons développé...} \\ + & = (a+b)^2 + 2(a+b) +1 \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 +\Arrow[jump=2,tikz={text width=5.3cm}]{Nous avons développé en deux étapes mais il aurait été plus habile + d'utiliser la formule du multinôme.} \\ +& = (a+b)^2 + 2(a+b) +1 \\ +& = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ + + +\bigskip +Dans les environnements \verb|{DispWithArrows}| et \verb|{DispWithArrows*}|, il y a une +option \verb|wrap-lines|. Lorsque cette option est utilisée, les lignes des étiquettes sont +automatiquement coupées sur la marge droite : voir p.~\pageref{wrap-lines}. + +\interitem +Si on veut changer la fonte du texte associé à une flèche, on peut, bien entendu, placer une commande comme +\verb|\bfseries|, \verb|\large| ou \verb|\sffamily| au début du texte. +Mais, par défaut, les étiquettes sont composées avec une combinaison +de \verb|\small| et \verb|\itshape|. En ajoutant \verb|\bfseries| au début du texte, on ne va pas supprimer le +\verb|\small| et le \verb|\itshape| et, par conséquent, on aura un texte en gras, italique et petite taille. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{~emphase#\bfseries@ on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{\bfseries on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + +\interitem +Il est possible de placer des commandes \verb|\\| dans le texte pour forcer des retours à la ligne\footnote{Par +défaut, ce n'est pas possible dans un nÅ“ud Tikz. Néanmoins, dans \pkg{witharrows}, +les nÅ“uds sont construits avec l'option \verb|align=left|, et, ainsi, cela devient possible.}. Néanmoins, si on utilise des commandes \verb|\\|, une instruction de fonte placée au début +du texte aura un effet seulement jusqu'à la première occurrence de~\verb|\\| (comme +dans un environnement \verb|{tabular}|). C'est pourquoi Tikz fournit une option +\verb|font| pour modifier la fonte de tout le texte de l'étiquette. Cette fois-ci, si on utilise une option +\verb|tikz={font={\bfseries}}|, la spécification par défaut constituée par \verb|\small| et \verb|\itshape| va être +écrasée. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[~emphase#tikz={font={\bfseries}}@]{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[tikz={font={\bfseries}}]{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + +\medskip +Si on veut exactement le même résultat que précédemment, on doit donner à l'option \verb|font| la valeur +\verb|\itshape\small\bfseries|. + + +\interitem +Presque toutes les options peuvent être données entre crochets à l'environnement \verb|{WithArrows}|. Il ne doit +pas y avoir d'espace entre le \verb|\begin{WithArrows}| et le crochet ouvrant (\verb|[|) des options de +l'environnement. Ces options s'appliquent à toutes les flèches de l'environnement.\footnote{Elles s'appliquent + aussi aux environnements imbriqués dans un environnement \verb|{WithArrows}| donné (avec des exceptions attendues + pour les options \verb|interline|, \verb|code-before| et \verb|code-after|).} +% +\begin{Verbatim} +$\begin{WithArrows}[~emphase#tikz=blue@] +A & = \bigl((a+b)+1\bigr)^2 \Arrow{premier développement} \\ + & = (a+b)^2 + 2(a+b) +1 \Arrow{second développement} \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows}[tikz=blue] +A & = \bigl((a+b)+1\bigr)^2 \Arrow{premier développement} \\ + & = (a+b)^2 + 2(a+b) +1 \Arrow{second développement} \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ + + +\interitem +L'environnement \verb|{WithArrows}| a une option \verb|displaystyle|. Avec cette option, +tous les éléments sont composés en \verb|\displaystyle| (comme dans un environnement +\verb|{aligned}| de l'\pkg{amsmath}). + +\medskip +Sans l'option \verb|displaystyle|: +% +\begin{Verbatim} +$\begin{WithArrows} +\int_0^1 (x+1)^2 dx +& = \int_0^1 (x^2+2x+1) dx +\Arrow{linéarité de l'intégration} \\ +& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\ +& = \frac13 + 2\frac12 + 1 \\ +& = \frac73 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +\int_0^1 (x+1)^2 dx +& = \int_0^1 (x^2+2x+1) dx +\Arrow{linéarité de l'intégration} \\ +& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\ +& = \frac13 + 2\frac12 + 1 \\ +& = \frac73 +\end{WithArrows}$ + + +\medskip +Le même exemple avec l'option \verb|displaystyle|:\par\nobreak + +$\begin{WithArrows}[displaystyle] +\int_0^1 (x+1)^2 dx +& = \int_0^1 (x^2+2x+1) dx +\Arrow{linéarité de l'intégration} \\ +& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\ +& = \frac13 + 2\frac12 + 1 \\ +& = \frac73 +\end{WithArrows}$ + + + +\interitem +Presque toutes les options peuvent aussi être fixées au niveau du document avec la commande +\verb|\WithArrowsOptions|. Dans ce cas, la portée des déclarations est le groupe TeX courant (de telles +déclarations sont parfois qualifiées de «semi-globales»). Par exemple, si nous voulons que tous les environnements +\verb|{WithArrows}| soient composés en \verb|\displaystyle| avec des flèches bleues, nous pouvons écrire +\verb|\WithArrowsOptions{displaystyle,tikz=blue}|.\footnote{Il est aussi possible de configurer \pkg{witharrows} en + modifiant le style Tikz \verb|WithArrows/arrow| qui est le style utilisé par \pkg{witharrows} lors du tracé d'une + flèche. Par exemple, pour avoir les étiquettes en bleu et en caractères droits, on peut utiliser l'instruction + suivante : \verb|\tikzset{WithArrows/arrow/.append style = {blue,font = {}}}|.} + +\begin{Verbatim} +~emphase#\WithArrowsOptions{displaystyle,tikz=blue}@ +$\begin{WithArrows} +\sum_{i=1}^n (x_i+1)^2 +& = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{par linéarité}\\ +& = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n +\end{WithArrows}$ +\end{Verbatim} + +\begin{scope} +\WithArrowsOptions{displaystyle,tikz=blue} +$\begin{WithArrows} +\sum_{i=1}^n (x_i+1)^2 +& = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{par linéarité}\\ +& = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n +\end{WithArrows}$ +\end{scope} + + +\interitem +La commande \verb|\Arrow| est reconnue seulement dans les environnements \verb|{WithArrows}|. Si on +dispose d'une commande \verb|\Arrow| précédemment définie, il est possible de continuer à l'utiliser à +l'extérieur des environnements \verb|{WithArrows}|. + +Néanmoins, une commande \verb|\Arrow| définie précédemment pourrait encore être utile dans un environnement \verb|{WithArrows}|. +Si vous voulez l'utiliser dans un tel environnement, il est possible de changer le nom de la commande \verb|\Arrow| de +l'extension \pkg{witharrows} grâce à une option \verb|command-name|\footnote{Pour des raisons historiques, il y a + un alias pour cette option : \verb|CommandeName|.} dédiée. Le nouveau nom de la commande doit être fourni à +l'option \emph{sans} la contre-oblique. +% +\begin{Verbatim} +\NewDocumentCommand {\Arrow} {} {\longmapsto} +$\begin{WithArrows}[~emphase#command-name=Explication@] +f & = \bigl(x \Arrow (x+1)^2\bigr) +~emphase#\Explication{on travaille directement sur les fonctions}@\\ +& = \bigl(x \Arrow x^2+2x+1\bigr) +\end{WithArrows}$ +\end{Verbatim} +% +\begin{scope} +\NewDocumentCommand {\Arrow} {} {\longmapsto} +$\begin{WithArrows}[command-name=Explication] +f & = \bigl(x \Arrow (x+1)^2\bigr) +\Explication{on travaille directement sur les fonctions}\\ +& = \bigl(x \Arrow x^2+2x+1\bigr) +\end{WithArrows}$ +\end{scope} + + +\interitem +L'environnement \verb|{WithArrows}| fournit aussi deux options \verb|code-before| et +\verb|code-after|\footnote{Pour des raisons historiques, il y a aussi des alias pour ces options : + \verb|CodeBefore| et \verb|CodeAfter|.} pour du code LaTeX qui sera exécuté au début et à la fin de +l'environnement. Ces options ne sont pas conçues pour être utilisées comme des \emph{hooks} (elles sont disponibles +uniquement au niveau de l'environnement et ne s'appliquent pas aux environnements imbriqués). +% +\begin{Verbatim} +$\begin{WithArrows}[~emphase#code-before = \color{blue}@] +A & = (a+b)^2 \Arrow{on développe} \\ + & = a^2 + 2ab + b^2 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows}[code-before = \color{blue}] +A & = (a+b)^2 \Arrow{on développe} \\ + & = a^2 + 2ab + b^2 +\end{WithArrows}$ + +\medskip +Des commandes spéciales sont disponibles dans le \verb|code-after| : une commande \verb|\WithArrowsNbLines| qui +indique le nombre de lignes (=rangées) de l'environnement courant (pour TeX, il s'agit d'une commande et non d'un +compteur), une forme spéciale de la commande \verb|\Arrow| et la commande \verb|\MultiArrow| : ces commandes sont +décrites à partir de la page~\pageref{NestedEnv}. + +\section{Nombre et formats des colonnes} + +Jusqu'à présent, nous n'avons utilisé l'environnement \verb|{WithArrows}| qu'avec deux colonnes. Néanmoins, il est +possible de l'utiliser avec un nombre arbitraire de colonnes grâce à l'option \verb|format|. La valeur +donnée à cette option est similaire au préambule d'un environnement \verb|{array}|: il s'agit d'une séquence de +lettres \verb|r|, \verb|c| et \verb|l|. La valeur par défaut de cette option \verb|format| est, en fait, \verb|rl|. + + +\bigskip +Par exemple, si on veut seulement une colonne alignée à gauche, on peut utiliser l'option \verb|format=l|. +\begin{Verbatim} +$\begin{WithArrows}[~emphase#format = l@] +f(x) \ge g(x) \Arrow{on élève les deux membres au carré} \\ +f(x)^2 \ge g(x)^2 \Arrow{on fait tout passer à gauche} \\ +f(x)^2 - g(x)^2 \ge 0 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows}[format = l] +f(x) \ge g(x) \Arrow{on élève les deux membres au carré} \\ +f(x)^2 \ge g(x)^2 \Arrow{on fait tout passer à gauche} \\ +f(x)^2 - g(x)^2 \ge 0 +\end{WithArrows}$ + +\interitem +Dans l'exemple suivant, on utilise cinq colonnes toutes centrées (l'environnement +\verb|{DispWithArrows*}| utilisé est présenté p.~\pageref{DispWithArrows}). + +\begin{Verbatim} +\begin{DispWithArrows*}[~emphase#format = ccccc@, + wrap-lines, + tikz = {align = flush left}, + interline=1mm] +k & \;\le\; & t & \;\le\; & k+1 \\ +\frac{1}{k+1} & \le & \frac{1}{t} & \le & \frac{1}{k} +\Arrow{nous pouvons intégrer les inégalités puisque $k \leq k+1$ } \\ +\int\limits_k^{k+1} \frac{dt}{k+1} +& \le & \int\limits_k^{k+1} \frac{dt}{t} +& \le & \int\limits_k^{k+1} \frac{dt}{k} \\ +\frac{1}{k+1} & \le & \ln(k+1)-\ln(k) & \le & \frac{1}{k} +\end{DispWithArrows*} +\end{Verbatim} +\begin{DispWithArrows*}[format = ccccc, + wrap-lines, + tikz = {align = flush left}, + interline=1mm] +k & \;\le\; & t & \;\le\; & k+1 \\ +\frac{1}{k+1} & \le & \frac{1}{t} & \le & \frac{1}{k} +\Arrow{nous pouvons intégrer les inégalités puisque $k \leq k+1$} \\ +\int\limits_k^{k+1} \frac{dt}{k+1} +& \le & \int\limits_k^{k+1} \frac{dt}{t} +& \le & \int\limits_k^{k+1} \frac{dt}{k} \\ +\frac{1}{k+1} & \le & \ln(k+1)-\ln(k) & \le & \frac{1}{k} +\end{DispWithArrows*} + + +\section{Positionnement précis des flèches} + +L'environnement \verb|{WithArrows}| construit, lors de la composition du tableau, +deux séries de nÅ“uds représentés en rouge dans l'exemple suivant.\footnote{L'option +\verb|show-nodes| peut être utilisée pour visualiser ces nÅ“uds. Les nÅ“uds sont en fait des nÅ“uds Tikz de forme +rectangulaire et de largeur nulle. Une flèche entre deux nÅ“uds part de l'ancre sud (\emph{south + anchor}) du premier nÅ“ud et arrive à l'ancre nord (\emph{north anchor}) du deuxième nÅ“ud.} + + +\smallskip +$\begin{WithArrows}[displaystyle,show-nodes] +I +& = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) \\ +& = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\ +& = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\ +& =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u \\ +& =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\ +& =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\ +& =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u \\ +& =\frac{\pi}4\ln2-I +\end{WithArrows}$ + +\bigskip +Les nÅ“uds sur la gauche sont à la fin de chaque ligne de texte. Ces nÅ“uds seront appelés \emph{nÅ“uds de gauche}. Les +nÅ“uds du côté droit sont alignés verticalement sur le bord droit de l'alignement d'équations. Ces nÅ“uds seront +appelés \emph{nÅ“uds de droite}. + + +Par défaut, les flèches utilisent les nÅ“uds de droite. Nous dirons que ces flèches sont dans le mode \verb|rr| (\emph{r} +for \emph{right} en anglais). Ces flèches sont verticales (nous dirons qu'une flèche est \emph{verticale} lorsque +ses deux extrémités sont à la même abscisse). + + + +\smallskip +Néanmoins, il est possible d'utiliser les nÅ“uds de gauche, ou une combinaison de nÅ“uds de gauche et de droite avec +l'une des options \verb|lr|, \verb|rl| et \verb|ll| (\emph{l} for \emph{left} en anglais). Ces flèches sont, la +plupart du temps, non verticales. + + +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]{Cette flèche utilise une option \texttt{lr}.}\\ +& = \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}]{Cette flèche utilise une option \texttt{ll} +et une option \texttt{jump} fixée à $2$}\\ +& =\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 +Il y a aussi une option nommée \verb|i| (\emph{i} pour \emph{intermédiaire}). Avec cette option, la flèche est +verticale et calée à gauche. + +\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]@{parce que $(x-y)(x+y)=x^2-y^2$}\\ +& = 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]{parce que $(x-y)(x+y)=x^2-y^2$}\\ +& = a^4-b^4 +\end{WithArrows}$ + + +\interitem +L'environnement \verb|{WithArrows}| propose aussi une option \verb|group|. Avec cette option, +\emph{toutes} les flèches de l'environnement sont regroupées sur une même verticale calée à gauche. +% +\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{on remplace $y_0$ par sa valeur}\\ +& \Longleftrightarrow 2xK'x^{\frac32} = x^{\frac12} \Arrow{simplification par $x$}\\ +& \Longleftrightarrow K' = \tfrac1{2x^2} \Arrow{on primitive}\\ +& \Longleftrightarrow K = -\tfrac1{2x} +\end{WithArrows}$ + + +\bigskip +L'environnement \verb|{WithArrows}| fournit encore une autre option, nommée \verb|groups| (avec un \emph{s} dans le +nom). Avec cette option, les flèches sont divisées en plusieurs «groupes». Chaque groupe est un ensemble de flèches +connectées entre elles\footnote{Plus précisément : pour chaque flèche $a$, notons $i(a)$ le numéro de sa rangée de + départ et + $f(a)$ le numéro de sa rangée d'arrivée ; pour deux flèches $a$ et $b$, nous noterons $a \sim b$ lorsque + $\llbracket i(a),f(a)\rrbracket \cap \llbracket i(b),f(b)\rrbracket \neq \varnothing$ ; les groupes sont les + classes d'équivalence de la clôture transitive de la relation $\sim$.}. Toutes les flèches d'un même groupe sont placées sur +une même verticale qui est calée à gauche. + + +\bigskip +$\begin{WithArrows}[groups] +A & = B \Arrow{one} \\ + & = C+D \Arrow{two} \\ + & = D' \\ + & = E+F+G+H+I \\ + & = K + L + M \Arrow{three}\\ + & = N \Arrow{four}\\ + & = O +\end{WithArrows}$ + +\bigskip +Dans un environnement qui utilise l'option \verb|group| ou l'option \verb|groups|, il est encore possible de donner +une option de position (\verb|ll|, \verb|lr|, \verb|rl|, \verb|rr| ou \verb|i|) à une flèche individuelle. Une +telle flèche sera tracée indépendamment des groupes. Il est aussi possible de commencer un nouveau groupe avec +l'option \verb|new-group| pour une certaine flèche. + + +\bigskip +Si on le souhaite, on peut passer l'option \verb|group| ou \verb|groups| à la commande \verb|WithArrowsOptions| de +telle sorte qu'elle deviendra la valeur par défaut (jusqu'à la fin du groupe TeX). Dans ce cas, il est encore +possible de revenir au comportement par défaut pour un environnement \verb|{WithArrows}| donné avec l'option +\verb|rr|: \verb|\begin{WithArrows}[rr]|. + + +\vspace{1cm} +Dans l'exemple suivant, nous avons utilisé l'option \verb|group| pour l'environnement +et l'option \verb|rr| pour la dernière flèche (c'est pourquoi cette dernière flèche n'est pas alignée avec les +premières). + +$\begin{WithArrows}[interline=1mm,group] +\sum\limits_{k=0}^n\frac{\cos kx}{\cos^k x} +& = \sum\limits_{k=0}^n \frac{\Re (e^{ikx})}{(\cos x)^k} +\Arrow{$(\cos x)^k$ est réel} \\ +& = \sum\limits_{k=0}^n \Re\left(\frac{e^{ikx}}{(\cos x)^k}\right) +\Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\ +& = \Re \left(\sum\limits_{k=0}^n \left(\frac{e^{ix}}{\cos x}\right)^k\right) +\Arrow{somme de termes d'une suite géométrique} \\ +& = \Re \left(\frac{1-\left(\frac{e^{ix}}{\cos x}\right)^{n+1}}{1-\frac{e^{ix}}{\cos x}} \right) +\Arrow{calcul algébrique} \\ +& = \Re \left(\frac{1-\frac{e^{i(n+1)x}}{\cos^{n+1}x}}{1-\frac{e^{ix}}{\cos x}}\right) +\Arrow{réduction au même dénominateur} \\ +& = \Re \left(\frac{\frac{\cos^{n+1}x-e^{i(n+1)x}}{\cos^{n+1}x}}{\frac{\cos x-e^{ix}}{\cos x}}\right) +\Arrow{$\Re(kz) = k\cdot\Re(z)$ lorsque $k$ est réel} \\ +& = \frac1{\cos^n x}\Re \left(\frac{\cos^{n+1}x-e^{i(n+1)x}}{\cos x-e^{ix}}\right) +\Arrow[rr]{forme algébrique des nombres complexes} \\ +& =\frac1{\cos^n x}\Re\left(\frac{\cos^{n+1}x-(\cos(n+1)x+i\sin(n+1)x)}{\cos x-(\cos x+i\sin x)}\right) \\ +& =\frac1{\cos^n x}\Re\left(\frac{(\cos^{n+1}x-\cos(n+1)x)-i\sin(n+1)x}{-i\sin x}\right) \\ +& = \frac1{\cos^nx}\cdot\frac{\sin(n+1)x}{\sin x} +\end{WithArrows}$ + +\interitem + +\section{Les options «up» et «down» pour des flèches individuelles} + +\label{up-and-down} +Au niveau local, il y a deux options pour les flèches individuelles, nommée «\verb|up|» et «\verb|down|». L'exemple +suivant illustre ces types de flèches: + + +\begin{Verbatim} +\(\begin{WithArrows} +A & = B +\Arrow~emphase#[up]@{une flèche de type \texttt{up}} \\ + & = C + C + C + C + C + C + C + C \\ + & = C + C + C + C + C + C + C + C +\Arrow~emphase#[down]@{une flèche de type \texttt{down}} \\ + & = E + E +\end{WithArrows}\) +\end{Verbatim} + +\vspace{1cm} +\(\begin{WithArrows} +A & = B +\Arrow[up]{une flèche de type \texttt{up}} \\ + & = C + C + C + C + C + C + C + C \\ + & = C + C + C + C + C + C + C + C +\Arrow[down]{une flèche de type \texttt{down}} \\ + & = E + E +\end{WithArrows}\) + + +\vspace{1cm} +Les options \verb|up| et \verb|down| nécessitent l'extension \pkg{varwidth} et l'extension Tikz +\pkg{calc}. Si elles ne sont pas chargées, une erreur sera levée. + + +\interitem + +\section{Comparaison avec l'environnement \{aligned\}} + +L'environnement \verb|{WithArrows}| présente des similitudes avec l'environnement \verb|{aligned}| de l'extension +\pkg{amsmath}. Ce sont seulement des similitudes car \verb|{WithArrows}| n'a pas été écrit en s'appuyant sur +\verb|{aligned}|.\footnote{En fait, il est +possible d'utiliser l'extension \pkg{witharrows} sans l'extension \pkg{amsmath}.} + +\interitem +Comme dans les environnements de l'\pkg{amsmath}, il est possible de changer l'espacement entre deux rangées avec +l'option de la commande \verb|\\| de fin de ligne (il est aussi possible d'utiliser \verb|\\*| mais cela a +exactement le même effet que \verb|\\| puisqu'un environnement \verb|{WithArrows}| est toujours insécable). Cette +option est conçu pour être utilisée avec des valeurs positives uniquement. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{on développe} ~emphase#\\[2ex]@ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{on développe} \\*[2ex] +\noalign{\vspace{3mm}} + & = a^2 + 2a + 1 +\end{WithArrows}$ + + +\interitem +Dans les environnements de l'\pkg{amsmath} (ou de \pkg{mathtools}), l'espace entre deux rangées +est fixé par un paramètre appelé \verb|\jot| (il s'agit d'une dimension et non d'un ressort). C'est aussi le cas +pour l'environnement \verb|{WithArrows}|. Une option \verb|jot| a été ajoutée à l'environnement \verb|{WithArrows}| +dans le but de changer ce paramètre \verb|\jot| pour un environnement donné.\footnote{Il est aussi possible de +changer \verb|\jot| avec l'environnement \verb|{spreadlines}| de \pkg{mathtools}.} +% +\begin{Verbatim} +$\begin{WithArrows}[displaystyle,~emphase#jot=2ex@] +F & = \frac12G \Arrow{on développe}\\ + & = H + \frac12K \Arrow{on continue}\\ + & = K +\end{WithArrows}$ +\end{Verbatim} + + +$\begin{WithArrows}[displaystyle,jot=2ex] +F & = \frac12G \Arrow{on développe}\\ + & = H + \frac12K \Arrow{on continue}\\ + & = K +\end{WithArrows}$ + + +\bigskip +Néanmoins, cette nouvelle valeur de \verb|\jot| sera aussi utilisée dans les nouveaux alignements +inclus dans l'environnement~\verb|{WithArrows}|: +% +\begin{Verbatim} +$\begin{WithArrows}[jot=2ex] +\varphi(x,y) = 0 & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 +\Arrow{$x$ et $y$ sont réels}\\ +& \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$ et $y$ sont réels}\\ +& \Leftrightarrow \left\{ +\begin{aligned} +x+y & = 0 \\ +x+2y & = 0 +\end{aligned} +\right. +\end{WithArrows}$ + +\bigskip +Peut-être que cela ne correspond pas au résultat souhaité. C'est pourquoi une option +\verb|interline| est fournie. Il est possible d'utiliser un ressort (\emph{skip}) pour cette option. +% +\begin{Verbatim} +$\begin{WithArrows}[~emphase#interline=2ex@] +\varphi(x,y) = 0 & \Leftrightarrow (x+y)^2 + (x+2y)^2 = 0 +\Arrow{$x$ et $y$ sont réels}\\ +& \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$ et $y$ sont réels}\\ +& \Leftrightarrow \left\{ +\begin{aligned} +x+y & = 0 \\ +x+2y & = 0 \\ +\end{aligned} +\right. +\end{WithArrows}$ + + +\interitem +De même que l'environnement \verb|{aligned}|, \verb|{WithArrows}| a une option de placement qui peut prendre les valeurs +\verb|t|, \verb|c| ou \verb|b|. Néanmoins, la valeur par défaut n'est pas \verb|c| mais \verb|t|. +Si on le souhaite, il est possible d'avoir la valeur \verb|c| comme valeur par défaut +en utilisant l'instruction \verb|\WithArrowsOptions{c}| au début du document. +% +\begin{Verbatim} +Ainsi\enskip +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +Ainsi\enskip +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + +\bigskip +La valeur \verb|c| peut être utile, par exemple, si on souhaite mettre une accolade : + +\smallskip +\begin{Verbatim} +On pose\enskip $~emphase#\left\{@ +\begin{WithArrows}[~emphase#c@] +f(x) & = 3x^3+2x^2-x+4 +\Arrow[tikz=-]{les deux sont des polynômes}\\ +g(x) & = 5x^2-5x+6 +\end{WithArrows} +~emphase#\right.@$ +\end{Verbatim} + + +On pose\enskip $\left\{ +\begin{WithArrows}[c] +f(x) & = 3x^3+2x^2-x+4 +\Arrow[tikz=-]{les deux sont des polynômes}\\ +g(x) & = 5x^2-5x+6 +\end{WithArrows} +\right.$ + + +\interitem +Contrairement à \verb|{aligned}|, l'environnement \verb|{WithArrows}| utilise \verb|\textstyle| par +défaut. + +Là aussi, il est possible de changer ce comportement avec \verb|\WithArrowsOptions|: + +\quad \verb|\WithArrowsOptions{displaystyle}|. + + +\smallskip +L'exemple suivant est composé avec \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 +L'exemple suivant est composé avec \verb|{WithArrows}[c,displaystyle]|. Les résultats +sont parfaitement identiques.\footnote{Dans les versions de l'\pkg{amsmath} antérieures au +5~novembre~2016, un espace fin était ajouté sur la gauche de l'environnement \verb|{aligned}|. +Les versions plus récentes n'ajoutent pas d'espace et \verb|{WithArrows}| non plus.}\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{Les flèches dans les environnements imbriqués} + +\label{NestedEnv} + +Les environnements \verb|{WithArrows}| peuvent être imbriqués. Dans ce cas, les options fournies +à l'environnement englobant s'appliquent aussi aux environnements imbriqués (avec des +exceptions tout à fait attendues pour \verb|interline|, \verb|code-before| et \verb|code-after|). La commande +\verb|Arrow| peut être utilisée dans chaque environnement \verb|{WithArrows}|. + +\begin{Verbatim}[formatcom=\small\color{gray}] +$~emphase#\begin{WithArrows}@ +\varphi(x,y)=0 + & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \Arrow{les nombres sont réels}\\ + & \Leftrightarrow + \left\{~emphase#\begin{WithArrows}@[c] + x+2y & = 0 \\ + 2x+4y & = 0 + ~emphase#\end{WithArrows}@\right. \\ + & \Leftrightarrow + \left\{~emphase#\begin{WithArrows}@[c] + x+2y & = 0 \Arrow[tikz=-]{la même équation}\\ + x+2y & = 0 + ~emphase#\end{WithArrows}@\right. \\ + & \Leftrightarrow x+2y=0 +~emphase#\end{WithArrows}@$ +\end{Verbatim} + +$\begin{WithArrows} +\varphi(x,y)=0 + & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \Arrow{les nombres sont réels}\\ + & \Leftrightarrow + \left\{\begin{WithArrows}[c] + x+2y & = 0 \\ + 2x+4y & = 0 + \end{WithArrows}\right. \\ + & \Leftrightarrow + \left\{\begin{WithArrows}[c] + x+2y & = 0 \Arrow[tikz=-]{la même équation}\\ + x+2y & = 0 + \end{WithArrows}\right. \\ + & \Leftrightarrow x+2y=0 +\end{WithArrows}$ + +\bigskip +Néanmoins, on peut souhaiter tracer une flèche entre des rangées qui ne sont pas dans le même +environnement. Par exemple, on pourrait souhaiter tracer la flèche suivante : + +\bigskip +$\begin{WithArrows}[code-after = \Arrow[v]{1-2}{2-2}{division par $2$} ] +\varphi(x,y)=0 + & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ + & \Leftrightarrow + \left\{\begin{WithArrows}[c] + x+2y & = 0 \\ + 2x+4y & = 0 + \end{WithArrows}\right. \\ + & \Leftrightarrow + \left\{\begin{WithArrows}[c] + x+2y & = 0 \\ + x+2y & = 0 + \end{WithArrows}\right. \\ + & \Leftrightarrow x+2y=0 +\end{WithArrows}$ + + +\bigskip +Une telle construction est possible en utilisant \verb|\Arrow| dans le \verb|code-after| : +dans le \verb|code-after|, une version spéciale de la commande \verb|\Arrow| est disponible +(nous l'appellerons «\verb|\Arrow| dans le \verb|code-after|»). + +\smallskip +Une commande \verb|\Arrow| dans le \verb|code-after| prend trois arguments : +\begin{itemize} +\item une spécification pour la rangée de départ de la flèche ; +\item une spécification pour la rangée d'arrivée ; +\item une étiquette pour la flèche. +\end{itemize} +Comme d'habitude, il est possible de donner des options entre crochets avant ou après les trois arguments +obligatoires. Néanmoins, ces options sont limitées (voir plus bas). + +\interitem +La spécification de rangée est construite avec la position de l'environnement conidéré dans l'arbre des +imbrications, suivie, après un trait d'union, par le numéro de la rangée. + +\bigskip +Dans l'exemple précédent, il y a deux environnements \verb|{WithArrows}| imbriqués dans l'environnement +\verb|{WithArrows}| principal. + +\medskip +$\begin{WithArrows}[tikz-code = {\path (#1) to node {#3} (#2) ; }] +\varphi(x,y)=0 + & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ + & \Leftrightarrow \color{blue} + \left\{\begin{WithArrows}[c] + x+2y & = 0 \Arrow{environnement \no 1}\\ + 2x+4y & = 0 + \end{WithArrows}\right. \\ + & \Leftrightarrow \color{red} + \left\{\begin{WithArrows}[c] + x+2y & = 0 \Arrow{environnement \no 2}\\ + x+2y & = 0 + \end{WithArrows}\right. \\ + & \Leftrightarrow x+2y=0 +\end{WithArrows}$ + +\bigskip +La flèche que nous voulons tracer part de la rangée~$2$ du sous-environnement +\no $1$ (et, par conséquent, la spécification est \verb|1-2|) et arrive à la rangée~$2$ +du sous-environnement \no $2$ (et, par conséquent, la spécification est \verb|2-2|). +Nous pouvons tracer la flèche avec une commande \verb|\Arrow| dans le \verb|code-after| de la manière suivante : +\begin{Verbatim} +$\begin{WithArrows}[~emphase#code-after = \Arrow{1-2}{2-2}{division par $2$}@ ] +\varphi(x,y)=0 + & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ +......... +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows}[code-after = \Arrow{1-2}{2-2}{division par $2$} ] +\varphi(x,y)=0 + & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ + & \Leftrightarrow + \left\{\begin{WithArrows}[c] + x+2y & = 0 \\ + 2x+4y & = 0 + \end{WithArrows}\right. \\ + & \Leftrightarrow + \left\{\begin{WithArrows}[c] + x+2y & = 0 \\ + x+2y & = 0 + \end{WithArrows}\right. \\ + & \Leftrightarrow x+2y=0 +\end{WithArrows}$ + +\bigskip +Les options autorisées pour une commande \verb|\Arrow| dans le \verb|code-after| sont : \verb|ll|, \verb|lr|, +\verb|rl|, \verb|rr|, \verb|v|, \verb|xoffset|, \verb|tikz| et \verb|tikz-code|. Exceptée \verb|v|, qui est +spécifique à \verb|\Arrow| dans le \verb|code-after|, toutes ces options ont leur signification habituelle. + + +Avec l'option \verb|v|, la flèche tracée est verticale à une abscisse calculée avec +la rangée de départ et la rangée d'arrivée uniquement : les lignes intermédiaires ne sont pas prises en compte +contrairement à ce qui se passe avec l'option \verb|i|. Pour le moment, l'option \verb|i| n'est pas disponible +pour la commande~\verb|\Arrow| dans le \verb|code-after|. Néanmoins, il est toujours possible +de déplacer une flèche avec \verb|xoffset| (ou \verb|xshift| de Tikz). +\begin{Verbatim} +$\begin{WithArrows}[code-after=\Arrow~emphase#[v]@{1-2}{2-2}{division by $2$}] +\varphi(x,y)=0 + & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ +......... +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows}[code-after = \Arrow[v]{1-2}{2-2}{division par $2$} ] +\varphi(x,y)=0 + & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ + & \Leftrightarrow + \left\{\begin{WithArrows}[c] + x+2y & = 0 \\ + 2x+4y & = 0 + \end{WithArrows}\right. \\ + & \Leftrightarrow + \left\{\begin{WithArrows}[c] + x+2y & = 0 \\ + x+2y & = 0 + \end{WithArrows}\right. \\ + & \Leftrightarrow x+2y=0 +\end{WithArrows}$ + + +\interitem +L'extension \pkg{witharrows} fournit une autre commande disponible dans le \verb|code-after| : la commande +\verb|\MultiArrow|. Cette commande dessine un «rateau». La liste des rangées concernées par ce rateau +est donnée dans le premier argument de la commande \verb|\MultiArrow|. La syntaxe utilisée pour décrire cette liste +est celle de la commande \verb|\foreach| de \pkg{pgffor}. + +\begin{Verbatim} +$\begin{WithArrows}[tikz = rounded corners, + code-after = {~emphase#\MultiArrow{1,...,4}{text}@} ] +A & = B \\ + & = C \\ + & = D \\ + & = E \\ + & = F +\end{WithArrows}$ +\end{Verbatim} + + +$\begin{WithArrows}[tikz = rounded corners, + code-after = {\MultiArrow{1,...,4}{text}}] +A & = B \\ + & = C \\ + & = D \\ + & = E \\ + & = F +\end{WithArrows}$ + +\medskip +Pour le moment, aucune option n'est disponible pour cette commande \verb|\MultiArrow|. + + +\medskip +\section{Dessiner des flèches depuis l'extérieur des environnements \{WithArrows\}} + +Si on désire dessiner des flèches depuis l'extérieur des environnements \verb|{WithArrows}|, il est possible de le +faire en utilisant les nÅ“uds Tikz créés par ces environnements. + +Le nom d'un nÅ“ud Tikz crée par \pkg{witharrows} est préfixé par \verb|wa-|. Ensuite, on trouve une liste de nombres +qui indique quelle est la position de l'environnement dans l'arbre d'imbrication des environnements. À la fin, on a +le suffixe \verb|l| pour un nÅ“ud de gauche et le suffixe \verb|r| pour un nÅ“ud de droite. + +\smallskip +À titre d'illustration, nous donnons un exemple d'environnements \verb|{WithArrows}| imbriqués et, pour chaque nÅ“ud +de droite, le nom de ce nÅ“ud.\footnote{Il existe une option \verb|show-node-names| pour faire afficher les noms de + ces nÅ“uds.} + + +\medskip +\[\begin{WithArrows}[show-nodes,show-node-names] +A & \vartriangleleft B+B+B+B+B+B+B+B+B+B+B+B+B \\ +& \vartriangleleft \left\{ +\begin{WithArrows}[c] +C & \vartriangleleft D \\ +E & \vartriangleleft F +\end{WithArrows} +\right. \\ + & \vartriangleleft +\left\{ +\begin{WithArrows}[c] +G & \vartriangleleft H+H+H+H+H+H+H \\ +I & \vartriangleleft +\left\{ +\begin{WithArrows} +J &\vartriangleleft K \\ +L &\vartriangleleft M +\end{WithArrows} +\right. +\end{WithArrows} +\right. \\ + & \vartriangleleft +\left\{ +\begin{WithArrows}[c] +N & \vartriangleleft O \\ +P & \vartriangleleft Q +\end{WithArrows} +\right. +\end{WithArrows}\] + +\medskip +The package \pkg{witharrows} fournit quelques outils pour faciliter l'utilisation de ces nÅ“uds : +\begin{itemize} +\item la commande \verb|\WithArrowsLastEnv| donne le numéro du dernier environnement de niveau~$0$ (c'est-à-dire +non imbriqué dans un autre environnement de \pkg{witharrows}) ; + +\item un nom peut être donné à un environnement avec l'option \verb|name| et, dans ce cas, les nÅ“uds créés dans +l'environnement auront des alias construits en utilisant ce nom ; + +\item le style Tikz \verb|WithArrows/arrow| est le style utilisé par \pkg{witharrows} pour dessiner une +flèche\footnote{Plus précisément, ce style est passé à Tikz via l'option «\verb|every path|» avant le dessin de la + flèche (qui se fait avec l'instruction Tikz stockée dans \verb|tikz-code|). Ce style est modifié par l'option + \verb|tikz| de \pkg{witharrows} (avec une portée correspondant au groupe TeX courant).} ; + +\item le style Tikz \verb|WithArrows/arrow/tips| est le style utilisé pour la pointe de flèche (ce style est +lui-même chargé par le style \verb|WithArrows/arrow|). +\end{itemize} + +Par exemple, nous pouvons tracer une flèche allant de \texttt{wa-\WithArrowsLastEnv-2-1-2-r.south} +à \texttt{wa-\WithArrowsLastEnv-3-2-r.north} avec l'instruction Tikz suivante : + +\begin{Verbatim} +\begin{tikzpicture}[remember picture,overlay] +\draw [WithArrows/arrow] + ([xshift=3mm]wa-\WithArrowsLastEnv-2-1-2-r.south) + to ([xshift=3mm]wa-\WithArrowsLastEnv-3-2-r.north) ; +\end{tikzpicture} +\end{Verbatim} + +\[\begin{WithArrows} +A & \vartriangleleft B+B+B+B+B+B+B+B+B+B+B+B+B \\ +& \vartriangleleft \left\{ +\begin{WithArrows}[c] +C & \vartriangleleft D \\ +E & \vartriangleleft F +\end{WithArrows} +\right. \\ + & \vartriangleleft +\left\{ +\begin{WithArrows}[c] +G & \vartriangleleft H+H+H+H+H+H+H \\ +I & \vartriangleleft +\left\{ +\begin{WithArrows} +J &\vartriangleleft K \\ +L &\vartriangleleft M +\end{WithArrows} +\right. +\end{WithArrows} +\right. \\ + & \vartriangleleft +\left\{ +\begin{WithArrows}[c] +N & \vartriangleleft O \\ +P & \vartriangleleft Q +\end{WithArrows} +\right. +\end{WithArrows}\] + +\begin{tikzpicture}[remember picture,overlay] +\draw [WithArrows/arrow] + ([xshift=3mm]wa-\WithArrowsLastEnv-2-1-2-r.south) + to ([xshift=3mm]wa-\WithArrowsLastEnv-3-2-r.north) ; +\end{tikzpicture} + +\medskip +Dans le cas présent, il aurait été plus facile d'utiliser une commande \verb|\Arrow| dans le \verb|code-after| mais +c'était seulement un exemple pour expliquer comment les nÅ“uds Tikz créés par \pkg{witharrows} peuvent être utilisés. + +\bigskip +Dans l'exemple suivant, on crée deux environnements \verb|{WithArrows}| nommés +«\verb|premier|» et «\verb|second|» et on dessine une flèche entre un nÅ“ud du premier et un nÅ“ud du second. + +\begin{Verbatim} +$\begin{WithArrows}[~emphase#name=premier@] +A & = B \\ + & = C +\end{WithArrows}$ + +\bigskip +$\begin{WithArrows}[~emphase#name=second@] +A' & = B' \\ + & = C' +\end{WithArrows}$ + +\begin{tikzpicture}[remember picture,overlay] +\draw [WithArrows/arrow] + ([xshift=3mm]~emphase#premier@-1-r.south) + to ([xshift=3mm]~emphase#second@-1-r.north) ; +\end{tikzpicture} +\end{Verbatim} + + +\begin{center} +$\begin{WithArrows}[name=premier] +A & = B \\ + & = C +\end{WithArrows}$ + +\bigskip +$\begin{WithArrows}[name=second] +A' & = B' \\ + & = C' +\end{WithArrows}$ +\end{center} + +\begin{tikzpicture}[remember picture,overlay] +\draw [WithArrows/arrow] + ([xshift=3mm]premier-1-r.south) + to ([xshift=3mm]second-1-r.north) ; +\end{tikzpicture} + +\section{L'environnement \{DispWithArrows\}} +\label{DispWithArrows} + +Comme dit précédemment, l'environnement \verb|{WithArrows}| présente des similitudes avec l'environnement +\verb|{aligned}| de l'\pkg{amsmath} (et de \verb|mathtools|). L'extension \pkg{witharrows} +fournit aussi un environnement \verb|{DispWithArrows}| qui est similaire aux +environnements \verb|{align}| et \verb|{flalign}| de l'\pkg{amsmath}. + +\medskip +L'environnement \verb|{DispWithArrows}| doit être utilisé \emph{hors} du mode mathématique. Comme +\verb|{align}|, il doit être utilisé en mode horizontal. +\begin{Verbatim} +\begin{~emphase#DispWithArrows@} +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{~emphase#DispWithArrows@} +\end{Verbatim} +\begin{DispWithArrows} +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{DispWithArrows} + +\medskip +Il est possible d'utiliser la commande \verb|\notag| (ou \verb|\nonumber|) pour supprimer un numéro d'équation. + +Il est possible d'utiliser la commande \verb|\tag| pour placer une étiquette spéciale (par ex. $\star$). + +Il est aussi possible de placer un label pour une ligne de l'environnement avec la commande +\verb|\label|. + +Ces commandes doivent être utilisées dans la dernière colonne de l'environnement. +\begin{Verbatim} +\begin{DispWithArrows} +A & = (a+1)^2 \Arrow{on développe} ~emphase#\notag@ \\ + & = a^2 + 2a + 1 ~emphase#\tag{$\star$} \label{mon-équation}@ +\end{DispWithArrows} +\end{Verbatim} +\begin{DispWithArrows} +A & = (a+1)^2 \Arrow{on développe} \notag \\ + & = a^2 + 2a + 1 \tag{$\star$} \label{mon-équation} +\end{DispWithArrows} +Un lien vers l'équation \eqref{mon-équation}. On a obtenu ce lien avec la commande +\verb|\eqref{mon-équation}| (la commande \verb|\eqref| est une commande de l'extension \pkg{amsmath}). + +\medskip +Si \pkg{amsmath} (ou \pkg{mathtools}) est chargée, il est toujours possible d'utiliser +\verb|\tag*| qui, comme dans l'extension\pkg{amsmath}, compose le label sans les parenthèses. +Par exemple, il est possible de l'utiliser pour mettre le symbole \verb|\square| de +\pkg{amssymb}. Ce symbole est souvent utilisé pour marquer la fin d'une démonstration.\footnote{Signalons que l'environnement \verb|{DispWithArrows}| est compatible +avec la commande \verb|\qedhere| de \pkg{amsthm}.} +\begin{Verbatim} +\begin{DispWithArrows} +A & = (a+1)^2 \Arrow{on développe} \notag \\ + & = a^2 + 2a + 1 ~emphase#\tag*{$\square$}@ +\end{DispWithArrows} +\end{Verbatim} +\begin{DispWithArrows} +A & = (a+1)^2 \Arrow{on développe} \notag \\ + & = a^2 + 2a + 1 \tag*{$\square$} +\end{DispWithArrows} + +\medskip +Il est également possible de supprimer tous les numéros d'équations avec l'option booléenne \verb|notag| (ou +\verb|nonumber|), au niveau global ou bien au niveau d'un environnement. + +Enfin, il existe aussi +un environnement \verb|{DispWithArrows*}| qui supprime tous les numéros.\footnote{Même dans ce cas, il est possible +de mettre une étiquette manuellement avec la commande \verb|\tag|.} +\begin{Verbatim} +\begin{~emphase#DispWithArrows*@} +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{~emphase#DispWithArrows*@} +\end{Verbatim} +\begin{DispWithArrows*} +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{DispWithArrows*} + +\medskip +En fait, il y a une autre option, nommée \verb|tagged-lines|, qui peut être utilisée pour contrôler quelles lignes +seront numérotées. La valeur de cette option est la liste des numéros de lignes (dans l'environnement) qui seront +numérotées (par le système de numérotage des équations). Par exemple, avec l'option +\verb|tagged-lines = {first,3,last}|, seulement la première, la troisième et la dernière lignes seront numérotées. +Il y a aussi une valeur spéciale \verb|all| qui signifie que toutes les lignes doivent être numérotées. +\begin{Verbatim} +\begin{DispWithArrows}[~emphase#tagged-lines = last@] +A & = A_1 \Arrow{première étape} \\ + & = A_2 \Arrow{deuxième étape} \\ + & = A_3 +\end{DispWithArrows} +\end{Verbatim} +\begin{DispWithArrows}[tagged-lines = last] +A & = A_1 \Arrow{première étape} \\ + & = A_2 \Arrow{deuxième étape} \\ + & = A_3 +\end{DispWithArrows} + +\bigskip +Avec l'option \verb|fleqn|, l'environnement est composé calé à gauche (d'une manière similaire +à l'option \verb|fleqn| des classes standard de LaTeX). Dans ce cas, la marge gauche peut être réglée avec +l'option \verb|mathindent| (qui a un nom inspiré du paramètre \verb|\mathindent| de LaTeX). La valeur par défaut +pour cette option est de 25~pt. + +\begin{Verbatim} +\begin{DispWithArrows}[~emphase#fleqn,mathindent = 1cm@] +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{DispWithArrows} +\end{Verbatim} +\begin{DispWithArrows}[fleqn,mathindent = 1cm] +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{DispWithArrows} + +\medskip +\emph{Remarque} : Par conception, l'option \verb|fleqn| de \pkg{witharrows} est +indépendante de l'option de classe \verb|fleqn| de LaTeX. En effet, puisque les environnement de +\pkg{witharrows} sont conçus pour être utilisés avec des flèches sur le côté droit, l'utilisateur +peut souhaiter utiliser \pkg{witharrows} avec l'option \verb|fleqn| (de manière à avoir plus de place sur la droite +des équations pour les flèches) tout en continuant à centrer les équations classiques. + +\medskip +Si l'option \verb|leqno| est utilisée comme option de classe, les labels seront composés +à gauche également pour les environnements \verb|{DispWithArrows}|.\footnote{L'extension \pkg{amsmath} a une option \verb|leqno| +mais \pkg{witharrows}, bien entendu, ne tient pas compte de cette option : \pkg{witharrows} +vérifie seulement l'option \verb|leqno| de la classe du document.} + + +\medskip +Si l'extension \pkg{amsmath} est chargée, il est possible d'utiliser la commande \verb|\intertext| dans les +environnements \verb|{DispWithArrows}|. Il est également possible d'utiliser l'environnement \verb|{subequations}|. +Néanmoins, il existe pour les environnements \verb|{DispWithArrows}| une option \verb|subequations| qui demande +d'encapsuler l'environnement dans un environnement \verb|{subequations}|. + + +\medskip +Dans l'exemple suivant, l'option \verb|subequations| est fixée via la commande \verb|\WithArrowsOptions|. Chacun +des environnements suivants sera alors sous-numéroté (dans la portée de la commande \verb|WithArrowsOptions|). + +\begin{Verbatim} +~emphase#\WithArrowsOptions{subequations}@ +Premier environnement. +\begin{DispWithArrows} +A & = B \\ + & = C +\end{DispWithArrows} +Deuxième environnement. +\begin{DispWithArrows} +D & = E \\ + & = F +\end{DispWithArrows} +\end{Verbatim} +% +\begin{scope} +\WithArrowsOptions{subequations} +Premier environnement. +\begin{DispWithArrows} +A & = B \\ + & = C +\end{DispWithArrows} +Deuxième environnement. +\begin{DispWithArrows} +D & = E \\ + & = F +\end{DispWithArrows} +\end{scope} + +\bigskip +S'il n'y a pas suffisamment de place pour faire appraraître le numéro d'équation à la fin de la ligne, il n'y a pas +de positionnement automatique de ce numéro sur la ligne suivante (comme dans les environnements de +l'\pkg{amsmath}) : il y aura surimpression de texte. Néanmoins, dans \verb|{DispWithArrows}|, l'utilisateur peut +utiliser la commande \verb|\tagnextline| pour demander manuellement la composition du numéro sur la ligne suivante. +\begin{Verbatim} +\begin{DispWithArrows}[displaystyle] +S_{2(p+1)} +& =\sum_{k=1}^{2(p+1)} (-1)^k k^2 \\ +& \smash[b]{=\sum_{k=1}^{2p}(-1)^kk² + +(-1)^{2p+1}(2p+1)^2+(-1)^{2p+2}(2p+2)^2} ~emphase#\tagnextline@ \\ +&= S_{2p}-(2p+1)^2+(2p+2)^2\\ +&=p(2p+1)-(2p+1)^2+(2p+2)^2\\ +&= 2p^2+5p+3 +\end{DispWithArrows} +\end{Verbatim} +\begin{center} +\color{gray}\vrule% +\begin{minipage}{275pt}\color{black} +\begin{DispWithArrows}[displaystyle] +S_{2(p+1)} +& =\sum_{k=1}^{2(p+1)} (-1)^k k^2 \\ +& \smash[b]{=\sum_{k=1}^{2p}(-1)^kk^2+(-1)^{2p+1}(2p+1)^2+(-1)^{2p+2}(2p+2)^2} +\tagnextline \\ +&= S_{2p}-(2p+1)^2+(2p+2)^2\\ +&= 2p^2+p-4p^2-4p-1+4p^2+8p+4\\ +&= 2p^2+5p+3 +\end{DispWithArrows} +\end{minipage}% +\color{gray}\vrule +\end{center} + + + +\bigskip +Les environnements \verb|{DispWithArrows}| et \verb|{DispWithArrows*}| fournissent également une option +\verb|wrap-lines|. Avec cette option, les lignes de l'étiquette sont automatiquement coupées à droite.\footnote{Il + est possible d'éviter la coupure des mots avec l'option «\verb|align = flush left|» de Tikz.}\label{wrap-lines} + +\begin{Verbatim} +\begin{DispWithArrows*}[displaystyle,~emphase#wrap-lines@] +S_n +& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +\Arrow{somme des termes d'une suite géométrique de raison $e^{i\frac{2\pi}n}$}\\ +& = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n} + {1-e^{i\frac{\pi}{2n}}}\right) +\Arrow{cette ligne de texte a été coupée automatiquement} \\ +& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +\end{DispWithArrows*} +\end{Verbatim} +\begin{DispWithArrows*}[displaystyle,wrap-lines] +S_n +& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +\Arrow{somme des termes d'une suite géométrique de raison $e^{i\frac{2\pi}n}$}\\ +& = \frac1n \Re \left( +\frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}} \right) +\Arrow{cette ligne de texte a été coupée automatiquement} \\ +& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +\end{DispWithArrows*} + +\bigskip +L'option \verb|wrap-lines| ne s'applique pas aux environnements \verb|{WithArrows}| +imbriqués dans un environnement \verb|{DispWithArrows}| ou \verb|{DispWithArrows*}|. Néanmoins, +elle s'applique aux instructions \verb|\Arrow| et \verb|\MultiArrow| du \verb|code-after| +de l'environnement englobant. + +\vspace{1cm} +Nous avons dit que les environnements \verb|{DispWithArrows}| et \verb|{DispWithArrows*}| +devaient être utilisés en mode horizontal et non en mode vertical. Il y a néanmoins +une exception. Ces environnements peuvent être utilisés directement après un \verb|\item| d'une liste +LaTeX. Dans ce cas, aucun espace vertical n'est ajouté avant l'environnement.\footnote{Il est possible de désactiver + cette fonctionnalité avec l'option \verb|standard-behaviour-with-items|.} + +\medskip +Voici un exemple où, avec \verb|{DispWithArrows}|, on peut insérer l'équation dans un environnement +\verb|{enumerate}| tout en utilisant l'option \verb|wrap-lines|. + +\begin{Verbatim} +~emphase#\begin{enumerate}@ +~emphase#\item @ +\begin{DispWithArrows}% + [displaystyle, wrap-lines, tagged-lines = last, fleqn, mathindent = 0 pt] +S_n +& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +\Arrow{on utilise la formule pour la somme de termes d'une suite géométrique de raison +$e^{i\frac{2\pi}n}$} \\ +& = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n} + {1-e^{i\frac{\pi}{2n}}}\right) +\Arrow{$\bigl(e^{i\frac{\pi}{2n}}\bigr)^n = e^{i\frac{\pi}2}=i$} \\ +& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +\end{DispWithArrows} +~emphase#\end{enumerate}@ +\end{Verbatim} +\begin{enumerate} +\item +\begin{DispWithArrows}[displaystyle, wrap-lines, tagged-lines = last, fleqn, mathindent = 0 pt] +S_n +& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +\Arrow{on utilise la formule pour la somme de termes d'une suite géométrique de raison +$e^{i\frac{2\pi}n}$}\\ +& = \frac1n \Re \left( +\frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}} \right) +\Arrow{$\bigl(e^{i\frac{\pi}{2n}}\bigr)^n = e^{i\frac{\pi}2}=i$} \\ +& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +\end{DispWithArrows} +\end{enumerate} + +\vspace{1cm} +L'environnement \verb|{DispWithArrows}| est similaire à l'environnement \verb|{align}| de +l'\pkg{amsmath}. Néanmoins, \verb|{DispWithArrows}| n'est pas construit en utilisant \verb|{align}| +(en fait, il est possible d'utiliser \pkg{witharrows} sans \pkg{amsmath}). + +Il y a quelques différences entre \verb|{DispWithArrows}| et \verb|{align}|. +\begin{itemize} +\item L'environnement \verb|{DispWithArrows}| ne peut pas être inséré dans un environment +\verb|{gather}| de l'\pkg{amsmath}. +\item Un environment \verb|{DispWithArrows}| est toujours insécable (même avec +\verb|\allowdisplaybreaks| de l'\pkg{amsmath}). +\item Les commandes \verb|\label|, \verb|\tag|, \verb|\notag| et \verb|\nonumber| ne sont autorisées +que dans la dernière colonne. +\item Après un \verb|\item| d'une liste LaTeX, aucun espace vertical n'est ajouté (cela peut être +modifié avec l'option \verb|standard-behaviour-with-items|). +\item +\begin{bfseries} +Enfin, par défaut, les éléments d'un environnement \verb|\{DispWithArrows\}| +sont composés en \verb|textstyle| et non en \verb|displaystyle| (il est possible de modifier +ce point avec l'option \verb|displaystyle|). +\end{bfseries} +\end{itemize} + +\bigskip +En ce qui concerne les références, l'extension \pkg{witharrows} est compatible avec les +extensions \pkg{autonum}, \pkg{cleveref}, \pkg{fancyref}, \pkg{fncylab}, +\pkg{hyperref}, \pkg{listlbls}, \pkg{prettyref}, \pkg{refcheck}, +\pkg{refstyle}, \pkg{showlabels}, \pkg{smartref}, \pkg{typedref} et +\pkg{varioref} et avec les options \verb|showonlyrefs| et \verb|showmanualtags| de +\pkg{mathtools}.\footnote{Rappelons que \pkg{varioref}, \pkg{hyperref}, +\pkg{cleveref} et \pkg{autonum} doivent être chargés dans cet ordre. L'extension +\pkg{witharrows} peut être chargée n'importe où.} + +Elle n'est pas compatible avec \pkg{showkeys} (certains labels ne sont pas affichés). + + + + +\subsection*{L'option <...> de DispWithArrows} + +L'environnement \verb|{DispWithArrows}| propose une option \verb|left-brace|. Si cette option est présente, son +contenu est composé à gauche, suivi d'une accolade (d'où le nom) puis du corps de +l'environnement.\footnote{L'option \verb|left-brace| peut aussi être utilisée sans valeur: dans ce cas, seule + l'accolade est tracée.} + +Pour la lisibilité, cette option \verb|left-brace| est aussi disponible avec une syntaxe spéciale : on peut la +rentrer en la mettant entre chevrons (\verb|<| et \verb|>|) juste après le \verb|{DispWithArrows}| (et donc avant +les éventuels arguments optionnels entre crochets). + +\bigskip +On peut alors faire des constructions avec distinctions de cas, comme dans l'exemple +suivant.\footnote{L'environnement \verb|{cases}| de l'\pkg{amsmath} permet de réaliser de telles distinctions de + cas mais on ne peut pas utiliser la numérotation automatique des équations. L'environnement \verb|{numcases}| de + l'extension \pkg{cases} (de Donald Arseneau) permet d'utiliser ces numéros d'équations, mais, bien entendu, il + n'y a pas de composition de flèches.} + + + +\medskip + +\begin{BVerbatim} +\begin{DispWithArrows}~emphase#< \binom{n}{p} = >@[format = ll,fleqn,displaystyle] +0 & \quad \text{si } p > n +\Arrow{ce cas peut en fait rentrer\\ dans le suivant} \\ +\frac{n(n-1)\cdots(n-p+1)}{p!} & \quad \text{si } 0 \leq p \leq n \\ +0 & \quad \text{si } p < 0 +\end{DispWithArrows} +\end{BVerbatim} +% +\begin{DispWithArrows}< \binom{n}{p} = >[format = ll,fleqn,displaystyle] +0 & \quad \text{si } p > n +\Arrow{ce cas peut en fait rentrer\\ dans le suivant} \\ +\frac{n(n-1)\cdots(n-p+1)}{p!} & \quad \text{si } 0 \leq p \leq n \\ +0 & \quad \text{si } p < 0 +\end{DispWithArrows} + +\interitem +Dans l'exemple suivant, on sous-numérote les équations d'un système avec l'option \verb|subnumerate| (disponible +quand l'\verb|amsmath| est chargé). + +\begin{Verbatim} +\begin{DispWithArrows}~emphase#< \label{système} (\ref*{système}) \Leftrightarrow >@% + [format = l, subequations] +x+y+z = -3 \Arrow[tikz=-,jump=2]{3 equations} \\ +xy+xz+yz=-2 \\ +xyz = -15 \label{dernière-équation} +\end{DispWithArrows} +\end{Verbatim} +% +\begin{DispWithArrows}< \label{système} (\ref*{système}) \Leftrightarrow >% + [format = l, subequations] +x+y+z = -3 \Arrow[tikz=-,jump=2]{3 équations} \\ +xy+xz+yz=-2 \\ +xyz = -15 \label{dernière-équation} +\end{DispWithArrows} + +\bigskip +Le système complet est l'équation \eqref{système} (cette référence a été obtenue avec \verb|\eqref{système}|) et la +dernière équation est l'équation \eqref{dernière-équation} (référence obtenue avec +\verb|\eqref{dernière-équation}|). Notons que \verb|\ref*|, utilisé dans le code ci-dessus, est une variante de +\verb|ref| proposée par \pkg{hyperref} pour composer une référence sans créer de lien. + +\bigskip +On peut souhaiter remplacer l'accolade gauche par un autre délimiteur extensible (gauche). On peut le faire avec +l'option \verb|replace-left-brace-by|. Par exemple «\verb|replace-left-brace-by = [\enskip|» va composer avec un +crochet et ajouter aussi un espace de 1~em après le crochet. + +\bigskip +\section{Fonctionnalités avancées} + +\subsection{Utilisation avec plain-TeX} +\label{plain-TeX} + +L'extension \pkg{witharrows} peut être utilisée avec plain-TeX. Pour cela, on doit charger l'extension avec +\verb|\input|: +% +\begin{Verbatim} +\input{witharrows.tex} +\end{Verbatim} + +\medskip +En plain-TeX, il n'y a pas d'environnements comme dans LaTeX. + +Au lieu de \verb|\begin{WithArrows}| et \verb|\end{WithArrows}| comme en LaTeX, on doit utiliser un +pseudo-environnement délimité par \verb|\Witharrows| et \verb|\endWithArrows| (de même pour +\verb|{DispWithArrows}|). +% +\begin{Verbatim} +$\WithArrows +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\endWithArrows$ +\end{Verbatim} + +\medskip +La version pour plain-TeX de \pkg{witharrows} ne propose pas toutes les fonctionnalités proposées pour la version +LaTeX. En particulier, les fonctionnalités concernant les numéros d'équations ne sont pas disponibles (puisqu'elles +reposent sur le système de numérotation de LaTeX). + +\subsection{L'option tikz-code : comment changer la forme des flèches} + +\label{tikz-code} + +L'option \verb|tikz-code|\footnote{Pour des raisons historiques, l'option \verb|tikz-code| a un alias : + \verb|TikzCode|.} permet à l'utilisateur de changer la forme des flèches.\footnote{Si l'option \verb|wrap-lines| + est utilisée dans un environnement \verb|{DispWithArrows}| ou \verb|{DispWithArrows*}|, l'option \verb|tikz-code| + n'aura pas d'effet sur les flèches de cet environnement mais uniquement sur les flèches des environnements + \verb|{WithArrows}| imbriqués.} + +\smallskip +Par exemple, les options «\verb|up|» et «\verb|down|» décrites précédemment (cf. +p.~\pageref{up-and-down}) sont programmées en interne avec \verb|tikz-code|. + +\smallskip +La valeur de cette option doit être une instruction de tracé Tikz valide (avec le point-virgule final) où les trois +marqueurs \verb|#1|, \verb|#2| et \verb|#3| représentent le point de départ, le point d'arrivée et l'étiquette de +la flèche. + + +\bigskip +Par défaut, la valeur de \verb|tikz-code| est la suivante : + +\smallskip +\qquad \verb|\draw (#1) to node {#3} (#2) ;| + + +\bigskip +Dans l'exemple suivant, nous remplaçons le chemin par défaut par un chemin avec trois segments (et un +nÅ“ud recouvrant le deuxième segment). +\begin{Verbatim} +\begin{WithArrows}[format=c,ygap=5pt,interline=4mm, + ~emphase#tikz-code = {\draw[rounded corners]@ + ~emphase# (~#1) -- ([xshift=5mm]~#1)@ + ~emphase# -- node[circle,@ + ~emphase# draw,@ + ~emphase# auto = false,@ + ~emphase# fill = gray!50,@ + ~emphase# inner sep = 1pt] {\tiny ~#3}@ + ~emphase# ([xshift=5mm]~#2)@ + ~emphase# -- (~#2) ; }@] +3 (2x+4) = 6 \Arrow{$\div 3$} \\ +2x+4 = 2 \Arrow{$-4$} \\ +2x = -2 \Arrow{$\div 2$} \\ + x = -1 +\end{WithArrows} +\end{Verbatim} + + +\[\begin{WithArrows}[format=c, + ygap=5pt, + interline=4mm, + tikz-code = {\draw[rounded corners] + (#1) + -- + ([xshift=5mm]#1) + -- node[circle, + draw, + auto=false, + fill=gray!50, + inner sep = 1pt] {\tiny #3} + ([xshift=5mm]#2) + -- + (#2) ; }] +3 (2x+4) = 6 \Arrow{$\div 3$} \\ +2x+4 = 2 \Arrow{$-4$} \\ +2x = -2 \Arrow{$\div 2$} \\ + x = -1 +\end{WithArrows}\] + +\bigskip +L'environnement \verb|{DispWithArrows}| et sa version étoilée \verb|{DispWithArrows*}| fournissent une commande +\verb|\WithArrowsRightX| qui peut être utilisée dans l'option \verb|tikz-code|. Cette commande fournit +l'abscisse de la marge droite de la boîte de composition courante (en prenant en compte les éventuels numéros des +équations). Pour un exemple d'utilisation, voir p.~\pageref{example-WithArrowsRightX}. + + +\bigskip +\subsection{La commande \textbackslash WithArrowsNewStyle} + +L'extension \pkg{witharrows} fournit une commande \verb|\WithArrowsNewStyle| pour définir +des styles d'une manière similaire aux «styles» de Tikz. + +La commande \verb|\WithArrowsNewStyle| prend deux arguments obligatoires. Le premier est +le nom du style et le second est une liste de couples clé-valeur. La portée +de la definition ainsi faite par \verb|\WithArrowsNewStyle| est le groupe TeX courant. + +Le style peut être utilisé comme une clé au niveau du document (avec \verb|\WithArrowsOptions|), au niveau d'un +environnement (via les arguments optionnels) ou bien encore dans une autre commande \verb|\WithArrowsNewStyle|. + +Pour un exemple d'utilisation, voir p.~\pageref{example-WithArrowsRightX}. + + +\bigskip +\subsection{Positionnement vertical des flèches} + +Il y a quatre paramètres pour ajuster finement la position verticale des flèches : +\verb|ygap|, \verb|ystart|, \verb|start-adjust| et \verb|end-adjust|. + +\medskip +Nous expliquons d'abord le comportement quand les paramètres \verb|start-adjust| et \verb|end-adjust| sont égaux à +zéro: +\begin{itemize} +\item l'option \verb|ystart| représente la distance verticale entre la ligne de base du +texte et le début de la flèche (valeur par défaut : $0.4$~ex); +\item l'option \verb|ygap| représente la distance verticale entre deux flèches consécutives +(valeur par défaut : $0.4$~ex). +\end{itemize} + + +\bigskip +$\begin{WithArrows}[interline=1mm, adjust = 0pt] + (\cos x + \sin x)^2 & = \cos^2 x +2 \cos x \sin x + \sin^2 x\Arrow{}\tikz[remember picture] \coordinate (A) ; \\ + & = \cos^2x + \sin^2x + 2\sin x\cos x \Arrow{} \\ + & = 1 + \sin(2x) +\end{WithArrows}$ + +\begin{tikzpicture}[remember picture,overlay,blue] +\draw (wa-\WithArrowsLastEnv-1-r.south) to ++(1,0) coordinate (B) to ++(0.1,0) ;; +\draw (A) to ++(1,0) coordinate (C) to ++(0.1,0) ;; +\draw (B) -- (C) ; +\draw[<-] (B) to ++(0,0.2) ; +\draw[<-] (C) to ++(0,-0.2) ; +\path (C) node[right=1mm] {\texttt{ystart}} ; +\draw (wa-\WithArrowsLastEnv-2-r.north) to ++(3,0) coordinate (E) to ++(0.1,0); +\draw (wa-\WithArrowsLastEnv-2-r.south) to ++(3,0) coordinate (F) to ++(0.1,0); +\draw (E) -- (F) ; +\draw[<-] (E) to ++(0,0.2) ; +\draw[<-] (F) to ++(0,-0.2) ; +\path (F) node[right=1mm] {\texttt{ygap}} ; +\end{tikzpicture} + +\interitem +Néanmoins, pour des raisons esthétiques, quand il est possible, \pkg{witharrows} commence +la flèche un peu plus haut (d'une quantité \verb|start-adjust|) et termine la flèche un peu plus +bas (par une quantité \verb|end-adjust|). Par défaut, ces deux paramètres \verb|start-adjust| +est \verb|end-adjust| sont égaux à $0.4$~ex. + +\bigskip +Voici par exemple le comportement sans le mécanisme de \verb|start-adjust| et +\verb|end-adjust| (c'était le comportement par défaut dans les versions antérieures à la version 1.13). +\begin{Verbatim} +$\begin{WithArrows}~emphase#[start-adjust=0pt, end-adjust=0pt]@ +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows}[start-adjust=0pt, end-adjust=0pt] +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + + +\bigskip +Voici le comportement par défaut depuis la version 1.13 (les paramètres +\verb|start-adjust| et \verb|end-ajust| sont utilisés avec la valeur par défaut $0.4$~ex). La flèche +est plus longue et le résultat est plus esthétique. + +\medskip +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{on développe} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + + +\bigskip +Il est possible d'utiliser l'option \verb|adjust| qui fixe à la fois \verb|start-adjust| et \verb|end-ajust|. + +\bigskip +Puisque le mécanisme de \verb|start-adjust| et \verb|end-ajust| a été ajouté dans la +version 1.13 of \pkg{witharrows}, cette version n'est pas strictement compatible avec +les versions précédentes. Néanmoins, il est possible de retrouver le comportement précédent +en fixant simplement \verb|start-adjust| et \verb|end-adjust| à $0$~pt: +\begin{Verbatim} +\WithArrowsOptions{adjust = 0pt} +\end{Verbatim} + +\bigskip +\subsection{Notes de pied de page dans les environnements de witharrows} + +Si vous voulez mettre des notes de pied de page dans un environnement de \pkg{witharrows}, +vous pouvez utiliser une paire \verb|\footnotemark|--\verb|\footnotetext|. + +\smallskip +Il est aussi possible d'extraire les notes de pieds de page avec l'extension \pkg{footnote} ou bien l'extension +\pkg{footnotehyper}. + +\smallskip +Si \pkg{witharrows} est chargée avec l'option \verb|footnote| (avec \verb|\usepackage[footnote]{witharrows}| ou +avec \verb|\PassOptionsToPackage|), l'extension \pkg{footnote} est chargée (si elle ne l'est pas déjà) et elle est +utilisée pour extraire les notes de pied de page. + +\smallskip +Si \pkg{witharrows} est chargée avec l'option \verb|footnotehyper|, l'extension \pkg{footnotehyper} est chargée (si +elle ne l'est pas déjà) et elle est utilisée pour extraire les notes de pied de page. + +\smallskip +Attention : Les extensions \pkg{footnote} et \pkg{footnotehyper} sont incompatibles. +L'extension \pkg{footnotehyper} est le successeur de l'extension \pkg{footnote} +et devrait être utilisée préférentiellement. L'extension \pkg{footnote} a quelques défauts ; +en particulier, elle doit être chargée après l'extension \pkg{xcolor} et elle n'est pas parfaitement +compatible avec \pkg{hyperref}. + +\medskip +Dans ce document, l'extension \pkg{witharrows} a été chargée avec l'option \verb|footnotehyper| et nous donnons un +exemple avec une note de pied de page dans l'étiquette d'une flèche : + + +\smallskip +$\begin{WithArrows} +A & = (a+b)^2 +\Arrow{on développe\,\footnote{Une note de pied de page.}} \\ + & = a^2+b^2+2ab +\end{WithArrows}$ + +\bigskip +\subsection{L'option no-arrows} + +L'option \verb|no-arrows| est une facilité donnée à l'utilisateur. Avec cette option, +les flèches ne sont pas tracées. Néanmoins, une analyse des flèches est effectuée et certaines erreurs sont +détectées (par exemple, si une flèche arrive après la dernière ligne de l'environnement). + + +\bigskip +\subsection{Note pour les développeurs} + +Si vous définissez un environnement s'appuyant sur un environnement de +\pkg{witharrows}, nous recommandons de faire appel à l'environnement de \pkg{witharrows} avec +\verb|\WithArrows|--\verb|\endWithArrows| ou \verb|\DispWithArrows|--\verb|\endDispWithArrows| (et +non \verb|\begin{WithArrows}|--\verb|\end{WithArrows}|, etc.). + +\smallskip +En faisant ainsi, les messages d'erreur affichés par \pkg{witharrows} mentionneront (le cas échéant) le nom de +votre environnement et seront plus faciles à comprendre pour l'utilisateur final. + +\smallskip +Par exemple, vous pouvez définir un environnement \verb|{DWA}| qui va être un alias de \verb|{DispWithArrows}|: +\begin{BVerbatim} +\NewDocumentEnvironment {DWA} {} {\DispWithArrows}{\endDispWithArrows} +\end{BVerbatim} + +\smallskip +Si vous utilisez cet environnement \verb|{DWA}| en mode mathématique, vous aurez le message d'erreur suivant : + +\begin{BVerbatim} +L'environnement {DWA} should be used only outside math mode. +\end{BVerbatim} + +\interitem +Une autre exemple est donné en interne par la définition de l'environnement \verb|{DispWithArrows*}| +dans l'extension \pkg{witharrows} avec le code suivant: +\begin{Verbatim} +\NewDocumentEnvironment {DispWithArrows*} {} + {\WithArrowsOptions{notag}% + \DispWithArrows} + {\endDispWithArrows} +\end{Verbatim} + + + +\section{Examples} + +\subsection{\textbackslash MoveEqLeft} + +Il est possible d'utiliser \verb|\MoveEqLeft| de \pkg{mathtools}. Dans ce cas, on doit se souvenir que la commande +\verb|\MoveEqLeft| a aussi la valeur d'une esperluette (\verb|&|). Il faut en tenir compte pour le positionnement +d'une éventuelle commande \verb|\Arrow|. + + +% +\begin{Verbatim}[formatcom=\small\color{gray}] +$\begin{WithArrows}[interline=0.5ex] +~emphase#\MoveEqLeft@ \arccos(x) = \arcsin \frac45 + \arcsin \frac5{13} +\Arrow{parce que les deux sont dans $[-\frac{\pi}2,\frac{\pi}2]$} \\ +& \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}[interline=0.5ex] +\MoveEqLeft \arccos(x) = \arcsin \frac45 + \arcsin \frac5{13} +\Arrow{parce que les deux sont dans $[-\frac{\pi}2,\frac{\pi}2]$} \\ +& \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}$ + + +\bigskip +\subsection{Modifier la forme des nÅ“uds} + +Il est possible de changer la forme des étiquettes, qui sont des nÅ“uds Tikz, en +modifiant la clé «\verb|every node|» de Tikz. + +\begin{Verbatim} +\begin{WithArrows}% + [format = c, + interline = 4mm, + tikz = {~emphase#every node/.style = {circle,@ + ~emphase# draw,@ + ~emphase# auto = false,@ + ~emphase# fill = gray!50,@ + ~emphase# inner sep = 1pt,@ + ~emphase# font = \tiny}@}] + 3 (2x+4) = 6 \Arrow{$\div 3$} \\ + 2x+4 = 2 \Arrow{$-4$} \\ + 2x = -2 \Arrow{$\div 2$} \\ + 2x = -1 +\end{WithArrows} +\end{Verbatim} + +\[\begin{WithArrows}[% + format = c, + interline = 4mm, + tikz = {every node/.style = {circle, + draw, + auto = false, + fill = gray!50, + inner sep = 1pt, + font = \tiny}}] + 3 (2x+4) = 6 \Arrow{$\div 3$} \\ + 2x+4 = 2 \Arrow{$-4$} \\ + 2x = -2 \Arrow{$\div 2$} \\ + 2x = -1 +\end{WithArrows}\] + + +\bigskip +\subsection{Exemples avec l'option tikz-code} + +Rappelons que l'option \verb|tikz-code| est le code Tikz utilisé par \pkg{witharrows} +pour tracer les flèches.\footnote{Si un environnement \verb|{DispWithArrows}| ou +\verb|{DispWithArrows*}| est utilisé avec l'option \verb|wrap-lines|, la valeur de l'option +\verb|tikz-code| n'est pas utilisée pour cet environnement (mais est utilisée pour les +environnements imbriqués à l'intérieur).} + +\smallskip +La valeur par défaut de \verb|tikz-code| est \verb|\draw (#1) to node {#3} (#2) ;| +où les trois marqueurs \verb|#1|, \verb|#2| et \verb|#3| représentent le point de départ, le point d'arrivée +et l'étiquette de la flèche. + + +\bigskip +\subsubsection{Exemple 1} +Dans l'exemple suivant, nous définissons la valeur de \verb|tikz-code| avec deux +instructions \verb|\path| : la première instruction trace la flèche elle-même et la seconde +place l'étiquette dans un nÅ“ud Tikz dans le rectangle délimité par la flèche. + +\begin{Verbatim} +\begin{DispWithArrows*}% + [displaystyle, + ygap = 2mm, + ystart = 0mm, + ~emphase#tikz-code = {\draw (~#1) -- ++(4.5cm,0) \verb|- (~#2) ;@ + ~emphase# \path (~#1) -- (~#2) @ + ~emphase# node[text width = 4.2cm, right, midway] {~#3} ;}@] +S_n +& = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr) +........... +\end{Verbatim} + + +\bigskip +\begin{DispWithArrows*}[ + displaystyle, + ygap = 2mm, + ystart = 0mm, + tikz-code = {\draw (#1) -- ++(4.5cm,0) |- (#2) ; + \path (#1) -- (#2) + node[text width = 4.2cm, right, midway] {#3} ;}] +S_n +& = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr) +\Arrow{$\cos x = \Re(e^{ix})$}\\ +& = \frac1n\sum_{k=0}^{n-1} \Re\left(e^{i\frac{k\pi}{2n}}\right) +\Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\ +& = \frac1n \Re\left(\sum_{k=0}^{n-1} e^{i\frac{k\pi}{2n}}\right) +\Arrow{$\exp$ est un morphisme pour $\times$ et $+$} \\ +& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +\Arrow{somme de termes d'une suite géométrique de raison $e^{i\frac{2\pi}n}$}\\ +& = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}}\right)\\ +& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +\end{DispWithArrows*} + +\bigskip +\subsubsection{Exemple 2} + +\label{example-WithArrowsRightX} +Il est possible de modifier l'exemple précédent pour avoir «\verb|text width|» calculé automatiquement en fonction +de la marge droite (d'une manière similaire à l'option \verb|wrap-lines|) dans les environnements +\verb|{DispWithArrows}| et \verb|{DispWithArrows*}|. Dans la définition de \verb|tikz-code|, nous utilisons la commande +\verb|\WithArrowsRightX| qui donne l'abscisse de la marge droite de la boîte de composition (pour TeX, il s'agit d'une commande +et non d'une dimension). Pour la lisibilité, nous avons utilisé un style de \pkg{witharrows}. Cet exemple nécessite +l'extension Tikz \pkg{calc}. + +\begin{Verbatim} +\WithArrowsNewStyle{MonStyle} + {displaystyle, + ygap = 2mm, + xoffset = 0pt, + ystart = 0mm, + tikz-code = {\path let \p1 = (~#~#1) + in (~#~#1) + -- node [anchor = west, + text width = {~emphase#\WithArrowsRightX@ - \x1 - 0.5 em}] + {~#~#3} + (~#~#2) ; + \draw let \p1 = (~#~#1) + in (~#~#1) -- ++(~emphase#\WithArrowsRightX@ - \x1,0) |- (~#~#2) ; }} +\end{Verbatim} + +\begin{Verbatim} +\begin{DispWithArrows}[MonStyle] + S_n + & = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr) + \Arrow{$\cos x = \Re(e^{ix})$}\\ +........... +\end{Verbatim} + +\WithArrowsNewStyle{MonStyle} +{displaystyle, + ygap = 2mm, + xoffset = 0pt, + ystart = 0mm, + tikz-code = {\path let \p1 = (##1) + in (##1) + -- node [anchor = west, + text width = {\WithArrowsRightX - \x1 - 0.5 em}] {##3} + (##2) ; + \draw let \p1 = (##1) + in (##1) -- ++(\WithArrowsRightX - \x1,0) |- (##2) ; }} + +\begin{DispWithArrows}[MonStyle] +S_n +& = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr) +\Arrow{$\cos x = \Re(e^{ix})$}\\ +& = \frac1n\sum_{k=0}^{n-1} \Re\left(e^{i\frac{k\pi}{2n}}\right) +\Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\ +& = \frac1n \Re\left(\sum_{k=0}^{n-1} e^{i\frac{k\pi}{2n}}\right) +\Arrow{$\exp$ est un morphisme pour $\times$ et $+$} \\ +& = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +\Arrow{somme de termes d'une suite géométrique $e^{i\frac{2\pi}n}$}\\ +& = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}}\right)\\ +& = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +\end{DispWithArrows} + + + +\bigskip +\subsubsection{Exemple 3} + +Dans l'exemple suivant, nous changeons la forme de la flèche selon que la rangée de départ est plus longue ou +plus courte que la rangée d'arrivée. Cet exemple nécessite l'extension \pkg{calc} de Tikz. + + +\begin{Verbatim} +\begin{WithArrows}[ll,interline=5mm,xoffset=5mm, + ~emphase#tikz-code = {\draw[rounded corners,@ + ~emphase# every node/.style = {circle,@ + ~emphase# draw,@ + ~emphase# auto = false,@ + ~emphase# inner sep = 1pt,@ + ~emphase# fill = gray!50,@ + ~emphase# font = \tiny }]@ + ~emphase# let \p1 = (~#1),@ + ~emphase# \p2 = (~#2)@ + ~emphase# dans \ifdim \x1 > \x2@ + ~emphase# (\p1) -- node {~#3} (\x1,\y2) -- (\p2)@ + ~emphase# \else@ + ~emphase# (\p1) -- (\x2,\y1) -- node {~#3} (\p2)@ + ~emphase# \fi ;}@] +E & \Longleftrightarrow \frac{(x+4)}3 + \frac{5x+3}5 = 7 +\Arrow{$\times 15$}\\ + & \Longleftrightarrow 5(x+4) + 3(5x+3) = 105 \\ + & \Longleftrightarrow 5x+20 + 15x+9 = 105 \\ + & \Longleftrightarrow 20x+29 = 105 +\Arrow{$-29$}\\ + & \Longleftrightarrow 20x = 76 +\Arrow{$\div 20$}\\ + & \Longleftrightarrow x = \frac{38}{10} +\end{WithArrows} +\end{Verbatim} + + +\[\begin{WithArrows}[ll,interline=5mm,xoffset=5mm, + tikz-code = {\draw[rounded corners, + every node/.style = {circle, + draw, + auto = false, + inner sep = 1pt, + fill = gray!50, + font = \tiny}] + let \p1 = (#1), + \p2 = (#2) + in \ifdim \x1 > \x2 + (\p1) -- node {#3} (\x1,\y2) -- (\p2) + \else + (\p1) -- (\x2,\y1) -- node {#3} (\p2) + \fi ;}] +E & \Longleftrightarrow \frac{(x+4)}3 + \frac{5x+3}5 = 7 +\Arrow{$\times 15$}\\ + & \Longleftrightarrow 5(x+4) + 3(5x+3) = 105 \\ + & \Longleftrightarrow 5x+20 + 15x+9 = 105 \\ + & \Longleftrightarrow 20x+29 = 105 +\Arrow{$-29$}\\ + & \Longleftrightarrow 20x = 76 +\Arrow{$\div 20$}\\ + & \Longleftrightarrow x = \frac{38}{10} +\end{WithArrows}\] + + + +\subsection{Boucle numérotée automatique} + +Supposons que nous voulions tracer une boucle avec des flèches numérotées. Dans ce but, il est +possible d'écrire une commande dédiée \verb|\BoucleNumérotée| qui fera le travail quand elle +sera utilisée dans le \verb|code-after|. Dans l'exemple suivant, nous avons écrit cette commande avec +\verb|\NewDocumentCommand| de \pkg{xparse} et \verb|\foreach| de \pkg{pgffor} (ces deux +extensions sont chargées quand \pkg{witharrows} est chargé.). + +\begin{Verbatim} +\NewDocumentCommande \NombreedLoop {} + {\foreach \j dans {2,...,\WithArrowsNbLines} + { \pgfmathtruncatemacro{\i}{\j-1} + \Arrow[rr]{\i}{\j}{\i} } + \Arrow[rr,xoffset=1cm,tikz=<-]{1}{\WithArrowsNbLines}{\WithArrowsNbLines}} +\end{Verbatim} + +La commande \verb|\WithArrowsNbLines| est une commande disponible dans le \verb|code-after| qui donne +le nombre total de lignes (=rangées) dans l'environnement courant (pour TeX, il s'agit d'une commande et non d'un +compteur). + + +\bigskip +\begin{Verbatim} +$\begin{WithArrows}[~emphase#code-after = \BoucleNumérotée@] +a.\;& f \text{ est continue sur } E \\ +b.\;& f \text{ est continue en } 0 \\ +c.\;& f \text{ est bornée sur la sphère unité} \\ +d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\ +e.\;& f \text{ est lipschitzienne} +\end{WithArrows}$ +\end{Verbatim} + +\bigskip +\begin{scope} +\NewDocumentCommand \BoucleNumérotée {} + {\foreach \j in {2,...,\WithArrowsNbLines} + { \pgfmathtruncatemacro{\i}{\j-1} + \Arrow[rr]{\i}{\j}{\i} } + \Arrow[rr,xoffset=1cm,tikz=<-]{1}{\WithArrowsNbLines}{\WithArrowsNbLines}} + + +$\begin{WithArrows}[code-after = \BoucleNumérotée] +a.\;& f \text{ est continue sur } E \\ +b.\;& f \text{ est continue en } 0 \\ +c.\;& f \text{ est bornée sur la sphère unité} \\ +d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\ +e.\;& f \text{ est lipschitzienne} +\end{WithArrows}$ + + +\bigskip +Comme d'habitude, il est possible changer les caractéristiques des flèches et des nÅ“uds +avec l'option \verb|tikz|. Néanmoins, si nous voulons changer le style pour avoir, par +exemple, les numéros entre parenthèses, le moyen le plus rapide est de changer la valeur de +\verb|tikz-code|: + +\begin{Verbatim} +tikz-code = {\draw (~#1) to node {\footnotesize (~#3)} (~#2) ;} +\end{Verbatim} + +\WithArrowsOptions{tikz-code = {\draw (#1) to node {\footnotesize (#3)} (#2) ;}} + +$\begin{WithArrows}[code-after = \BoucleNumérotée] +a.\;& f \text{ est continue on } E \\ +b.\;& f \text{ est continue dans } 0 \\ +c.\;& f \text{ est bornée sur la sphère unité} \\ +d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\ +e.\;& f \text{ est lipschitzienne} +\end{WithArrows}$ + +\end{scope} + + + + + +\end{document} diff --git a/macros/generic/witharrows/witharrows.dtx b/macros/generic/witharrows/witharrows.dtx new file mode 100644 index 0000000000..8dc046bd9d --- /dev/null +++ b/macros/generic/witharrows/witharrows.dtx @@ -0,0 +1,6977 @@ +% \iffalse meta-comment +% +% Copyright (C) 2017-2019 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{2.0} +\def\myfiledate{2019/07/30} +% +% +%<*batchfile> +\begingroup +\input l3docstrip.tex +\keepsilent +\usedir{tex/latex/witharrows} +\preamble + +Copyright (C) 2017-2019 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 +% +% +%<*driver> +\documentclass[dvipsnames]{l3doc}% dvipsnames is for xcolor (loaded by Tikz, loaded by witharrows) +\usepackage{xltxtra} +\usepackage[xetex]{geometry} +\geometry{left=2.8cm,right=2.8cm,top=2.5cm,bottom=2.5cm,papersize={21cm,29.7cm}} +\usepackage[footnotehyper]{witharrows} +\usetikzlibrary{calc} +\usepackage{mathtools} +\usepackage{amssymb} +\usepackage[only,llbracket,rrbracket]{stmaryrd} +\usepackage{varwidth} +\NewDocumentEnvironment {scope} {} {} {} +\def\interitem{\vskip 7mm plus 2 mm minus 3mm} +\def\emphase{\bgroup\color{RoyalPurple}\let\next=} +\fvset{commandchars=\~\#\@,formatcom={\color{gray}}} +\DeclareMathOperator{\re}{Re} +\skip \footins = 2 \bigskipamount +\parindent 0pt +\DisableCrossrefs +\begin{document} +\DocInput{witharrows.dtx} +\end{document} +% +% \fi +% \VerbatimFootnotes +% \title{The package \pkg{witharrows} for plain-TeX and LaTeX\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 +% +% \hypersetup{ +% pdfinfo = { +% Title = { The extension 'witharrows' }, +% Subject = { A extension for plain-TeX and LaTeX} , +% Author = { F. Pantigny } +% } +% } +% +% +% \begin{abstract} +% The LaTeX package \pkg{witharrows} provides environments |{WithArrows}| and +% |{DispWithArrows}| similar to the environments |{aligned}| and |{align}| of +% \pkg{amsmath} but with 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} +% +% +% \vspace{1cm} In this document, we describe the LaTeX extension +% \pkg{witharrows} (however, \pkg{witharrows} can also be used with plain-TeX: +% see p.~\pageref{plain-TeX}). This package can be used with |xelatex|, +% |lualatex|, |pdflatex| but also by the classical workflow +% |latex|-|dvips|-|ps2pdf| (or Adobe Distiller). This package loads the packages +% \pkg{expl3}, \pkg{l3keys2e}, \pkg{xparse}, \pkg{tikz} and the Tikz libraries +% \pkg{arrows.meta} and \pkg{bending}. The arrows are drawn with Tikz and that's +% why several compilations may be necessary. +% +% \bigskip +% This package provides an environment |{WithArrows}| to construct alignments of +% equations with arrows for the explanations on the right side: +% +% \begin{Verbatim} +% $\begin{WithArrows} +% A & = (a+1)^2 ~emphase#\Arrow{we expand}@ \\ +% & = a^2 + 2a + 1 % don't put \\ here +% \end{WithArrows}$ +% \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 row from which it +% starts. The command |\Arrow| must be used in the second column (the best way +% is to put it at the end of the second cell of the row as in the previous +% example). +% +% \medskip +% The environment |{WithArrows}| bears similarities with the environment +% |{aligned}| of \pkg{amsmath} (and |mathtools|). The extension \pkg{witharrows} +% also provides an environment |{DispWithArrows}| which is similar to the +% environment |{align}| of \pkg{amsmath}: cf. p. \pageref{DispWithArrows}. +% +% +% \section{Options for the shape of the arrows} +% +% The command |\Arrow| has several options. These options can be put between +% square brackets, before, or after the mandatory argument. +% +% The option |jump| gives the number\footnote{It's not possible to give a +% non-positive value to |jump|. See below (p.~\pageref{Backwards}) the way to +% draw an arrow which goes backwards.} of rows the arrow must jump (the default +% value is, of course,~$1$). +% +% +% \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} +% +% $\begin{WithArrows} +% A & = \bigl((a+b)+1\bigr)^2 \Arrow[jump=1+1]{we expand} \\ +% & = (a+b)^2 + 2(a+b) +1 \\ +% & = a^2 + 2ab + b^2 + 2a + 2b +1 +% \end{WithArrows}$ +% +% \interitem +% It's possible to put several arrows which start from the same row. +% \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| shifts the arrow 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 thick arrow. +% \begin{Verbatim} +% $\begin{WithArrows} +% A & = (a+1)^2 \Arrow[~emphase#tikz=thick@]{we expand} \\ +% & = a^2 + 2a + 1 +% \end{WithArrows}$ +% \end{Verbatim} +% +% $\begin{WithArrows} +% A & = (a+1)^2 \Arrow[tikz=thick]{we expand} \\ +% & = a^2 + 2a + 1 +% \end{WithArrows}$ +% +% \interitem +% It's also possible to change the arrowheads. For example, we can draw an arrow +% which goes backwards with the Tikz option~|<-|. +% \label{Backwards} +% +% \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} +% +% $\begin{WithArrows} +% A & = (a+1)^2 \Arrow[tikz={bend left=0}]{we expand} \\ +% & = a^2 + 2a + 1 +% \end{WithArrows}$ +% +% \smallskip +% In fact, it's possible to change more drastically the shape or the arrows with +% the option |tikz-code| (presented p.~\pageref{tikz-code}). +% +% \interitem +% It's possible to use the Tikz option ``|text width|'' to control the width of +% the text associated to the arrow.\footnote{It's possible to avoid the +% hyphenations of the words with the option ``|align = flush left|'' of Tikz.} +% % +% \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} +% +% $\begin{WithArrows} +% A & = \bigl((a+b)+1\bigr)^2 +% \Arrow[jump=2,tikz={text width=5.3cm}]{We have done a two-stages expansion but +% it would have been clever +% to expand with the multinomial theorem.} \\ +% & = (a+b)^2 + 2(a+b) +1 \\ +% & = a^2 + 2ab + b^2 + 2a + 2b +1 +% \end{WithArrows}$ +% +% +% \bigskip +% In the environments |{DispWithArrows}| and |{DispWithArrows*}|, there is an +% option |wrap-lines|. With this option, the lines of the labels are +% automatically wrapped on the right: see p.~\pageref{wrap-lines}. +% +% \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 +% It's possible to put commands |\\| in the text to force new lines\footnote{By +% default, this is not possible in a Tikz node. However, in \pkg{witharrows}, +% the nodes are created with the option |align=left|, and, thus, it becomes +% possible.}. However, if we put a |\\| , a command of font placed in the +% beginning of the text will have effect only until the first command |\\| (like +% in an environment |{tabular}|). That's why Tikz gives an 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 +% The options can be given directly between square brackets to the environment +% |{WithArrows}|. There must be no space between the |\begin{WithArrows}| and +% the opening bracket (|[|) of the options of the environment. Such options +% apply to all the arrows of the environment.\footnote{They also apply to the +% nested environments |{WithArrows}| (with the logical exceptions of +% |interline|, |code-before| and |code-after|).} +% % +% \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 +% configure \pkg{witharrows} by modifying the Tikz style |WithArrows/arrow| +% which is the style used by \pkg{witharrows} when drawing an arrow. For +% example, to have the labels in blue with roman (upright) types, one can use +% the following instruction: +% |\tikzset{WithArrows/arrow/.append style = {blue,font = {}}}|.} +% +% \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 |command-name|\footnote{For historical +% reasons, there is an alias for this option: |CommandName|.} for this purpose. +% The new name of the command must be given to the option \emph{without} the +% leading backslash. +% % +% \begin{Verbatim} +% \NewDocumentCommand {\Arrow} {} {\longmapsto} +% $\begin{WithArrows}[~emphase#command-name=Explanation@] +% f & = \bigl(x \Arrow (x+1)^2\bigr) +% ~emphase#\Explanation{we work directly on fonctions}@\\ +% & = \bigl(x \Arrow x^2+2x+1\bigr) +% \end{WithArrows}$ +% \end{Verbatim} +% % +% \begin{scope} +% \NewDocumentCommand {\Arrow} {} {\longmapsto} +% $\begin{WithArrows}[command-name=Explanation] +% f & = \bigl(x \Arrow (x+1)^2\bigr) +% \Explanation{we work directly on fonctions}\\ +% & = \bigl(x \Arrow x^2+2x+1\bigr) +% \end{WithArrows}$ +% \end{scope} +% +% +% \interitem +% The environment |{WithArrows}| provides also two options |code-before| and +% |code-after|\footnote{For historical reasons, there are aliases for these +% options: |CodeBefore| and |CodeAfter|.} for LaTeX code that will be executed +% at the beginning and at the end of the environment. These options are not +% designed to be hooks (they are available only at the environment level and +% they do not apply to the nested environments). +% % +% \begin{Verbatim} +% $\begin{WithArrows}[~emphase#code-before = \color{blue}@] +% A & = (a+b)^2 \Arrow{we expand} \\ +% & = a^2 + 2ab + b^2 +% \end{WithArrows}$ +% \end{Verbatim} +% +% $\begin{WithArrows}[code-before = \color{blue}] +% A & = (a+b)^2 \Arrow{we expand} \\ +% & = a^2 + 2ab + b^2 +% \end{WithArrows}$ +% +% \medskip +% Special commands are available in |code-after|: a command |\WithArrowsNbLines| +% which gives the number of lines (=rows) of the current environment (this is a +% command and not a counter), a special form of the command |\Arrow| and the +% command |\MultiArrow|: these commands are described in the section concerning +% the nested environments, p.~\pageref{NestedEnv}. +% +% \section{Numbers of columns} +% +% So far, we have used the environment |{WithArrows}| with two columns. However, +% it's possible to use the environment with an arbitrary number of columns with +% the option |format|. The value given to this option is like the preamble of an +% environment |{array}|, that is to say a sequence of letters |r|, |c| and |l|. +% The default value of the option |format| is, in fact, |rl|. +% +% \bigskip +% For exemple, if we want only one column left-aligned, we use the option |format=l|. +% \begin{Verbatim} +% $\begin{WithArrows}[~emphase#format = l@] +% f(x) \ge g(x) \Arrow{by squaring both sides} \\ +% f(x)^2 \ge g(x)^2 \Arrow{by moving to left side} \\ +% f(x)^2 - g(x)^2 \ge 0 +% \end{WithArrows}$ +% \end{Verbatim} +% +% $\begin{WithArrows}[format = l] +% f(x) \ge g(x) \Arrow{by squaring both sides} \\ +% f(x)^2 \ge g(x)^2 \Arrow{by moving to left side} \\ +% f(x)^2 - g(x)^2 \ge 0 +% \end{WithArrows}$ +% +% \interitem +% In the following example, we use five columns all centered (the environment +% |{DispWithArrows*}| is presented p.~\pageref{DispWithArrows}). +% +% \begin{Verbatim} +% \begin{DispWithArrows*}[~emphase#format = ccccc@, +% wrap-lines, +% tikz = {align = flush left}, +% interline=1mm] +% k & \;\le\; & t & \;\le\; & k+1 \\ +% \frac{1}{k+1} & \le & \frac{1}{t} & \le & \frac{1}{k} +% \Arrow{we can integrate the inequalities since $k \leq k+1$ } \\ +% \int\limits_k^{k+1} \frac{d t}{k+1} +% & \le & \int\limits_k^{k+1} \frac{dt}{t} +% & \le & \int\limits_k^{k+1} \frac{dt}{k} \\ +% \frac{1}{k+1} & \le & \ln(k+1)-\ln(k) & \le & \frac{1}{k} +% \end{DispWithArrows*} +% \end{Verbatim} +% \begin{DispWithArrows*}[format = ccccc, +% wrap-lines, +% tikz = {align = flush left}, +% interline=1mm] +% k & \;\le\; & t & \;\le\; & k+1 \\ +% \frac{1}{k+1} & \le & \frac{1}{t} & \le & \frac{1}{k} +% \Arrow{we can integrate the inequalities since $k \leq k+1$ } \\ +% \int\limits_k^{k+1} \frac{d t}{k+1} +% & \le & \int\limits_k^{k+1} \frac{dt}{t} +% & \le & \int\limits_k^{k+1} \frac{dt}{k} \\ +% \frac{1}{k+1} & \le & \ln(k+1)-\ln(k) & \le & \frac{1}{k} +% \end{DispWithArrows*} +% +% +% \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 |show-nodes| can be used to materialize the nodes. The nodes are in +% fact Tikz nodes of shape ``rectangle'', but with zero width. An arrow between +% two nodes starts at the \emph{south} anchor of the first node and arrives at +% the \emph{north} anchor of the second node.} +% +% \smallskip +% $\begin{WithArrows}[displaystyle,show-nodes] +% I +% & = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) \\ +% & = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\ +% & = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\ +% & =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u \\ +% & =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\ +% & =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\ +% & =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u \\ +% & =\frac{\pi}4\ln2-I +% \end{WithArrows}$ +% +% \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}. +% +% 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 |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 |ll| option +% and a |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 |i| (\emph{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 +% The environment |{WithArrows}| gives also a |groups| option (with a \emph{s} +% in the name). With this option, the arrows are divided into several +% ``groups''. Each group is a set of connected\footnote{More precisely: for each +% arrow $a$, we note $i(a)$ the number of its initial row and $f(a)$ the number +% of its final row; for two arrows $a$ and $b$, we say that $a \sim b$ when +% $\llbracket i(a),f(a)\rrbracket \cap \llbracket i(b),f(b)\rrbracket \neq +% \varnothing$; the groups are the equivalence classes of the transitive closure +% of $\sim$.} arrows. All the arrows of a given group are grouped on a same +% vertical line and at a leftmost position. +% +% \bigskip +% $\begin{WithArrows}[groups] +% A & = B \Arrow{one} \\ +% & = C+D \Arrow{two} \\ +% & = D' \\ +% & = E+F+G+H+I \\ +% & = K + L + M \Arrow{three}\\ +% & = N \Arrow{four}\\ +% & = O +% \end{WithArrows}$ +% +% \bigskip +% In an environment which uses the option |group| or the option |groups|, it's +% still possible to give an option of position (|ll|, |lr|, |rl|, |rr| or |i|) +% to an individual arrow. Such arrow will be drawn irrespective of the groups. +% It's also possible to start a new group by applying the option |new-group| to +% an given arrow. +% +% \bigskip +% If desired, the option |group| or the option |groups| can be given to the +% command |\WithArrowsOptions| so that it will become the default value. In this +% case, it's still possible to come back to the default behaviour for a given +% environment |{WithArrows}| with the option |rr|: |\begin{WithArrows}[rr]| +% +% +% \vspace{1cm} +% In the following example, we have used the option |group| for the environment +% and the option |rr| for the last arrow (that's why the last arrow is not +% aligned with the others). +% +% $\begin{WithArrows}[interline=1mm,group] +% \sum\limits_{k=0}^n\frac{\cos kx}{\cos^k x} +% & = \sum\limits_{k=0}^n \frac{\Re (e^{ikx})}{(\cos x)^k} +% \Arrow{$(\cos x)^k$ is real} \\ +% & = \sum\limits_{k=0}^n \Re\left(\frac{e^{ikx}}{(\cos x)^k}\right) +% \Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\ +% & = \Re \left(\sum\limits_{k=0}^n \left(\frac{e^{ix}}{\cos x}\right)^k\right) +% \Arrow{sum of terms of a geometric progression} \\ +% & = \Re \left(\frac{1-\left(\frac{e^{ix}}{\cos x}\right)^{n+1}}{1-\frac{e^{ix}}{\cos x}} \right) +% \Arrow{algebraic calculation} \\ +% & = \Re \left(\frac{1-\frac{e^{i(n+1)x}}{\cos^{n+1}x}}{1-\frac{e^{ix}}{\cos x}}\right) +% \Arrow{reduction to common denominator} \\ +% & = \Re \left(\frac{\frac{\cos^{n+1}x-e^{i(n+1)x}}{\cos^{n+1}x}}{\frac{\cos x-e^{ix}}{\cos x}}\right) +% \Arrow{$\Re(kz) = k\cdot\Re(z)$ if $k$ is real} \\ +% & = \frac1{\cos^n x}\Re \left(\frac{\cos^{n+1}x-e^{i(n+1)x}}{\cos x-e^{ix}}\right) +% \Arrow[rr]{algebraic form of the complexes} \\ +% & =\frac1{\cos^n x}\Re\left(\frac{\cos^{n+1}x-(\cos(n+1)x+i\sin(n+1)x)}{\cos x-(\cos x+i\sin x)}\right) \\ +% & =\frac1{\cos^n x}\Re\left(\frac{(\cos^{n+1}x-\cos(n+1)x)-i\sin(n+1)x}{-i\sin x}\right) \\ +% & = \frac1{\cos^nx}\cdot\frac{\sin(n+1)x}{\sin x} +% \end{WithArrows}$ +% +% \interitem +% +% \section[The options 'up' and 'down' for individual arrows]% +% {The options ``up'' and ``down'' for individual arrows} +% +% \label{up-and-down} +% At the local level, there are also two options for individuals arrows, called +% ``|up|'' and ``|down|''. The following example illustrates these types of +% arrows: +% +% \begin{Verbatim} +% \(\begin{WithArrows} +% A & = B +% \Arrow~emphase#[up]@{an arrow of type \texttt{up}} \\ +% & = C + C + C + C + C + C + C + C \\ +% & = C + C + C + C + C + C + C + C +% \Arrow~emphase#[down]@{an arrow of type \texttt{down}} \\ +% & = E + E +% \end{WithArrows}\) +% \end{Verbatim} +% +% \vspace{1cm} +% \(\begin{WithArrows} +% A & = B +% \Arrow[up]{an arrow of type \texttt{up}} \\ +% & = C + C + C + C + C + C + C + C \\ +% & = C + C + C + C + C + C + C + C +% \Arrow[down]{an arrow of type \texttt{down}} \\ +% & = E + E +% \end{WithArrows}\) +% +% +% \vspace{1cm} +% The options |up| and |down| require the package \pkg{varwidth} and the Tikz +% library \pkg{calc}. It they are not loaded, an error will be raised. +% +% +% \interitem +% +% \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 package +% \pkg{amsmath}.} +% +% \interitem +% As in the environments of \pkg{amsmath}, it's possible to change the spacing +% between two given rows with the option of the command |\\| of end of line +% (it's also possible to use |\\*| but it has exactly the same effect as |\\| +% since an environment |{WithArrows}| is always unbreakable). This option is +% designed to be used with positive values only. +% % +% \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 +% rows 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 a given environment.\footnote{It's also possible to +% change |\jot| with the environment |{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} +% So\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} +% Let's set\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} +% +% +% Let's set\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 +% strictly identical.\footnote{In versions of \pkg{amsmath} older than the +% 5~nov.~2016, a thin space was added on the left of an environment |{aligned}|. +% The new versions do not add this space and neither do +% |{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{Arrows in nested environments} +% +% \label{NestedEnv} +% +% The environments |{WithArrows}| can be nested. In this case, the options given +% to the encompassing environment applies also to the inner ones (with logical +% exceptions for |interline|, |code-before| and |code-after|). The command |Arrow| +% can be used as usual in each environment |{WithArrows}|. +% +% \begin{Verbatim}[formatcom=\small\color{gray}] +% $~emphase#\begin{WithArrows}@ +% \varphi(x,y)=0 +% & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \Arrow{the numbers are real}\\ +% & \Leftrightarrow +% \left\{~emphase#\begin{WithArrows}@[c] +% x+2y & = 0 \\ +% 2x+4y & = 0 +% ~emphase#\end{WithArrows}@\right. \\ +% & \Leftrightarrow +% \left\{~emphase#\begin{WithArrows}@[c] +% x+2y & = 0 \Arrow[tikz=-]{the same equation}\\ +% x+2y & = 0 +% ~emphase#\end{WithArrows}@\right. \\ +% & \Leftrightarrow x+2y=0 +% ~emphase#\end{WithArrows}@$ +% \end{Verbatim} +% +% $\begin{WithArrows} +% \varphi(x,y)=0 +% & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \Arrow{the numbers are real}\\ +% & \Leftrightarrow +% \left\{\begin{WithArrows}[c] +% x+2y & = 0 \\ +% 2x+4y & = 0 +% \end{WithArrows}\right. \\ +% & \Leftrightarrow +% \left\{\begin{WithArrows}[c] +% x+2y & = 0 \Arrow[tikz=-]{the same equation}\\ +% x+2y & = 0 +% \end{WithArrows}\right. \\ +% & \Leftrightarrow x+2y=0 +% \end{WithArrows}$ +% +% \bigskip +% However, one may want to draw an arrow between rows that are not in the same +% environment. For example, one may want to draw the following arrow : +% +% \bigskip +% $\begin{WithArrows}[code-after = \Arrow[v]{1-2}{2-2}{division by $2$} ] +% \varphi(x,y)=0 +% & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ +% & \Leftrightarrow +% \left\{\begin{WithArrows}[c] +% x+2y & = 0 \\ +% 2x+4y & = 0 +% \end{WithArrows}\right. \\ +% & \Leftrightarrow +% \left\{\begin{WithArrows}[c] +% x+2y & = 0 \\ +% x+2y & = 0 +% \end{WithArrows}\right. \\ +% & \Leftrightarrow x+2y=0 +% \end{WithArrows}$ +% +% +% \bigskip +% Such a construction is possible by using |\Arrow| in the |code-after| option. +% Indeed, in |code-after|, a special version of |\Arrow| is available (we will +% call it ``|\Arrow| in |code-after|''). +% +% \smallskip +% A command |\Arrow| in |code-after| takes three arguments : +% \begin{itemize} +% \item a specification of the start row of the arrow ; +% \item a specification of the end row of the arrow ; +% \item the label of the arrow. +% \end{itemize} +% As usual, it's also possible to give options within square brackets before or +% after the three arguments. However, these options are limited (see below). +% +% \bigskip +% The specification of the row is constructed with the position of the concerned +% environment in the nesting tree, followed (after an hyphen) by the number of +% the row. +% +% \bigskip +% In the previous example, there are two environments |{WithArrows}| nested in +% the main environment |{WithArrows}|. +% +% $\begin{WithArrows}[tikz-code = {\path (#1) to node {#3} (#2) ; }] +% \varphi(x,y)=0 +% & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ +% & \Leftrightarrow \color{blue} +% \left\{\begin{WithArrows}[c] +% x+2y & = 0 \Arrow{environment number 1}\\ +% 2x+4y & = 0 +% \end{WithArrows}\right. \\ +% & \Leftrightarrow \color{red} +% \left\{\begin{WithArrows}[c] +% x+2y & = 0 \Arrow{environment number 2}\\ +% x+2y & = 0 +% \end{WithArrows}\right. \\ +% & \Leftrightarrow x+2y=0 +% \end{WithArrows}$ +% +% \bigskip +% The arrow we want to draw starts in the row~$2$ of the sub-environment +% number~$1$ (and therefore, the specification is |1-2|) and ends in the row~$2$ +% of the sub-environment number~$2$ (and therefore, the specification is |2-2|). +% We can draw the arrow with the following command |\Arrow| in |code-after| : +% \begin{Verbatim} +% $\begin{WithArrows}[~emphase#code-after = \Arrow{1-2}{2-2}{division by $2$}@ ] +% \varphi(x,y)=0 +% & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ +% ......... +% \end{WithArrows}$ +% \end{Verbatim} +% +% $\begin{WithArrows}[code-after = \Arrow{1-2}{2-2}{division by $2$} ] +% \varphi(x,y)=0 +% & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ +% & \Leftrightarrow +% \left\{\begin{WithArrows}[c] +% x+2y & = 0 \\ +% 2x+4y & = 0 +% \end{WithArrows}\right. \\ +% & \Leftrightarrow +% \left\{\begin{WithArrows}[c] +% x+2y & = 0 \\ +% x+2y & = 0 +% \end{WithArrows}\right. \\ +% & \Leftrightarrow x+2y=0 +% \end{WithArrows}$ +% +% \bigskip +% The options allowed for a command |\Arrow| in |code-after| are : |ll|, |lr|, +% |rl|, |rr|, |v|, |xoffset|, |tikz| and |tikz-code|. Except |v|, which is +% specific to |\Arrow| in |code-after|, all these options have their usual +% meaning. +% +% With the option |v|, the arrow drawn is vertical to an abscissa computed with +% the start row and the end row only : the intermediate lines are not taken into +% account unlike with the option |i|. Currently, the option |i| is not available +% for the command~|\Arrow| in |code-after|. However, it's always possible to +% translate an arrow with |xoffset| (or |xshift| of Tikz). +% \begin{Verbatim} +% $\begin{WithArrows}[code-after=\Arrow~emphase#[v]@{1-2}{2-2}{division by $2$}] +% \varphi(x,y)=0 +% & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ +% ......... +% \end{WithArrows}$ +% \end{Verbatim} +% +% $\begin{WithArrows}[code-after = \Arrow[v]{1-2}{2-2}{division by $2$} ] +% \varphi(x,y)=0 +% & \Leftrightarrow (x+2y)^2+(2x+4y)^2 = 0 \\ +% & \Leftrightarrow +% \left\{\begin{WithArrows}[c] +% x+2y & = 0 \\ +% 2x+4y & = 0 +% \end{WithArrows}\right. \\ +% & \Leftrightarrow +% \left\{\begin{WithArrows}[c] +% x+2y & = 0 \\ +% x+2y & = 0 +% \end{WithArrows}\right. \\ +% & \Leftrightarrow x+2y=0 +% \end{WithArrows}$ +% +% +% \interitem +% The package \pkg{witharrows} gives also another command available only in +% |code-after|: the command |\MultiArrow|. This command draws a ``rak''. The list +% of the rows of the environment concerned by this rak are given in the first +% argument of the command |\MultiArrow|. This list is given with the syntax of +% the list in a |\foreach| command of \pkg{pgffor}. +% +% +% \begin{Verbatim} +% $\begin{WithArrows}[tikz = rounded corners, +% code-after = {~emphase#\MultiArrow{1,...,4}{text}@} ] +% A & = B \\ +% & = C \\ +% & = D \\ +% & = E \\ +% & = F +% \end{WithArrows}$ +% \end{Verbatim} +% +% +% $\begin{WithArrows}[tikz = rounded corners, +% code-after = {\MultiArrow{1,...,4}{text}}] +% A & = B \\ +% & = C \\ +% & = D \\ +% & = E \\ +% & = F +% \end{WithArrows}$ +% +% \medskip +% As of now, there is no option available for the command |\MultiArrow| (maybe +% in a future release). +% +% +% \bigskip +% \section{Arrows from outside environments \{WithArrows\}} +% +% If someone wants to draw arrows from outside the environments |{WithArrows}|, +% he can use the Tikz nodes created in the environments. +% +% The Tikz name of a node created by \pkg{witharrows} is prefixed by |wa-|. +% Then, we have a list of numbers which give the position in the nesting tree +% and the row number 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 |show-node-names| to show the names of these +% nodes.} +% +% \medskip +% \[\begin{WithArrows}[show-nodes,show-node-names] +% A & \vartriangleleft B+B+B+B+B+B+B+B+B+B+B+B+B \\ +% & \vartriangleleft \left\{ +% \begin{WithArrows}[c] +% C & \vartriangleleft D \\ +% E & \vartriangleleft F +% \end{WithArrows} +% \right. \\ +% & \vartriangleleft +% \left\{ +% \begin{WithArrows}[c] +% G & \vartriangleleft H+H+H+H+H+H+H \\ +% I & \vartriangleleft +% \left\{ +% \begin{WithArrows} +% J &\vartriangleleft K \\ +% L &\vartriangleleft M +% \end{WithArrows} +% \right. +% \end{WithArrows} +% \right. \\ +% & \vartriangleleft +% \left\{ +% \begin{WithArrows}[c] +% N & \vartriangleleft O \\ +% P & \vartriangleleft Q +% \end{WithArrows} +% \right. +% \end{WithArrows}\] +% +% \medskip +% The package \pkg{witharrows} provides some tools facilitating the use of these +% nodes: +% \begin{itemize} +% \item the command |\WithArrowsLastEnv| gives the number of the last +% environment of level~$0$ (\emph{i.e.} which is not included in another +% environnment of the package \pkg{witharrows}); +% +% \item a name can be given to a given environment with the option |name| and, +% in this case, the nodes created in the environment will have aliases +% constructed with this name; +% +% \item the Tikz style |WithArrows/arrow| is the style used by \pkg{witharrows} +% when drawing an arrow\footnote{More precisely, this style is given to the Tikz +% option ``|every path|'' before drawing the arrow with the code of the option +% |tikz-code|. This style is modified (in TeX scopes) by the option |tikz| of +% \pkg{witharrows}.}; +% +% \item the Tikz style |WithArrows/arrow/tips| is the style for the tip of the +% arrow (loaded by |WithArrows/arrow|). +% \end{itemize} +% +% For example, we can draw an arrow from \texttt{wa-\WithArrowsLastEnv-2-1-2-r.south} +% to \texttt{wa-\WithArrowsLastEnv-3-2-r.north} with the following Tikz command. +% +% \begin{Verbatim} +% \begin{tikzpicture}[remember picture,overlay] +% \draw [WithArrows/arrow] +% ([xshift=3mm]wa-\WithArrowsLastEnv-2-1-2-r.south) +% to ([xshift=3mm]wa-\WithArrowsLastEnv-3-2-r.north) ; +% \end{tikzpicture} +% \end{Verbatim} +% +% \[\begin{WithArrows} +% A & \vartriangleleft B+B+B+B+B+B+B+B+B+B+B+B+B \\ +% & \vartriangleleft \left\{ +% \begin{WithArrows}[c] +% C & \vartriangleleft D \\ +% E & \vartriangleleft F +% \end{WithArrows} +% \right. \\ +% & \vartriangleleft +% \left\{ +% \begin{WithArrows}[c] +% G & \vartriangleleft H+H+H+H+H+H+H \\ +% I & \vartriangleleft +% \left\{ +% \begin{WithArrows} +% J &\vartriangleleft K \\ +% L &\vartriangleleft M +% \end{WithArrows} +% \right. +% \end{WithArrows} +% \right. \\ +% & \vartriangleleft +% \left\{ +% \begin{WithArrows}[c] +% N & \vartriangleleft O \\ +% P & \vartriangleleft Q +% \end{WithArrows} +% \right. +% \end{WithArrows}\] +% +% \begin{tikzpicture}[remember picture,overlay] +% \draw [WithArrows/arrow] +% ([xshift=3mm]wa-\WithArrowsLastEnv-2-1-2-r.south) +% to ([xshift=3mm]wa-\WithArrowsLastEnv-3-2-r.north) ; +% \end{tikzpicture} +% +% \medskip +% In this case, it would be easier to use a command |\Arrow| in |code-after| but +% this is an example to explain how the Tikz nodes created by \pkg{witharrows} +% can be used. +% +% \bigskip +% In the following example, we create two environments |{WithArrows}| named +% ``|first|'' and ``|second|'' and we draw a line between a node of the first +% and a node of the second. +% +% \begin{Verbatim} +% $\begin{WithArrows}[~emphase#name=first@] +% A & = B \\ +% & = C +% \end{WithArrows}$ +% +% \bigskip +% $\begin{WithArrows}[~emphase#name=second@] +% A' & = B' \\ +% & = C' +% \end{WithArrows}$ +% +% \begin{tikzpicture}[remember picture,overlay] +% \draw [WithArrows/arrow] +% ([xshift=3mm]~emphase#first@-1-r.south) +% to ([xshift=3mm]~emphase#second@-1-r.north) ; +% \end{tikzpicture} +% \end{Verbatim} +% +% +% \begin{center} +% $\begin{WithArrows}[name=first] +% A & = B \\ +% & = C +% \end{WithArrows}$ +% +% \bigskip +% $\begin{WithArrows}[name=second] +% A' & = B' \\ +% & = C' +% \end{WithArrows}$ +% \end{center} +% +% \begin{tikzpicture}[remember picture,overlay] +% \draw [WithArrows/arrow] +% ([xshift=3mm]first-1-r.south) +% to ([xshift=3mm]second-1-r.north) ; +% \end{tikzpicture} +% +% \section{The environment \{DispWithArrows\}} +% \label{DispWithArrows} +% +% As previously said, the environment |{WithArrows}| bears similarities with the +% environment |{aligned}| of \pkg{amsmath} (and |mathtools|). This extension also +% provides an environment |{DispWithArrows}| which is similar to the +% environments |{align}| and |{flalign}| of \pkg{amsmath}. +% +% \medskip +% The environment |{DispWithArrows}| must be used \emph{outside} math mode. Like +% |{align}|, it should be used in horizontal mode. +% \begin{Verbatim} +% \begin{~emphase#DispWithArrows@} +% A & = (a+1)^2 \Arrow{we expand} \\ +% & = a^2 + 2a + 1 +% \end{~emphase#DispWithArrows@} +% \end{Verbatim} +% \begin{DispWithArrows} +% A & = (a+1)^2 \Arrow{we expand} \\ +% & = a^2 + 2a + 1 +% \end{DispWithArrows} +% +% \medskip +% It's possible to use the command |\notag| (or |\nonumber|) to suppress a tag. +% +% It's possible to use the command |\tag| to put a special tag (e.g. $\star$). +% +% It's also possible to put a label to the line of an equation with the command +% |\label|. +% +% These commands must be in the second column of the environment. +% \begin{Verbatim} +% \begin{DispWithArrows} +% A & = (a+1)^2 \Arrow{we expand} ~emphase#\notag@ \\ +% & = a^2 + 2a + 1 ~emphase#\tag{$\star$} \label{my-equation}@ +% \end{DispWithArrows} +% \end{Verbatim} +% \begin{DispWithArrows} +% A & = (a+1)^2 \Arrow{we expand} \notag \\ +% & = a^2 + 2a + 1 \tag{$\star$} \label{my-equation} +% \end{DispWithArrows} +% A link to the equation \eqref{my-equation}. This link has been composed with +% |\eqref{my-equation}| (the command |\eqref| is a command of \pkg{amsmath}). +% +% \medskip +% If \pkg{amsmath} (or \pkg{mathtools}) is loaded, it's also possible to use +% |\tag*| which, as in \pkg{amsmath}, typesets the tag without the parenthesis. +% For example, it's possible to use it to put the symbol |\square| of +% \pkg{amssymb}. This symbol is often used to mark the end of a +% proof.\footnote{Notice that the environment |{DispWithArrows}| is compatible +% with the command |\qedhere| of \pkg{amsthm}.} +% \begin{Verbatim} +% \begin{DispWithArrows} +% A & = (a+1)^2 \Arrow{we expand} \notag \\ +% & = a^2 + 2a + 1 ~emphase#\tag*{$\square$}@ +% \end{DispWithArrows} +% \end{Verbatim} +% \begin{DispWithArrows} +% A & = (a+1)^2 \Arrow{we expand} \notag \\ +% & = a^2 + 2a + 1 \tag*{$\square$} +% \end{DispWithArrows} +% +% \medskip +% It's also possible to suppress all the autogenerated numbers with the boolean +% option |notag| (or |nonumber|), at the global or environment level. There is +% also an environment |{DispWithArrows*}| which suppresses all these +% numbers.\footnote{Even in this case, it's possible to put a ``manual tag'' +% with the command |\tag|.} +% \begin{Verbatim} +% \begin{~emphase#DispWithArrows*@} +% A & = (a+1)^2 \Arrow{we expand} \\ +% & = a^2 + 2a + 1 +% \end{~emphase#DispWithArrows*@} +% \end{Verbatim} +% \begin{DispWithArrows*} +% A & = (a+1)^2 \Arrow{we expand} \\ +% & = a^2 + 2a + 1 +% \end{DispWithArrows*} +% +% \medskip +% In fact, there is also another option |tagged-lines| which can be used to +% control the lines that will be tagged. The value of this option is a list of +% the numbers of the lines that must to be tagged. For example, with the option +% |tagged-lines = {first,3,last}|, only the first, the third and the last line +% of the environment will be tagged. There is also the special value |all| which +% means that all the lines will be tagged. +% \begin{Verbatim} +% \begin{DispWithArrows}[~emphase#tagged-lines = last@] +% A & = A_1 \Arrow{first stage} \\ +% & = A_2 \Arrow{second stage} \\ +% & = A_3 +% \end{DispWithArrows} +% \end{Verbatim} +% \begin{DispWithArrows}[tagged-lines = last] +% A & = A_1 \Arrow{first stage} \\ +% & = A_2 \Arrow{second stage} \\ +% & = A_3 +% \end{DispWithArrows} +% +% \bigskip +% With the option |fleqn|, the environment is composed flush left (in a way +% similar to the option |fleqn| of the standard classes of LaTeX). In this case, +% the left margin can be controlled with the option |mathindent| (with a name +% inspired by the parameter |\mathindent| of standard LaTeX). The default value +% of this parameter is 25~pt. +% +% \begin{Verbatim} +% \begin{DispWithArrows}[~emphase#fleqn,mathindent = 1cm@] +% A & = (a+1)^2 \Arrow{we expand} \\ +% & = a^2 + 2a + 1 +% \end{DispWithArrows} +% \end{Verbatim} +% \begin{DispWithArrows}[fleqn,mathindent = 1cm] +% A & = (a+1)^2 \Arrow{we expand} \\ +% & = a^2 + 2a + 1 +% \end{DispWithArrows} +% +% \medskip +% \emph{Remark} : By design, the option |fleqn| of \pkg{witharrows} is +% independent of the option |fleqn| of LaTeX. Indeed, since the environments of +% \pkg{witharrows} are meant to be used with arrows on the right side, the user +% may want to use \pkg{witharrows} with the option |fleqn| (in order to have +% more space on the right of the equations for the arrows) while still centering +% the classical equations. +% +% \medskip +% If the option |leqno| is used as a class option, the labels will be composed +% on the left also for the environments |{DispWithArrows}| and +% |{DispWithArrows*}|.\footnote{The package \pkg{amsmath} has an option |leqno| +% but \pkg{witharrows}, of course, is not aware of that option: \pkg{witharrows} +% only checks the option |leqno| of the document class.} +% +% \medskip +% If the package \pkg{amsmath} is loaded, it's possible to use the command +% |\intertext| in the environments |{DispWithArrows}|. It's also possible to use +% the environment |{subequations}|. However, there is, for the environments +% |{DispWithArrows}| an option |subequations| to encapsulate the environment in +% an environment |{subequations}|. +% +% \medskip +% In the following example, the key |{subequations}| is fixed by the command +% |\WithArrowsOptions|. Each environment |{DispWithArrows}| will subnumerated +% (in the scope of the |\WithArrowsOptions|) +% \begin{Verbatim} +% ~emphase#\WithArrowsOptions{subequations}@ +% First environment. +% \begin{DispWithArrows} +% A & = B \\ +% & = C +% \end{DispWithArrows} +% Second environment. +% \begin{DispWithArrows} +% D & = E \\ +% & = F +% \end{DispWithArrows} +% \end{Verbatim} +% % +% \begin{scope} +% \WithArrowsOptions{subequations} +% First environment. +% \begin{DispWithArrows} +% A & = B \\ +% & = C +% \end{DispWithArrows} +% Second environment. +% \begin{DispWithArrows} +% D & = E \\ +% & = F +% \end{DispWithArrows} +% \end{scope} +% +% \bigskip +% If there is not enough space to put the tag at the end of a line, there is no +% automatic positioning of the label on the next line (as in the environments of +% \pkg{amsmath}). However, in |{DispWithArrows}|, the user can use the command +% |\tagnextline| to manually require the composition of the tag on the following +% line. +% \begin{Verbatim} +% \begin{DispWithArrows}[displaystyle] +% S_{2(p+1)} +% & =\sum_{k=1}^{2(p+1)} (-1)^k k^2 \\ +% & \smash[b]{=\sum_{k=1}^{2p}(-1)^kk² +% +(-1)^{2p+1}(2p+1)^2+(-1)^{2p+2}(2p+2)^2} ~emphase#\tagnextline@ \\ +% &= S_{2p}-(2p+1)^2+(2p+2)^2\\ +% &=p(2p+1)-(2p+1)^2+(2p+2)^2\\ +% &= 2p^2+5p+3 +% \end{DispWithArrows} +% \end{Verbatim} +% \begin{center} +% \color{gray}\vrule% +% \begin{minipage}{275pt}\color{black} +% \begin{DispWithArrows}[displaystyle] +% S_{2(p+1)} +% & =\sum_{k=1}^{2(p+1)} (-1)^k k^2 \\ +% & \smash[b]{=\sum_{k=1}^{2p}(-1)^kk^2+(-1)^{2p+1}(2p+1)^2+(-1)^{2p+2}(2p+2)^2} +% \tagnextline \\ +% &= S_{2p}-(2p+1)^2+(2p+2)^2\\ +% &= 2p^2+p-4p^2-4p-1+4p^2+8p+4\\ +% &= 2p^2+5p+3 +% \end{DispWithArrows} +% \end{minipage}% +% \color{gray}\vrule +% \end{center} +% +% +% +% \bigskip +% The environments |{DispWithArrows}| and |{DispWithArrows*}| provide an option +% |wrap-lines|. With this option, the lines of the label are automatically +% wrapped on the right.\footnote{It's possible to avoid the hyphenations of the +% words with the option ``|align = flush left|'' of Tikz.}\label{wrap-lines} +% +% \begin{Verbatim} +% \begin{DispWithArrows*}[displaystyle,~emphase#wrap-lines@] +% S_n +% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +% \Arrow{sum of terms of a geometric progression of ratio $e^{i\frac{2\pi}n}$}\\ +% & = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n} +% {1-e^{i\frac{\pi}{2n}}}\right) +% \Arrow{This line has been wrapped automatically.} \\ +% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +% \end{DispWithArrows*} +% \end{Verbatim} +% \begin{DispWithArrows*}[displaystyle,wrap-lines] +% S_n +% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +% \Arrow{sum of terms of a geometric progression of ratio $e^{i\frac{2\pi}n}$}\\ +% & = \frac1n \Re \left( +% \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}} \right) +% \Arrow{This line has been wrapped automatically.} \\ +% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +% \end{DispWithArrows*} +% +% \bigskip +% The option |wrap-lines| doesn't apply to the environments |{WithArrows}| +% nested in an environment |{DispWithArrows}| or |{DispWithArrows*}|. However, +% it applies to the instructions |\Arrow| and |\MultiArrow| of the |code-after| +% of the environments |{DispWithArrows}| or |{DispWithArrows*}|. +% +% \vspace{1cm} +% We have said that the environments |{DispWithArrows}| and |{DispWithArrows*}| +% should be used in horizontal mode and not in vertical mode. However, there is +% an exception. These environments can be used directly after a |\item| of a +% LaTeX list. In this case, no vertical space is added before the +% environment.\footnote{It's possible to disable this feature with the option |standard-behaviour-with-items|.} +% +% \medskip +% Here is an example. The use of |{DispWithArrows}| gives the ability to tag an +% equation (and also to use |wrap-lines|). +% +% \begin{Verbatim} +% ~emphase#\begin{enumerate}@ +% ~emphase#\item @ +% \begin{DispWithArrows}% +% [displaystyle, wrap-lines, tagged-lines = last, fleqn, mathindent = 0 pt] +% S_n +% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +% \Arrow{we use the formula for a sum of terms of a geometric progression of +% ratio $e^{i\frac{2\pi}n}$}\\ +% & = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n} +% {1-e^{i\frac{\pi}{2n}}}\right) +% \Arrow{$\bigl(e^{i\frac{\pi}{2n}}\bigr)^n = e^{i\frac{\pi}2}=i$} \\ +% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +% \end{DispWithArrows} +% ~emphase#\end{enumerate}@ +% \end{Verbatim} +% \begin{enumerate} +% \item +% \begin{DispWithArrows}[displaystyle, wrap-lines, tagged-lines = last, fleqn, mathindent = 0 pt] +% S_n +% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +% \Arrow{we use the formula for a sum of terms of a geometric progression of +% ratio $e^{i\frac{2\pi}n}$}\\ +% & = \frac1n \Re \left( +% \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}} \right) +% \Arrow{$\bigl(e^{i\frac{\pi}{2n}}\bigr)^n = e^{i\frac{\pi}2}=i$} \\ +% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +% \end{DispWithArrows} +% \end{enumerate} +% +% \vspace{1cm} +% The environment |{DispWithArrows}| is similar to the environment |{align}| of +% \pkg{amsmath}. However, |{DispWithArrows}| is not constructed upon |{align}| +% (in fact, it's possible to use \pkg{witharrows} without \pkg{amsmath}). +% +% There are differences between |{DispWithArrows}| and |{align}|. +% \begin{itemize} +% \item The environment |{DispWithArrows}| cannot be inserted in an environment +% |{gather}| of \pkg{amsmath}. +% \item An environment |{DispWithArrows}| is always unbreakable (even with +% |\allowdisplaybreaks| of \pkg{amsmath}). +% \item The commands |\label|, |\tag|, |\notag| and |\nonumber| are allowed only +% in the last column. +% \item After an |\item| of a LaTeX list, no vertical space is added (this can +% be changed with the option |standard-behaviour-with-items|). +% \item +% \begin{bfseries} +% Last but not least, by default, the elements of a |\{DispWithArrows\}| +% are composed in |textstyle| and not in |displaystyle| (it's possible to change +% this point with the option |displaystyle|). +% \end{bfseries} +% \end{itemize} +% +% \bigskip +% Concerning the references, the package \pkg{witharrows} is compatible with the +% extensions \pkg{autonum}, \pkg{cleveref}, \pkg{fancyref}, \pkg{fncylab}, +% \pkg{hyperref}, \pkg{listlbls}, \pkg{prettyref}, \pkg{refcheck}, +% \pkg{refstyle}, \pkg{showlabels}, \pkg{smartref}, \pkg{typedref} and +% \pkg{varioref}, and with the options |showonlyrefs| and |showmanualtags| of +% \pkg{mathtools}.\footnote{We recall that \pkg{varioref}, \pkg{hyperref}, +% \pkg{cleveref} and \pkg{autonum} must be loaded in this order. The package +% \pkg{witharrows} can be loaded anywhere.} +% +% It is not compatible with \pkg{showkeys} (not all the labels are shown). +% +% +% +% +% \subsection{The option <...> of DispWithArrows} +% +% The environment |{DispWithArrows}| provides an option |left-brace|. When present, +% the value of this option is composed on the left, followed by a curly brace +% (hence the name) and the body of the environment.\footnote{The option +% |left-brace| can also be used without value: in this case, only the brace is drawn...} +% +% For lisibility, this option |left-brace| is also available with a special +% syntax: it's possible to give this option between angle brackets +% (\verb|<| and \verb|>|) just after \verb|{DispWithArrows}| (before the optional +% arguments between square brackets). +% +% \bigskip +% The following code is an example of multi-case equations.\footnote{The +% environment |{cases}| of \pkg{amsmath} is a way to compose such multi-cases +% equations. However, it's not possible to use the automatic numbering of +% equations with this environment. The environment |{numcases}| of the extension +% \pkg{cases} (written by Donald Arseneau) provides this possibility but, of +% course, it's not possible to draw arrows with this extension.} +% +% \medskip +% +% \begin{BVerbatim} +% \begin{DispWithArrows}~emphase#< \binom{n}{p} = >@[format = ll,fleqn,displaystyle] +% 0 & \quad \text{if } p > n +% \Arrow{if fact, it's a special case\\ of the following one} \\ +% \frac{n(n-1)\cdots(n-p+1)}{p!} & \quad \text{if } 0 \leq p \leq n \\ +% 0 & \quad \text{if } p < 0 +% \end{DispWithArrows} +% \end{BVerbatim} +% % +% \begin{DispWithArrows}< \binom{n}{p} = >[format = ll,fleqn,displaystyle] +% 0 & \quad \text{if } p > n +% \Arrow{if fact, it's a special case\\ of the following one} \\ +% \frac{n(n-1)\cdots(n-p+1)}{p!} & \quad \text{if } 0 \leq p \leq n \\ +% 0 & \quad \text{if } p < 0 +% \end{DispWithArrows} +% +% \interitem +% In the following example, we subnumerate the equations with the option +% |subnumerate| (available when the package \pkg{amsmath} is loaded). +% +% \begin{Verbatim} +% \begin{DispWithArrows}~emphase#< \label{system} (\ref*{system}) \Leftrightarrow >@[ +% format = l, subequations ] +% x+y+z = -3 \Arrow[tikz=-,jump=2]{3 equations} \\ +% xy+xz+yz=-2 \\ +% xyz = -15 \label{last-equation} +% \end{DispWithArrows} +% \end{Verbatim} +% % +% \begin{DispWithArrows}< \label{system} (\ref*{system}) \Leftrightarrow >[ +% format = l, subequations] +% x+y+z = -3 \Arrow[tikz=-,jump=2]{3 equations} \\ +% xy+xz+yz=-2 \\ +% xyz = -15 \label{last-equation} +% \end{DispWithArrows} +% +% +% \bigskip +% The whole system is the equation \eqref{system} (this reference has been coded +% by |\eqref{system}|) whereas the last equation is the equation +% \eqref{last-equation} (this reference has been coded by +% |\eqref{last-equation}|). The command |\ref*| used in the code above is +% provided by \pkg{hyperref}. It's a variant of |\ref| which doesn't create +% interactive link. +% +% \bigskip +% With the option \verb|replace-left-brace-by|, it's possible to replace the +% left curly brace by another extensible delimiter. For example, +% ``|replace-left-brace-by = [\enskip|'' will compose with a bracket and add also a +% |\enskip| after this bracket. +% +% \bigskip +% \section{Advanced features} +% +% \subsection{Utilisation with plain-TeX} +% \label{plain-TeX} +% +% The extension \pkg{witharrows} can be used with plain-TeX. In this case, the +% extension must be loaded with |\input|: +% \begin{Verbatim} +% \input{witharrows.tex} +% \end{Verbatim} +% +% \medskip +% In plain-TeX, there is not environments as in LaTeX. Instead of using the +% environment |{Witharrows}|, with |\begin{WithArrows}| and |\end{WithArrows}|, +% one should use a pseudo-environnement delimited by |\WithArrows| and +% |\endWithArrows| (idem for |{DispWithArrows}|). +% +% \begin{Verbatim} +% $\WithArrows +% A & = (a+1)^2 \Arrow{we expand} \\ +% & = a^2 + 2a + 1 +% \endWithArrows$ +% \end{Verbatim} +% +% \medskip +% The version of \pkg{witharrows} for plain-TeX doesn't provide all the +% functionnlities of the LaTeX version. In particular, the funcionnalities which +% deal with the number of the equations are not available (since they rely upon +% the system of tags of LaTeX). +% +% \subsection{The option tikz-code : how to change the shape of the arrows} +% +% \label{tikz-code} +% +% The option |tikz-code|\footnote{For historical reasons, the option |tikz-code| +% has an alias: |TikzCode|.} allows the user to change the shape of the +% arrows.\footnote{If the option |wrap-lines| is used in an environment +% |{DispWithArrows}| or |{DispWithArrows*}|, the option |tikz-code| will have no +% effect for the arrows of this environment but only for the arrows in the +% nested environments |{WithArrows}|.} +% +% \smallskip +% For example, the options ``|up|'' and ``|down|'' described previously (cf. +% p.~\pageref{up-and-down}) are programmed internally with |tikz-code|. +% +% \smallskip +% The value of this option must be a valid Tikz drawing instruction (with the +% final semicolon) with three markers |#1|, |#2| and |#3| for the start point, +% the end point and the label of the arrow. +% +% \bigskip +% By default, the value is the following: +% +% \smallskip +% \qquad \verb|\draw (#1) to node {#3} (#2) ;| +% +% +% \bigskip +% In the following example, we replace this default path by a path with three +% segments (and the node overwriting the second segment). +% \begin{Verbatim} +% \begin{WithArrows}[format=c,ygap=5pt,interline=4mm, +% ~emphase#tikz-code = {\draw[rounded corners]@ +% ~emphase# (~#1) -- ([xshift=5mm]~#1)@ +% ~emphase# -- node[circle,@ +% ~emphase# draw,@ +% ~emphase# auto = false,@ +% ~emphase# fill = gray!50,@ +% ~emphase# inner sep = 1pt] {\tiny ~#3}@ +% ~emphase# ([xshift=5mm]~#2)@ +% ~emphase# -- (~#2) ; }@] +% 3 (2x+4) = 6 \Arrow{$\div 3$} \\ +% 2x+4 = 2 \Arrow{$-4$} \\ +% 2x = -2 \Arrow{$\div 2$} \\ +% x = -1 +% \end{WithArrows} +% \end{Verbatim} +% +% +% \[\begin{WithArrows}[format=c, +% ygap=5pt, +% interline=4mm, +% tikz-code = {\draw[rounded corners] +% (#1) +% -- +% ([xshift=5mm]#1) +% -- node[circle, +% draw, +% auto=false, +% fill=gray!50, +% inner sep = 1pt] {\tiny #3} +% ([xshift=5mm]#2) +% -- +% (#2) ; }] +% 3 (2x+4) = 6 \Arrow{$\div 3$} \\ +% 2x+4 = 2 \Arrow{$-4$} \\ +% 2x = -2 \Arrow{$\div 2$} \\ +% x = -1 +% \end{WithArrows}\] +% +% \bigskip +% The environments |{DispWithArrows}| and its starred version +% |{DispWithArrows*}| provide a command |\WithArrowsRightX| which can be used in +% a definition of |tikz-code|. This command gives the $x$-value of the right side +% of the composition box (taking into account the eventual tags of the +% equations). For an example of use, see p.~\pageref{example-WithArrowsRightX}. +% +% +% \bigskip +% \subsection{The command \textbackslash WithArrowsNewStyle} +% +% The extension \pkg{witharrows} provides a command |\WithArrowsNewStyle| to +% define styles in a way similar to the ``styles'' of Tikz. +% +% The command |\WithArrowsNewStyle| takes two mandatory arguments. The first is +% the name of the style and the second is a list of key-value pairs. The scope +% of the definition done by |\WithArrowsNewStyle| is the current TeX scope. +% +% The style can be used as a key at the document level (with +% |\WithArrowsOptions|) or at the environment level (in the optional arguments +% of |{WithArrows}| and |{DispWithArrows}|). The style can also be used in +% another command |\WithArrowsNewStyle|. +% +% For an example of use, see p.~\pageref{example-WithArrowsRightX}. +% +% +% \bigskip +% \subsection{Vertical positioning of the arrows} +% +% There are four parameters for fine tuning of the vertical positioning of the +% arrows : |ygap|, |ystart|, |start-adjust| and |end-adjust|. +% +% \medskip +% We first explain the behaviour when the parameters |start-adjust| and +% |end-adjust| are equal to zero: +% \begin{itemize} +% \item the option |ystart| sets the vertical distance between the base line of +% the text and the start of the arrow (default value: 0.4 ex); +% \item the option |ygap| sets the vertical distance between two consecutive +% arrows (default value: 0.4~ex). +% \end{itemize} +% +% +% \bigskip +% $\begin{WithArrows}[interline=1mm, adjust = 0pt] +% (\cos x + \sin x)^2 & = \cos^2 x +2 \cos x \sin x + \sin^2 x\Arrow{}\tikz[remember picture] \coordinate (A) ; \\ +% & = \cos^2x + \sin^2x + 2\sin x\cos x \Arrow{} \\ +% & = 1 + \sin(2x) +% \end{WithArrows}$ +% +% \begin{tikzpicture}[remember picture,overlay,blue] +% \draw (wa-\WithArrowsLastEnv-1-r.south) to ++(1,0) coordinate (B) to ++(0.1,0) ;; +% \draw (A) to ++(1,0) coordinate (C) to ++(0.1,0) ;; +% \draw (B) -- (C) ; +% \draw[<-] (B) to ++(0,0.2) ; +% \draw[<-] (C) to ++(0,-0.2) ; +% \path (C) node[right=1mm] {|ystart|} ; +% \draw (wa-\WithArrowsLastEnv-2-r.north) to ++(3,0) coordinate (E) to ++(0.1,0); +% \draw (wa-\WithArrowsLastEnv-2-r.south) to ++(3,0) coordinate (F) to ++(0.1,0); +% \draw (E) -- (F) ; +% \draw[<-] (E) to ++(0,0.2) ; +% \draw[<-] (F) to ++(0,-0.2) ; +% \path (F) node[right=1mm] {|ygap|} ; +% \end{tikzpicture} +% +% \interitem +% However, for aesthetic reasons, when it's possible, \pkg{witharrows} starts +% the arrow a bit higher (by an amount |start-adjust|) and ends the arrow a bit +% lower (by an amount |end-adjust|). By default, both parameters |start-adjust| +% and |end-adjust| are equal to $0.4$~ex. +% +% \bigskip +% Here is for example the behaviour without the mechanism of |start-adjust| and +% |end-adjust| (this was the standard behaviour for versions prior to 1.13). +% % \begin{Verbatim} +% $\begin{WithArrows}~emphase#[start-adjust=0pt, end-adjust=0pt]@ +% A & = (a+1)^2 \Arrow{we expand} \\ +% & = a^2 + 2a + 1 +% \end{WithArrows}$ +% \end{Verbatim} +% +% $\begin{WithArrows}[start-adjust=0pt, end-adjust=0pt] +% A & = (a+1)^2 \Arrow{we expand} \\ +% & = a^2 + 2a + 1 +% \end{WithArrows}$ +% +% +% \bigskip +% Here is the standard behaviour since version 1.13 (the parameters +% |start-adjust| and |end-ajust| are used with the default value $0.4$~ex). The +% arrow is longer and the result is more aesthetic. +% +% \medskip +% $\begin{WithArrows} +% A & = (a+1)^2 \Arrow{we expand} \\ +% & = a^2 + 2a + 1 +% \end{WithArrows}$ +% +% +% \bigskip +% It's also possible to use the option |adjust| which sets both |start-adjust| +% and |end-ajust|. +% +% \bigskip +% Since the mechanism of |start-adjust| and |end-ajust| has been added in +% version 1.13 of \pkg{witharrows}, that version is not stricty compatible with +% older versions. However, it's possible to restore the previous behaviour +% simply by setting |start-adjust| and |end-adjust| to $0$~pt: +% \begin{Verbatim} +% \WithArrowsOptions{adjust = 0pt} +% \end{Verbatim} +% +% \bigskip +% \subsection{Footnotes in the environments of witharrows} +% +% If you want to put footnotes in an environment |{WithArrows}| or +% |{DispWithArrows}|, you can use a pair |\footnotemark|--|\footnotetext|. +% +% \smallskip +% It's also possible to extract the footnotes with the help of the package +% \pkg{footnote} or the package \pkg{footnotehyper}. +% +% \smallskip +% If \pkg{witharrows} is loaded with the option |footnote| (with +% |\usepackage[footnote]{witharrows}| or with |\PassOptionsToPackage|), the +% package \pkg{footnote} is loaded (if it is not yet loaded) and it is used to +% extract the footnotes. +% +% \smallskip +% If \pkg{witharrows} is loaded with the option |footnotehyper|, the package +% \pkg{footnotehyper} is loaded (if it is not yet loaded) ant it is used to +% extract footnotes. +% +% \smallskip +% Caution: The packages \pkg{footnote} and \pkg{footnotehyper} are incompatible. +% The package \pkg{footnotehyper} is the successor of the package \pkg{footnote} +% and should be used preferently. The package \pkg{footnote} has some drawbacks, +% in particular: it must be loaded after the package \pkg{xcolor} and it is not +% perfectly compatible with \pkg{hyperref}. +% +% \medskip +% In this document, the package \pkg{witharrows} has been loaded with the option +% |footnotehyper| and we give an example with a footnote in the label of an +% arrow: +% +% \smallskip +% $\begin{WithArrows} +% A & = (a+b)^2 +% \Arrow{We expand\,\footnote{A footnote.}} \\ +% & = a^2+b^2+2ab +% \end{WithArrows}$ +% +% \bigskip +% \subsection{Option no-arrows} +% +% The option |no-arrows| is a convenience given to the user. With this option +% the arrows are not drawn. However, an analyse of the arrows is done and some +% errors can be raised, for example if an arrow would arrive after the last row +% of the environment. +% +% +% \bigskip +% \subsection{Note for developpers} +% +% If you want to construct an environment upon an environment of +% \pkg{witharrows}, we recommand to call the environment with the construction +% |\WithArrows|-|\endWithArrows| or |\DispWithArrows|-|\endDispWithArrows| (and +% not |\begin{WithArrows}|-|\end{WithArrows}|, etc.). +% +% \smallskip +% By doing so, the error messages generated by \pkg{witharrows} will (usually) +% mention the name of your environment and they will be easier to understand by +% the final user. +% +% \smallskip +% By example, you can define an environment |{DWA}| which is an alias of +% |{DispWithArrows}|: +% \begin{BVerbatim} +% \NewDocumentEnvironment {DWA} {} {\DispWithArrows}{\endDispWithArrows} +% \end{BVerbatim} +% +% \smallskip +% If you use this environment |{DWA}| in math mode, you will have the following +% error message: +% +% \begin{BVerbatim} +% The environment {DWA} should be used only outside math mode. +% \end{BVerbatim} +% +% \interitem +% Another example is the definition of the environment |{DispWithArrows*}| +% internally in the package \pkg{witharrows} by the following code: +% \begin{Verbatim} +% \NewDocumentEnvironment {DispWithArrows*} {} +% {\WithArrowsOptions{notag}% +% \DispWithArrows} +% {\endDispWithArrows} +% \end{Verbatim} +% +% +% +% \section{Examples} +% +% \subsection{\textbackslash MoveEqLeft} +% +% It's possible to use |\MoveEqLeft| of \pkg{mathtools}. Don't forget that +% |\MoveEqLeft| has also the value of an ampersand (|&|). That's important for the +% placement of an eventual command |\Arrow|. +% +% +% +% \begin{Verbatim}[formatcom=\small\color{gray}] +% $\begin{WithArrows}[interline=0.5ex] +% ~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}[interline=0.5ex] +% \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}$ +% +% +% \bigskip +% \subsection{Modifying the shape of the nodes} +% +% It's possible to change the shape of the labels, which are Tikz nodes, by +% modifying the key ``|every node|'' of Tikz. +% +% \begin{Verbatim} +% \begin{WithArrows}% +% [format = c, +% interline = 4mm, +% tikz = {~emphase#every node/.style = {circle,@ +% ~emphase# draw,@ +% ~emphase# auto = false,@ +% ~emphase# fill = gray!50,@ +% ~emphase# inner sep = 1pt,@ +% ~emphase# font = \tiny}@}] +% 3 (2x+4) = 6 \Arrow{$\div 3$} \\ +% 2x+4 = 2 \Arrow{$-4$} \\ +% 2x = -2 \Arrow{$\div 2$} \\ +% 2x = -1 +% \end{WithArrows} +% \end{Verbatim} +% +% \[\begin{WithArrows}[% +% format = c, +% interline = 4mm, +% tikz = {every node/.style = {circle, +% draw, +% auto = false, +% fill = gray!50, +% inner sep = 1pt, +% font = \tiny}}] +% 3 (2x+4) = 6 \Arrow{$\div 3$} \\ +% 2x+4 = 2 \Arrow{$-4$} \\ +% 2x = -2 \Arrow{$\div 2$} \\ +% 2x = -1 +% \end{WithArrows}\] +% +% +% \bigskip +% \subsection{Examples with the option tikz-code} +% +% We recall that the option |tikz-code| is the Tikz code used by \pkg{witharrows} +% to draw the arrows.\footnote{If an environment |{DispWithArrows}| or +% |{DispWithArrows*}| is used with the option |wrap-lines|, the value of the +% option |tikz-code| is not used for this environment (but is used for the +% environments nested inside).} +% +% \smallskip +% The value by defaut of |tikz-code| is \verb|\draw (#1) to node {#3} (#2) ;| +% where the three markers |#1|, |#2| and |#3| represent the start row, the end +% row and the label of the arrow. +% +% +% \bigskip +% \subsubsection{Example 1} +% In the following example, we define the value of |tikz-code| with two +% instructions |\path| : the first instruction draws the arrow itself and the +% second puts the label in a Tikz node in the rectangle delimited by the arrow. +% +% \begin{Verbatim} +% \begin{DispWithArrows*}% +% [displaystyle, +% ygap = 2mm, +% ystart = 0mm, +% ~emphase#tikz-code = {\draw (~#1) -- ++(4.5cm,0) |- (~#2) ;@ +% ~emphase# \path (~#1) -- (~#2) @ +% ~emphase# node[text width = 4.2cm, right, midway] {~#3} ;}@] +% S_n +% & = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr) +% ........... +% \end{Verbatim} +% +% +% \bigskip +% \begin{DispWithArrows*}[ +% displaystyle, +% ygap = 2mm, +% ystart = 0mm, +% tikz-code = {\draw (#1) -- ++(4.5cm,0) |- (#2) ; +% \path (#1) -- (#2) +% node[text width = 4.2cm, right, midway] {#3} ;}] +% S_n +% & = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr) +% \Arrow{$\cos x = \Re(e^{ix})$}\\ +% & = \frac1n\sum_{k=0}^{n-1} \Re\left(e^{i\frac{k\pi}{2n}}\right) +% \Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\ +% & = \frac1n \Re\left(\sum_{k=0}^{n-1} e^{i\frac{k\pi}{2n}}\right) +% \Arrow{$\exp$ is a morphism for $\times$ et $+$} \\ +% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +% \Arrow{sum of terms of a geometric progression of ratio $e^{i\frac{2\pi}n}$}\\ +% & = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}}\right)\\ +% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +% \end{DispWithArrows*} +% +% \bigskip +% \subsubsection{Example 2} +% +% \label{example-WithArrowsRightX} +% It's possible to modify the previous example to have the ``|text width|'' +% automatically computed with the right margin (in a way similar as the +% |wrap-lines| option) in the environments |{DispWithArrows}| and +% |{DispWithArrows*}|. In the definition of |tikz-code|, we use the command +% |\WithArrowsRightX| which is the $x$-value of the right margin of the current +% composition box (it's a TeX command and not a dimension). For lisibility, we +% use a style. This example requires the Tikz library \pkg{calc}. +% +% \begin{Verbatim} +% \WithArrowsNewStyle{MyStyle} +% {displaystyle, +% ygap = 2mm, +% xoffset = 0pt, +% ystart = 0mm, +% tikz-code = {\path let \p1 = (~#~#1) +% in (~#~#1) +% -- node [anchor = west, +% text width = {~emphase#\WithArrowsRightX@ - \x1 - 0.5 em}] +% {~#~#3} +% (~#~#2) ; +% \draw let \p1 = (~#~#1) +% in (~#~#1) -- ++(~emphase#\WithArrowsRightX@ - \x1,0) |- (~#~#2) ; }} +% \end{Verbatim} +% +% \begin{Verbatim} +%\begin{DispWithArrows}[MyStyle] +% S_n +% & = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr) +% \Arrow{$\cos x = \Re(e^{ix})$}\\ +% ........... +% \end{Verbatim} +% +% \WithArrowsNewStyle{MyStyle} +% {displaystyle, +% ygap = 2mm, +% xoffset = 0pt, +% ystart = 0mm, +% tikz-code = {\path let \p1 = (##1) +% in (##1) +% -- node [anchor = west, +% text width = {\WithArrowsRightX - \x1 - 0.5 em}] {##3} +% (##2) ; +% \draw let \p1 = (##1) +% in (##1) -- ++(\WithArrowsRightX - \x1,0) |- (##2) ; }} +% +%\begin{DispWithArrows}[MyStyle] +% S_n +% & = \frac1n \sum_{k=0}^{n-1}\cos\bigl(\tfrac{\pi}2\cdot\tfrac kn\bigr) +% \Arrow{$\cos x = \Re(e^{ix})$}\\ +% & = \frac1n\sum_{k=0}^{n-1} \Re\left(e^{i\frac{k\pi}{2n}}\right) +% \Arrow{$\Re(z+z')=\Re(z)+\Re(z')$}\\ +% & = \frac1n \Re\left(\sum_{k=0}^{n-1} e^{i\frac{k\pi}{2n}}\right) +% \Arrow{$\exp$ is a morphism for $\times$ et $+$} \\ +% & = \frac1n \Re \left(\sum_{k=0}^{n-1}\bigl(e^{i\frac{\pi}{2n}}\bigr)^k\right) +% \Arrow{sum of terms of a geometric progression of ratio $e^{i\frac{2\pi}n}$}\\ +% & = \frac1n \Re \left( \frac{1-\bigl(e^{i\frac{\pi}{2n}}\bigr)^n}{1-e^{i\frac{\pi}{2n}}}\right)\\ +% & = \frac1n \Re \left(\frac{1-i}{1-e^{i\frac{\pi}{2n}}}\right) +% \end{DispWithArrows} +% +% +% +% \bigskip +% \subsubsection{Example 3} +% +% In the following example, we change the shape of the arrow depending on whether +% the start row is longer than the end row or not. This example requires the +% Tikz library \pkg{calc}. +% +% \begin{Verbatim} +% \begin{WithArrows}[ll,interline=5mm,xoffset=5mm, +% ~emphase#tikz-code = {\draw[rounded corners,@ +% ~emphase# every node/.style = {circle,@ +% ~emphase# draw,@ +% ~emphase# auto = false,@ +% ~emphase# inner sep = 1pt,@ +% ~emphase# fill = gray!50,@ +% ~emphase# font = \tiny }]@ +% ~emphase# let \p1 = (~#1),@ +% ~emphase# \p2 = (~#2)@ +% ~emphase# in \ifdim \x1 > \x2@ +% ~emphase# (\p1) -- node {~#3} (\x1,\y2) -- (\p2)@ +% ~emphase# \else@ +% ~emphase# (\p1) -- (\x2,\y1) -- node {~#3} (\p2)@ +% ~emphase# \fi ;}@] +% E & \Longleftrightarrow \frac{(x+4)}3 + \frac{5x+3}5 = 7 +% \Arrow{$\times 15$}\\ +% & \Longleftrightarrow 5(x+4) + 3(5x+3) = 105 \\ +% & \Longleftrightarrow 5x+20 + 15x+9 = 105 \\ +% & \Longleftrightarrow 20x+29 = 105 +% \Arrow{$-29$}\\ +% & \Longleftrightarrow 20x = 76 +% \Arrow{$\div 20$}\\ +% & \Longleftrightarrow x = \frac{38}{10} +% \end{WithArrows} +% \end{Verbatim} +% +% +% \[\begin{WithArrows}[ll,interline=5mm,xoffset=5mm, +% tikz-code = {\draw[rounded corners, +% every node/.style = {circle, +% draw, +% auto = false, +% inner sep = 1pt, +% fill = gray!50, +% font = \tiny}] +% let \p1 = (#1), +% \p2 = (#2) +% in \ifdim \x1 > \x2 +% (\p1) -- node {#3} (\x1,\y2) -- (\p2) +% \else +% (\p1) -- (\x2,\y1) -- node {#3} (\p2) +% \fi ;}] +% E & \Longleftrightarrow \frac{(x+4)}3 + \frac{5x+3}5 = 7 +% \Arrow{$\times 15$}\\ +% & \Longleftrightarrow 5(x+4) + 3(5x+3) = 105 \\ +% & \Longleftrightarrow 5x+20 + 15x+9 = 105 \\ +% & \Longleftrightarrow 20x+29 = 105 +% \Arrow{$-29$}\\ +% & \Longleftrightarrow 20x = 76 +% \Arrow{$\div 20$}\\ +% & \Longleftrightarrow x = \frac{38}{10} +% \end{WithArrows}\] +% +% +% +% \subsection{Automatic numbered loop} +% +% Assume we want to draw a loop of numbered arrows. In this purpose, it's +% possible to write a dedicated command |\NumberedLoop| which will do the job +% when used in |code-after|. In the following example, we write this command with +% |\NewDocumentCommand| of \pkg{xparse} and |\foreach| of \pkg{pgffor} (both +% packages are loaded when \pkg{witharrows} is loaded). +% +% \begin{Verbatim} +% \NewDocumentCommand \NumberedLoop {} +% {\foreach \j in {2,...,\WithArrowsNbLines} +% { \pgfmathtruncatemacro{\i}{\j-1} +% \Arrow[rr]{\i}{\j}{\i} } +% \Arrow[rr,xoffset=1cm,tikz=<-]{1}{\WithArrowsNbLines}{\WithArrowsNbLines}} +% \end{Verbatim} +% +% The command |\WithArrowsNbLines| is a command available in |code-after| which +% gives the total number of lines (=rows) of the current environment (it's a +% command and not a counter). +% +% +% \bigskip +% \begin{Verbatim} +% $\begin{WithArrows}[~emphase#code-after = \NumberedLoop@] +% a.\;& f \text{ est continuous on } E \\ +% b.\;& f \text{ est continuous in } 0 \\ +% c.\;& f \text{ is bounded on the unit sphere} \\ +% d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\ +% e.\;& f \text{ is lipschitzian} +% \end{WithArrows}$ +% \end{Verbatim} +% +% \bigskip +% \begin{scope} +% \NewDocumentCommand \NumberedLoop {} +% {\foreach \j in {2,...,\WithArrowsNbLines} +% { \pgfmathtruncatemacro{\i}{\j-1} +% \Arrow[rr]{\i}{\j}{\i} } +% \Arrow[rr,xoffset=1cm,tikz=<-]{1}{\WithArrowsNbLines}{\WithArrowsNbLines}} +% +% +% $\begin{WithArrows}[code-after = \NumberedLoop] +% a.\;& f \text{ est continuous on } E \\ +% b.\;& f \text{ est continuous in } 0 \\ +% c.\;& f \text{ is bounded on the unit sphere} \\ +% d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\ +% e.\;& f \text{ is lipschitzian} +% \end{WithArrows}$ +% +% +% \bigskip +% As usual, it's possible to change the characteristic of both arrows and nodes +% with the option |tikz|. However, if we want to change the style to have, for +% example, numbers in parenthesis, the best way is to change the value of +% |tikz-code|: +% +% \begin{Verbatim} +% tikz-code = {\draw (~#1) to node {\footnotesize (~#3)} (~#2) ;} +% \end{Verbatim} +% +% \WithArrowsOptions{tikz-code = {\draw (#1) to node {\footnotesize (#3)} (#2) ;}} +% +% $\begin{WithArrows}[code-after = \NumberedLoop] +% a.\;& f \text{ est continuous on } E \\ +% b.\;& f \text{ est continuous in } 0 \\ +% c.\;& f \text{ is bounded on the unit sphere} \\ +% d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| \\ +% e.\;& f \text{ is lipschitzian} +% \end{WithArrows}$ +% +% \end{scope} +% +% \vspace{2cm} +% +% \section{Implementation} +% +% \subsection{Declaration of the package and extensions loaded} +% +% +% First, \pkg{tikz} and some Tikz libraries are loaded before the +% |\ProvidesExplPackage|. They are loaded this way because |\usetikzlibrary| in +% |expl3| code fails.\footnote{cf. +% |tex.stackexchange.com/questions/57424/using-of-usetikzlibrary-in-an-expl3-package-fails|} +% +% \begin{macrocode} +%<@@=wa> +% \end{macrocode} +% +% \begin{macrocode} +%<*LaTeX> +\RequirePackage{tikz} +\RequirePackage{expl3}[2019/02/15] +% +%<*plain-TeX> +\input tikz.tex +\input expl3-generic.tex +% +\usetikzlibrary{arrows.meta,bending} +% \end{macrocode} +% +% \bigskip +% Then, we can give the traditional declaration of a package written with +% |expl3|: +% \begin{macrocode} +%<*LaTeX> +\RequirePackage{l3keys2e} +\ProvidesExplPackage + {witharrows} + {\myfiledate} + {\myfileversion} + {Draws arrows for explanations on the right} +% \end{macrocode} +% +% \bigskip +% The package \pkg{xparse} will be used to define the environments +% |{WithArrows}|, |{DispWithArrows}|, |{DispWithArrows*}| and the commands +% |\Arrow|, |\WithArrowsOptions| and |\WithArrowsNewStyle|. +% \begin{macrocode} +\RequirePackage { xparse } [ 2018-10-17 ] +% +% \end{macrocode} +% +% \begin{macrocode} +%<*plain-TeX> +\ExplSyntaxOn +\catcode `\@ = 11 +% +% \end{macrocode} +% +% \bigskip +% \subsection{The packages footnote and footnotehyper} +% +% A few options can be given to the package \pkg{witharrows} when it is loaded +% (with |\usepackage|, |\RequirePackage| or |\PassOptionsToPackage|). Currently +% (version \myfileversion), there are two such options: |footnote| and +% |footnotehyper|. With the option |footnote|, \pkg{witharrows} loads +% \pkg{footnote} and uses it to extract the footnotes from the environments +% |{WithArrows}|. Idem for the option |footnotehyper|. +% +% \medskip +% The boolean |\g_@@_footnotehyper_bool| will indicate if the option +% |footnotehyper| is used. +% \begin{macrocode} +%<*LaTeX> +\bool_new:N \g_@@_footnotehyper_bool +% \end{macrocode} +% +% \medskip +% The boolean |\g_@@_footnote_bool| will indicate if the option |footnote| is +% used, but quicky, it will also be set to |true| if the option |footnotehyper| +% is used. +% \begin{macrocode} +\bool_new:N \g_@@_footnote_bool +% +% \end{macrocode} +% +% \bigskip +% \begin{macrocode} +\cs_new_protected:Npn \@@_msg_new:nn { \msg_new:nnn { witharrows } } +\cs_new_protected:Npn \@@_msg_new:nnn { \msg_new:nnnn { witharrows } } +\cs_new_protected:Npn \@@_msg_redirect_name:nn + { \msg_redirect_name:nnn { witharrows } } +\cs_new_protected:Npn \@@_error:n { \msg_error:nn { witharrows } } +\cs_new_protected:Npn \@@_warning:n { \msg_error:nn { witharrows } } +\cs_new_protected:Npn \@@_fatal:n { \msg_fatal:nn { witharrows } } +\cs_new_protected:Npn \@@_error:nn { \msg_error:nnn { witharrows } } +\cs_generate_variant:Nn \@@_error:nn { n x } +% \end{macrocode} +% +% \medskip +% We define a set of keys |WithArrows/package| for these options. +% \begin{macrocode} +%<*LaTeX> +\keys_define:nn { WithArrows / package } + { + footnote .bool_gset:N = \g_@@_footnote_bool , + footnotehyper .bool_gset:N = \g_@@_footnotehyper_bool , + unknown .code:n = + \@@_fatal:n { Option~unknown~for~package } + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Option~unknown~for~package } + { + You~can't~use~the~option~'\l_keys_key_tl'~when~loading~the~ + package~witharrows.~Try~to~use~the~command~ + \token_to_str:N\WithArrowsOptions. + } +% \end{macrocode} +% +% +% \bigskip +% We process the options when the package is loaded (with |\usepackage|). +% \begin{macrocode} +\ProcessKeysOptions { WithArrows / package } +% \end{macrocode} +% +% +% \medskip +% \begin{macrocode} +\@@_msg_new:nn { Option~incompatible~with~Beamer } + { + The~option~'\l_keys_key_tl'\ is~incompatible~ + with~Beamer~because~Beamer~has~its~own~system~to~extract~footnotes. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { footnote~with~footnotehyper~package } + { + You~can't~use~the~option~'footnote'~because~the~package~ + footnotehyper~has~already~been~loaded.~ + If~you~want,~you~can~use~the~option~'footnotehyper'~and~the~footnotes~ + within~the~environments~of~witharrows~will~be~extracted~with~the~tools~ + of~the~package~footnotehyper.\\ + If~you~go~on,~the~package~footnote~won't~be~loaded. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { footnotehyper~with~footnote~package } + { + You~can't~use~the~option~'footnotehyper'~because~the~package~ + footnote~has~already~been~loaded.~ + If~you~want,~you~can~use~the~option~'footnote'~and~the~footnotes~ + within~the~environments~of~witharrows~will~be~extracted~with~the~tools~ + of~the~package~footnote.\\ + If~you~go~on,~the~package~footnotehyper~won't~be~loaded. + } +% \end{macrocode} +% +% \medskip +% \begin{macrocode} +\bool_if:NT \g_@@_footnote_bool + { + \@ifclassloaded { beamer } + { \msg_info:nn { witharrows } { Option~incompatible~with~Beamer } } + { + \@ifpackageloaded { footnotehyper } + { \@@_error:n { footnote~with~footnotehyper~package } } + { \usepackage { footnote } } + } + } +% \end{macrocode} +% +% \begin{macrocode} +\bool_if:NT \g_@@_footnotehyper_bool + { + \@ifclassloaded { beamer } + { \@@_info:n { Option~incompatible~with~Beamer } } + { + \@ifpackageloaded { footnote } + { \@@_error:n { footnotehyper~with~footnote~package } } + { \usepackage { footnotehyper } } + } + \bool_gset_true:N \g_@@_footnote_bool + } +% \end{macrocode} +% The flag |\g_@@_footnote_bool| is raised and so, we will only have to test +% |\g_@@_footnote_bool| in order to know if we have to insert an environnement +% |{savenotes}| (the |\begin{savenotes}| is in |\@@_pre_halign:n| and +% |\end{savenotes}| at the end of the environments |{WithArrows}| and +% |{DispWithArrows}|). +% +% \bigskip +% \subsection{The class option leqno} +% +% The boolean |\c_@@_leqno_bool| will indicate if the class option |leqno| is +% used. When this option is used in LaTeX, the command |\@eqnnum| is redefined +% (as one can see in the file |leqno.clo|). That's enough to put the labels on +% the left in our environments |{DispWithArrows}| and |{DispWithArrows*}|. +% However, that's not enough when our option |wrap-lines| is used. That's why we +% have to know if this option is used as a class option. With the following +% programmation, |leqno| \emph{can't} be given as an option of \pkg{witharrows} +% (by design). +% \begin{macrocode} +\bool_new:N \c_@@_leqno_bool +\DeclareOption { leqno } { \bool_set_true:N \c_@@_leqno_bool } +\DeclareOption* { } +\ProcessOptions* +% +% \end{macrocode} +% +% +% +% \bigskip +% \subsection{Some technical definitions} +% +% +% \begin{macrocode} +\cs_generate_variant:Nn \tl_put_right:Nn { N v } +\cs_generate_variant:Nn \seq_set_split:Nnn { N x x } +% \end{macrocode} +% +% \medskip +% We create booleans in order to know if some packages are loaded. For example, +% for the package \pkg{amsmath}, the boolean is called +% |\c_@@_amsmath_loaded_bool|.\footnote{It's not possible to use +% |\@ifpackageloaded| in the core of the functions because |\@ifpackageloaded| +% is available only in the preamble.} +% \begin{macrocode} +\AtBeginDocument + { + \clist_map_inline:nn + { + amsmath, amsthm, autonum, cleveref, hyperref, mathtools, showlabels, + typedref, unicode-math, varwidth + } + { + \bool_new:c { c_@@_#1_loaded_bool } +%<*LaTeX> + \@ifpackageloaded { #1 } + { \bool_set_true:c { c_@@_#1_loaded_bool } } + { } +% +%<*plain-TeX> + \bool_set_false:c { c_@@_#1_loaded_bool } +% + } + } +% \end{macrocode} +% +% \bigskip +% We define a command |\@@_strcmp:nn| to compare two token lists. It will be +% available whether the engine is pdfTeX, XeTeX or LuaTeX. +% \begin{macrocode} +\sys_if_engine_luatex:TF + { + \cs_new_protected:Npn \@@_strcmp:nn #1 #2 + { \lua_now:e { l3kernel.strcmp('#1','#2') } } + } + { + \cs_new_protected:Npn \@@_strcmp:nn #1 #2 + { \pdftex_strcmp:D { #1 } { #2 } } + } +% \end{macrocode} +% +% \bigskip +% We can now define a command |\@@_sort_seq:N| which will sort a sequence. +% \begin{macrocode} +\cs_new_protected:Npn \@@_sort_seq:N #1 + { + \seq_sort:Nn #1 + { + \int_compare:nNnTF + { + \@@_strcmp:nn + { \str_lower_case:n { ##1 } } + { \str_lower_case:n { ##2 } } + } + > 0 + \sort_return_swapped: + \sort_return_same: + } + } +% \end{macrocode} +% +% \bigskip +% The following command converts each item of a sequence from |tl| to |str|. It +% will be used when creating list of keys (a key name is always a |str|). +% \begin{macrocode} +\cs_new_protected:Npn \@@_convert_to_str_seq:N #1 + { + \seq_clear:N \l_tmpa_seq + \seq_map_inline:Nn #1 + { + \seq_put_left:Nx \l_tmpa_seq { \tl_to_str:n { ##1 } } + } + \seq_set_eq:NN #1 \l_tmpa_seq + } +\cs_new_protected:Npn \@@_set_seq_of_str_from_clist:Nn #1 #2 + { + \seq_set_from_clist:Nn #1 { #2 } + \@@_convert_to_str_seq:N #1 + } +% \end{macrocode} +% +% \bigskip +% The command |\@@_save:N| saves a \pkg{expl3} variable by creating a global +% version of the variable. For a variable named |\l_|\texttt{\slshape +% name}|_|\texttt{\slshape type}, the corresponding global variable will be +% named |\g_|\texttt{\slshape name}|_|\texttt{\slshape type}. The type of the +% variable is determinated by the suffix \texttt{\slshape type} and is used to +% apply the corresponding \pkg{expl3} commands. +% \begin{macrocode} +\cs_new_protected:Npn \@@_save:N #1 + { + \seq_set_split:Nxx \l_tmpa_seq + { \char_generate:nn { `_ } { 12 } } + { \cs_to_str:N #1 } + \seq_pop_left:NN \l_tmpa_seq \l_tmpa_tl +% \end{macrocode} +% The string |\l_tmpa_str| will contains the \emph{type} of the variable. +% \begin{macrocode} + \str_set:Nx \l_tmpa_str { \seq_item:Nn \l_tmpa_seq { -1 } } + \use:c { \l_tmpa_str _if_exist:cF } + { g _\seq_use:Nnnn \l_tmpa_seq _ _ _ } + { + \use:c { \l_tmpa_str _new:c } + { g _\seq_use:Nnnn \l_tmpa_seq _ _ _ } + } + \use:c { \l_tmpa_str _gset_eq:cN } + { g _\seq_use:Nnnn \l_tmpa_seq _ _ _ } #1 + } +% \end{macrocode} +% +% \medskip +% The command |\@@_restore:N| affects to the \pkg{expl3} variable the value of +% the (previously) set value of the corresponding \emph{global} variable. +% \begin{macrocode} +\cs_new_protected:Npn \@@_restore:N #1 + { + \seq_set_split:Nxx \l_tmpa_seq + { \char_generate:nn { `_ } { 12 } } + { \cs_to_str:N #1 } + \seq_pop_left:NN \l_tmpa_seq \l_tmpa_tl + \str_set:Nx \l_tmpa_str { \seq_item:Nn \l_tmpa_seq { -1 } } + \use:c { \l_tmpa_str _set_eq:Nc } + #1 { g_\seq_use:Nnnn \l_tmpa_seq _ _ _ } + } +% \end{macrocode} +% +% +% \bigskip +% We define a Tikz style |@@_node_style| for the |l|-nodes and |r|-nodes that +% will be created in the |\halign|. These nodes are Tikz nodes of shape +% ``rectangle'' but with zero width. An arrow between two nodes starts from the +% \emph{south} anchor of the first node and arrives at the \emph{north} anchor +% of the second node. +% \begin{macrocode} +\tikzset + { + @@_node_style / .style = + { + above = \l_@@_ystart_dim , + inner~sep = \c_zero_dim , + minimum~width = \c_zero_dim , + minimum~height = \l_@@_ygap_dim + } + } +% \end{macrocode} +% If the user uses the option |show-nodes| (it's a \pkg{l3keys} option), the +% Tikz options |draw| and |red| will be appended to this style. This feature may +% be useful for debugging.\footnote{The |v|-nodes, created near the end of line +% in |{DispWithArrows}| and |{DispWithArrows*}| are not shown with the option +% |show-nodes|.} +% +% +% \bigskip +% The style |@@_standard| is loaded in standard in the |{tikzpicture}| we need. +% The names of the nodes are prefixed by |wa| (by security) but also by a prefix +% which is the position-in-the-tree of the nested environments. +% \begin{macrocode} +\tikzset + { + @@_standard / .style = + { + remember~picture , + overlay , + name~prefix = wa - \l_@@_prefix_str - + } + } +% \end{macrocode} +% +% \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 + { + WithArrows / arrow / tips / .style = + { > = { Straight~Barb [ scale = 1.2 , bend ] } } + } +% \end{macrocode} +% +% \bigskip +% The style |WithArrows/arrow| will be used to draw the arrows (more precisely, +% it will be passed to |every~path|). +% \begin{macrocode} +\tikzset + { + WithArrows / arrow / .style = + { + align = left , +% \end{macrocode} +% +% We have put the option |align = left| because we want to give the user the +% possibility of using |\\| in the labels. +% \begin{macrocode} + auto = left , +%<*LaTeX> + font = \small \itshape , +% + WithArrows / arrow / tips , + bend~left = 45 , + -> + } + } +% \end{macrocode} +% +% \bigskip +% The option |subequations| is an option which uses the environment +% |{subequations}| of \pkg{amsmath}. That's why, if \pkg{amsmath} is loaded, we +% add the key |subequations| to the list of the keys available in +% |\WithArrowsOptions| and |{DispWithArrows}|. +% \begin{macrocode} +%<*LaTeX> +\AtBeginDocument + { + \bool_if:NTF \c_@@_amsmath_loaded_bool + { + \seq_put_right:Nn \l_@@_options_WithArrowsOptions_seq { subequations } + \seq_put_right:Nn \l_@@_options_DispWithArrows_seq { subequations } + } +% \end{macrocode} +% +% \bigskip +% In order to increase the interline in the environments |{WithArrows}|, +% |{DispWithArrows}|, etc., 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} (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| if +% \pkg{amsmath} is not loaded (we put the code in a |\AtBeginDocument| because +% the flag |\c_@@_amsmath_loaded_bool| is itself set in a |\AtBeginDocument|). +% \begin{macrocode} + { +% + \cs_new_protected:Npn \spread@equation + { + \openup \jot + \cs_set_eq:NN \spread@equation \prg_do_nothing: + } +%<*LaTeX> + } + } +% +% \end{macrocode} +% +% \bigskip +% \begin{macrocode} +\tl_new:N \l_@@_left_brace_tl +\tl_set_eq:NN \l_@@_left_brace_tl \c_novalue_tl +% \end{macrocode} +% +% \bigskip +% \subsection{Variables} +% +% The boolean |\l_@@_in_WithArrows_bool| will be raised in an environment +% |{WithArrows}| and the boolean |\l_@@_in_dispwitharrows_bool| will be raised +% in an environment |{DispWithArrows}| or |{DispWithArrows*}|. The boolean +% |\l_@@_in_code_after_bool| will be raised during the execution of the +% |code-after| (option |code-after|). +% \begin{macrocode} +\bool_new:N \l_@@_in_WithArrows_bool +\bool_new:N \l_@@_in_DispWithArrows_bool +\bool_new:N \l_@@_in_code_after_bool +% \end{macrocode} +% +% \bigskip +% The following sequence is the position of the last environment |{WithArrows}| +% in the tree of the nested 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 integer indicates the position of the box that will be created +% for an environment |{WithArrows}| (not an environment |{DispWithArrows}|) : +% 0 (=|t|=|\vtop|), 1~(=|c|=|\vcenter|) or 2 (=|b|=|\vbox|). +% \begin{macrocode} +\int_new:N \l_@@_pos_env_int +% \end{macrocode} +% +% \bigskip +% The integer |\l_@@_pos_arrow_int| indicates the position of the arrow with the +% following code (the option |v| is accessible only for the arrows in +% |code-after| where the options |i|, |group| et |groups| are not available). +% +% \begin{center} +% \begin{tabular}{l} +% \begin{tabular}{@{}l*8c@{}} +% \toprule +% option & |lr| & |ll| & |rl| & |rr| & |v| & |i| & |groups| & |group| \\ +% \midrule +% |\l_@@_pos_arrow_int| & $0$ & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ \\ +% \bottomrule +% \end{tabular} \\ +% \footnotesize The option |v| can be used only in |\Arrow| in |code-after| (see +% below). +% \end{tabular} +% \end{center} +% +% \begin{macrocode} +\int_new:N \l_@@_pos_arrow_int +\int_set:Nn \l_@@_pos_arrow_int 3 +% \end{macrocode} +% +% +% \bigskip +% In the |\halign| of an environment |{WithArrows}| or |{DispWithArrows}|, we +% will have to use four 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_@@_col_int| to count the column of the |\halign|. +% \end{itemize} +% +% +% These 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_@@_arrow_int_seq +\int_new:N \g_@@_arrow_int +\seq_new:N \g_@@_line_int_seq +\int_new:N \g_@@_line_int +\seq_new:N \g_@@_col_int_seq +\int_new:N \g_@@_col_int +% \end{macrocode} +% +% +% \bigskip +% For the environment |{DispWithArrows}|, the comma list |\l_@@_tags_clist| will +% be the list of the numbers of lines to be tagged (with the counter |equation| +% of LaTeX). In fact, |\l_@@_tags_clist| may contain non negative integers but +% also three special values, |first|, |last| and |all|. +% \begin{macrocode} +%<*LaTeX> +\clist_new:N \l_@@_tags_clist +\clist_set:Nn \l_@@_tags_clist { all } +% \end{macrocode} +% +% \bigskip +% During the execution of an environment |{DispWithArrows}|, if a row must be +% tagged, the (local) value of |\l_@@_tags_clist| will be put (by convention) to +% |all|. +% \begin{macrocode} +\cs_new_protected:Npn \@@_test_if_to_tag: + { + \clist_if_in:NVT \l_@@_tags_clist \g_@@_line_int + { \clist_set:Nn \l_@@_tags_clist { all } } + } +% +% \end{macrocode} +% +% +% \bigskip +% If the user has given a value for the option |command-name| (at the global or +% at the \emph{environment} level), a command with this name is defined locally +% in the environment with meaning |\@@_Arrow|. The default value of the option +% |command-name| is ``|Arrow|'' and thus, by default, the name of the command +% will be |\Arrow|. +% \begin{macrocode} +\str_new:N \l_@@_command_name_str +\str_set:Nn \l_@@_command_name_str { Arrow } +% \end{macrocode} +% +% \bigskip +% The string |\l_@@_string_Arrow_for_msg_str| is only a string that will be +% displayed in some error messages. For example, if |command-name| is defined to +% be |Explanation|, this string will contain ``|\Arrow alias \Explanation|''. +% \begin{macrocode} +\str_new:N \l_@@_string_Arrow_for_msg_str +\str_set:Nx \l_@@_string_Arrow_for_msg_str { \token_to_str:N \Arrow } +% \end{macrocode} +% +% \bigskip +% The sequence |\g_@@_names_seq| will be the list of all the names of +% environments used (via the option |name|) in the document: two environments +% must not have the same name. However, it's possible to use the option +% |allow-duplicate-names|. +% \begin{macrocode} +\seq_new:N \g_@@_names_seq +% \end{macrocode} +% +% \bigskip +% The boolean |\l_@@_sbwi_bool| corresponds to the option +% |standard-behaviour-with-items|. Since the version 1.16 of \pkg{witharrows}, +% no vertical space is added between an |\item| of a LaTeX list and an +% environment |{DispWithArrows}|. With the option +% |standard-behaviour-with-items|, it's possible to restore the previous +% behaviour (which corresponds to the standard behaviour of |{align}| of +% \pkg{amsmath}). |\l_@@_sbwi_bool| is the boolean corresponding to this option. +% \begin{macrocode} +%<*LaTeX> +\bool_new:N \l_@@_sbwi_bool +% +% \end{macrocode} +% +% \bigskip +% \begin{macrocode} +%<*LaTeX> +\bool_new:N \l_@@_tag_star_bool +\bool_new:N \l_@@_tag_next_line_bool +\bool_new:N \l_@@_qedhere_bool +% +\bool_new:N \l_@@_in_first_columns_bool +\bool_new:N \l_@@_new_group_bool +\bool_new:N \l_@@_initial_r_bool +\bool_new:N \l_@@_final_r_bool +\tl_new:N \l_@@_initial_tl +\tl_new:N \l_@@_final_tl +\int_new:N \l_@@_nb_cols_int +% \end{macrocode} +% +% \bigskip +% The string |\l_@@_format_str| will contain the \emph{format} of the array +% which is a succession of letters |r|, |c| and |l| specifying the type of the +% columns of the |\halign| (except the column for the labels of the equations +% in the environment |{DispWithArrows}|). +% \begin{macrocode} +\str_new:N \l_@@_format_str +% \end{macrocode} +% +% \bigskip +% The option boolean corresponds to the option |subequations|. +% \begin{macrocode} +%<*LaTeX> +\bool_new:N \l_@@_subequations_bool +% +% \end{macrocode} +% +% \bigskip +% \subsection{The definition of the options} +% +% There are four levels where options can be set: +% \begin{itemize} +% \item with |\usepackage[...]{witharrows}|: this level will be called +% \emph{package} level; +% \item with |\WithArrowsOptions{...}|: this level will be called \emph{global} +% level\footnote{This level is called \emph{global level} but the settings done +% by |\WithArrowsOptions| are local in the TeX sense: their scope corresponds to +% the current TeX group.}; +% \item with |\begin{WithArrows}[...]|: this level will be called +% \emph{environment} level; +% \item with |\Arrow[...]| (included in |code-after|): this level will be called +% \emph{local} level. +% \end{itemize} +% +% +% \bigskip +% When we scan a list of options, we want to be able to raise an error if two +% options of position (|ll|, |rl|, |i|, etc.) of the arrows are present. That's +% why we keep the first option of position in a variable called +% |\l_@@_previous_key_str|. The following function |\@@_eval_if_allowed:n| will +% execute its argument only if a first key of position has not been set (and +% raise an error elsewhere). +% +% \begin{macrocode} +\cs_new_protected:Npn \@@_eval_if_allowed:n #1 + { + \str_if_empty:NTF \l_@@_previous_key_str + { + \str_set_eq:NN \l_@@_previous_key_str \l_keys_key_tl + #1 + } + { \@@_error:n { Incompatible~options } } + } +% \end{macrocode} +% +% +% \begin{macrocode} +\cs_new_protected:Npn \@@_fix_pos_option:n #1 + { \@@_eval_if_allowed:n { \int_set:Nn \l_@@_pos_arrow_int { #1 } } } +% \end{macrocode} +% +% \bigskip +% First a set of keys that will be used at the global or environment level of +% options. +% \begin{macrocode} +\keys_define:nn { WithArrows / Global } + { + ygap .dim_set:N = \l_@@_ygap_dim , + ygap .value_required:n = true , + ygap .initial:n = 0.4 ex , + ystart .dim_set:N = \l_@@_ystart_dim , + ystart .value_required:n = true , + ystart .initial:n = 0.4 ex , + more-columns .code:n = + \@@_msg_redirect_name:nn { Too~much~columns~in~WithArrows } { none } , + more-columns .value_forbidden:n = true, + command-name .code:n = + \str_set:Nn \l_@@_command_name_str { #1 } + \str_set:Nx \l_@@_string_Arrow_for_msg_str + { \c_backslash_str Arrow~alias~\c_backslash_str #1 } , + command-name .value_required:n = true , + tikz-code .tl_set:N = \l_@@_tikz_code_tl, + tikz-code .initial:n = \draw~(#1)~to~node{#3}~(#2)~; , + tikz-code .value_required:n = true , + TikzCode .meta:n = { tikz-code = #1 } , + displaystyle .bool_set:N = \l_@@_displaystyle_bool , + displaystyle .default:n = true , + show-nodes .code:n = + \tikzset { @@_node_style / .append~style = { draw , red } } , + show-nodes .value_forbidden:n = true, + show-node-names .bool_set:N = \l_@@_show_node_names_bool , + show-node-names .default:n = true , + group .code:n = + \str_if_empty:NTF \l_@@_previous_key_str + { + \str_set:Nn \l_@@_previous_key_str { group } + \seq_remove_all:Nn \l_@@_options_Arrow_seq { xoffset } + \int_set:Nn \l_@@_pos_arrow_int 7 + } + { \@@_error:n { Incompatible~options } } , + group .value_forbidden:n = true , + groups .code:n = + \str_if_empty:NTF \l_@@_previous_key_str + { + \str_set:Nn \l_@@_previous_key_str { groups } + \seq_if_in:NnF \l_@@_options_Arrow_seq { new-group } + { \seq_put_right:Nn \l_@@_options_Arrow_seq { new-group } } + \seq_remove_all:Nn \l_@@_options_Arrow_seq { xoffset } + \int_set:Nn \l_@@_pos_arrow_int 6 + } + { \@@_error:n { Incompatible~options } } , + groups .value_forbidden:n = true , + tikz .code:n = \tikzset { WithArrows / arrow / .append~style = { #1 } } , + tikz .initial:n = \c_empty_tl , + tikz .value_required:n = true , + rr .value_forbidden:n = true , + rr .code:n = \@@_fix_pos_option:n 3 , + ll .value_forbidden:n = true , + ll .code:n = \@@_fix_pos_option:n 1 , + rl .value_forbidden:n = true , + rl .code:n = \@@_fix_pos_option:n 2 , + lr .value_forbidden:n = true , + lr .code:n = \@@_fix_pos_option:n 0 , + i .value_forbidden:n = true , + i .code:n = \@@_fix_pos_option:n 5 , + xoffset .dim_set:N = \l_@@_xoffset_dim , + xoffset .value_required:n = true , + xoffset .initial:n = 3 mm , + jot .dim_set:N = \jot , + jot .value_required:n = true , + interline .skip_set:N = \l_@@_interline_skip , + interline .value_required:n = true , + start-adjust .dim_set:N = \l_@@_start_adjust_dim , + start-adjust .value_required:n = true , + start-adjust .initial:n = 0.4 ex , + end-adjust .dim_set:N = \l_@@_end_adjust_dim , + end-adjust .value_required:n = true , + end-adjust .initial:n = 0.4 ex , + adjust .meta:n = { start-adjust = #1 , end-adjust = #1 } , + adjust .value_required:n = true , +% \end{macrocode} +% +% \medskip +% With the option |no-arrows|, the arrows won't be drawn. However, the ``first +% pass'' of the arrows is done and some errors may be detected. The +% nullification of |\@@_draw_arrows:nn| is for the standard arrows and the +% nullification of |\@@_draw_arrow:nnn| is for ``Arrow in |code-after|''. +% \begin{macrocode} + no-arrows .code:n = + \cs_set_eq:NN \@@_draw_arrows:nn \use_none:nn + \cs_set_eq:NN \@@_draw_arrow:nnn \use_none:nnn , + no-arrows .value_forbidden:n = true , + } +% \end{macrocode} +% +% \bigskip +% Now a set of keys specific to the environments |{WithArrows}| (and not +% |{DispWithArrow}}|). Despite its name, this set of keys will also be used in +% |\WithArrowsOptions|. +% \begin{macrocode} +\keys_define:nn { WithArrows / WithArrowsSpecific } + { + t .code:n = \int_set:Nn \l_@@_pos_env_int O , + t .value_forbidden:n = true , + c .code:n = \int_set:Nn \l_@@_pos_env_int 1 , + c .value_forbidden:n = true , + b .code:n = \int_set:Nn \l_@@_pos_env_int 2 , + b .value_forbidden:n = true + } +% \end{macrocode} +% +% \bigskip +% The following list of the (left) extensible delimiters of LaTeX is only for +% the validation of the key |replace-left-brace-by|. +% \begin{macrocode} +\clist_new:N \c_@@_extensible_delimiters_clist +\clist_set:Nn \c_@@_extensible_delimiters_clist + { + ., \{, (, [, \lbrace, \lbrack, \lgroup, \langle, \lmoustache, \lceil, \lfloor + } +%<*LaTeX> +\AtBeginDocument + { + \bool_if:nT + { \c_@@_amsmath_loaded_bool || \use:c { c_@@_unicode-math_loaded_bool } } + { + \clist_put_right:Nn \c_@@_extensible_delimiters_clist { \lvert, \lVert } + } + } +% +% \end{macrocode} +% +% +% \bigskip +% Now a set of keys specific to the environments |{DispWithArrows}| and +% |{DispWithArrows*}| (and not |{WithArrows}|). Despite its name, this set of +% keys will also be used in |\WithArrowsOptions|. +% \begin{macrocode} +\keys_define:nn { WithArrows / DispWithArrowsSpecific } + { + fleqn .bool_set:N = \l_@@_fleqn_bool , + fleqn .default:n = true , + mathindent .dim_set:N = \l_@@_mathindent_dim , + mathindent .value_required:n = true , + mathindent .initial:n = 25 pt , +%<*LaTeX> + notag .code:n = + \str_if_eq:nnTF { #1 } { true } + { \clist_clear:N \l_@@_tags_clist } + { \clist_set:Nn \l_@@_tags_clist { all } } , + notag .default:n = true , +% \end{macrocode} +% Since the option |subequations| is an option which insert the environment +% |{DispWithArrows}| in an environment |{subequations}| of \pkg{amsmath}, we +% must test whether the package \pkg{amsmath} is loaded. +% \begin{macrocode} + subequations .code:n = + \bool_if:NTF \c_@@_amsmath_loaded_bool + { \bool_set_true:N \l_@@_subequations_bool } + { + \@@_error:n { amsmath~not~loaded } + \group_begin: + \globaldefs = 1 + \@@_msg_redirect_name:nn { amsmath~not~loaded } { info } + \group_end: + } , + subequations .default:n = true , + subequations .value_forbidden:n = true , + nonumber .meta:n = notag , + allow-multiple-labels .code:n = + \@@_msg_redirect_name:nn { Multiple~labels } { none } , + allow-multiple-labels .value_forbidden:n = true , + tagged-lines .code:n = + \clist_set:Nn \l_@@_tags_clist { #1 } + \clist_if_in:NnT \l_@@_tags_clist { first } + { + \clist_remove_all:Nn \l_@@_tags_clist { first } + \clist_put_left:Nn \l_@@_tags_clist \c_one_int + } , + tagged-lines .value_required:n = true , +% + wrap-lines .bool_set:N = \l_@@_wrap_lines_bool , + wrap-lines .default:n = true , + replace-left-brace-by .code:n = + { + \tl_set:Nx \l_tmpa_tl { \tl_head:n { #1 } } + \clist_if_in:NVTF + \c_@@_extensible_delimiters_clist + \l_tmpa_tl + { \tl_set:Nn \l_@@_replace_left_brace_by_tl { #1 } } + { \@@_error:n { Bad~value~for~replace~brace~by } } + } , + replace-left-brace-by .initial:n = \lbrace , +% \end{macrocode} +% +% Since the version 1.16 of \pkg{witharrows}, no vertical space is added between +% an |\item| of a LaTeX list and an environment |{DispWithArrows}|. With the +% option |standard-behaviour-with-items|, it's possible to restore the previous +% behaviour (which corresponds to the standard behaviour of |{align}| of +% \pkg{amsmath}). +% \begin{macrocode} +%<*LaTeX>> + standard-behaviour-with-items .bool_set:N = \l_@@_sbwi_bool , + standard-behaviour-with-items .default:n = true +% + } +% \end{macrocode} +% +% +% \bigskip +% Now a set of keys which will be used in all the environments (but not in +% |\WithArrowsOptions}|). +% +% \begin{macrocode} +\keys_define:nn { WithArrows / Env } + { + name .code:n = +% \end{macrocode} +% First, we convert the value in a |str| because the list of the names will be a +% list of |str|. +% \begin{macrocode} + \str_set:Nn \l_tmpa_str { #1 } + \seq_if_in:NVTF \g_@@_names_seq \l_tmpa_str + { \@@_error:n { Duplicate~name } } + { \seq_gput_left:NV \g_@@_names_seq \l_tmpa_str } + \str_set_eq:NN \l_@@_name_str \l_tmpa_str , + name .value_required:n = true , + code-before .code:n = \tl_put_right:Nn \l_@@_code_before_tl { #1 } , + code-before .value_required:n = true, + CodeBefore .meta:n = { code-before = #1 } , + code-after .code:n = \tl_put_right:Nn \l_@@_code_after_tl { #1 } , + code-after .value_required:n = true , + CodeAfter .meta:n = { code-after = #1 } , + format .code:n = + \tl_if_empty:nTF { #1 } + { \@@_error:n { Invalid~option~format } } + { + \regex_match:nnTF { \A[rcl]*\Z } { #1 } + { \tl_set:Nn \l_@@_format_str { #1 } } + { \@@_error:n { Invalid~option~format } } + } , + format .value_required:n = true , + } +% \end{macrocode} +% +% +% \bigskip +% Now, we begin the construction of the major sets of keys, named +% ``|WithArrows / WithArrows|'', ``|WithArrows / DispWithArrows|'' and +% ``|WithArrows / WithArrowsOptions|''. Each of these sets of keys will be +% completed after. +% \begin{macrocode} +\keys_define:nn { WithArrows } + { + WithArrows .inherit:n = + { + WithArrows / Global , + WithArrows / WithArrowsSpecific , + WithArrows / Env + } , + DispWithArrows .inherit:n = + { + WithArrows / DispWithArrowsSpecific , + WithArrows / Global , + WithArrows / Env , + } , + WithArrowsOptions .inherit:n = + { + WithArrows / Global , + WithArrows / WithArrowsSpecific , + WithArrows / DispWithArrowsSpecific + } + } +% \end{macrocode} +% +% +% \bigskip +% A sequence of |str| for the options available in |{WithArrows}|. This sequence +% will be used in the error messages and can be modified dynamically. +% \begin{macrocode} +\seq_new:N \l_@@_options_WithArrows_seq +\@@_set_seq_of_str_from_clist:Nn \l_@@_options_WithArrows_seq + { + adjust, b, c, code-after, code-before, command-name, + displaystyle, end-adjust, + format, group, groups, i, + interline, jot, ll, + lr, more-columns, name, + no-arrows, rl, rr, + show-node-names, show-nodes, start-adjust, + t, tikz, tikz-code, + xoffset, ygap, ystart + } +\@@_convert_to_str_seq:N \l_@@_options_WithArrows_seq +% \end{macrocode} +% +% \medskip +% \begin{macrocode} +\keys_define:nn { WithArrows / WithArrows } + { + unknown .code:n = + \@@_sort_seq:N \l_@@_options_WithArrows_seq + \@@_error:n { Unknown~option~WithArrows } + } +% \end{macrocode} +% +% \bigskip +% \begin{macrocode} +\keys_define:nn { WithArrows / DispWithArrows } + { + left-brace .tl_set:N = \l_@@_left_brace_tl , + unknown .code:n = + \@@_sort_seq:N \l_@@_options_DispWithArrows_seq + \@@_error:n { Unknown~option~DispWithArrows } + } +% \end{macrocode} +% +% \bigskip +% A sequence of the options available in |{DispWithArrows}|. This sequence will +% be used in the error messages and can be modified dynamically. +% \begin{macrocode} +\seq_new:N \l_@@_options_DispWithArrows_seq +\@@_set_seq_of_str_from_clist:Nn \l_@@_options_DispWithArrows_seq + { + code-after, code-before, command-name, tikz-code, adjust, + displaystyle, end-adjust, fleqn, group, format, groups, i, interline, jot, + left-brace, ll, lr, mathindent, name, no-arrows, replace-left-brace-by, rl, + rr, show-node-names, show-nodes, start-adjust, tikz, wrap-lines, xoffset, + ygap, ystart, +%<*LaTeX>> + allow-multiple-labels, tagged-lines, nonumber, notag +% + } +% \end{macrocode} +% +% +% \begin{macrocode} +\keys_define:nn { WithArrows / WithArrowsOptions } + { + allow-duplicate-names .code:n = + \@@_msg_redirect_name:nn { Duplicate~name } { none } , + allow-duplicate-names .value_forbidden:n = true , + unknown .code:n = + \@@_sort_seq:N \l_@@_options_WithArrowsOptions_seq + \@@_error:n { Unknown~option~WithArrowsOptions } + } +% \end{macrocode} +% +% +% \bigskip +% A sequence of the options available in |\WithArrowsOptions|. This sequence +% will be used in the error messages and can be modified dynamically. +% \begin{macrocode} +\seq_new:N \l_@@_options_WithArrowsOptions_seq +\@@_set_seq_of_str_from_clist:Nn \l_@@_options_WithArrowsOptions_seq + { + allow-duplicate-names, b, c, command-name, more-columns, tikz-code, adjust, + displaystyle, end-adjust, fleqn, group, groups, i, interline, jot, ll, lr, + mathindent, no-arrows, rl, rr, show-node-names, show-nodes, start-adjust, t, + tikz, wrap-lines, xoffset, ygap, ystart, +%<*LaTeX>> + allow-multiple-labels, nonumber, notag, standard-behaviour-with-items, + tagged-lines +% + } +% \end{macrocode} +% +% \bigskip +% The command |\@@_set_independent:| is a command without argument that will be +% used to specify that the arrow will be ``independent'' (of the potential +% groups of the option |group| or |groups|). This information will be stored in +% the field ``status'' of the arrow. Another value of the field ``status'' is +% ``new-group''. +% \begin{macrocode} +\cs_new_protected:Npn \@@_set_independent: + { + \str_if_empty:NTF \l_@@_previous_key_str + { + \str_set_eq:NN \l_@@_previous_key_str \l_keys_key_tl + \str_set:Nn \l_@@_status_arrow_str { independent } + \str_if_eq:VnF \l_keys_value_tl { NoValue } + { \@@_error:n { Value~for~a~key } } + } + { \@@_error:n { Incompatible~options~in~Arrow } } + } +% \end{macrocode} +% +% \bigskip +% The options of an individual arrow are parsed twice. The first pass is when +% the command |\Arrow| is read. The second pass is when the arrows are drawn +% (after the end of the environment |{WithArrows}| or |{DispWithArrows}|). Now, +% we present the keys set for the first pass. The main goal is to extract +% informations which will be necessary during the scan of the arrows. For +% instance, we have to know if some arrows are ``independent'' or use the +% option ``new-group''. +% \begin{macrocode} +\keys_define:nn { WithArrows / Arrow / FirstPass } + { + jump .code:n = + \int_compare:nTF { #1 > 0 } + { \int_set:Nn \l_@@_jump_int { #1 } } + { \@@_error:n { Negative~jump } } , + jump .value_required:n = true, + rr .code:n = \@@_set_independent: , + ll .code:n = \@@_set_independent: , + rl .code:n = \@@_set_independent: , + lr .code:n = \@@_set_independent: , + i .code:n = \@@_set_independent: , + rr .default:n = NoValue , + ll .default:n = NoValue , + rl .default:n = NoValue , + lr .default:n = NoValue , + i .default:n = NoValue , + new-group .value_forbidden:n = true, + new-group .code:n = + \int_compare:nTF { \l_@@_pos_arrow_int = 6 } + { \str_set:Nn \l_@@_status_arrow_str { new-group } } + { \@@_error:n { new-group~without~groups } } , +% \end{macrocode} +% +% \medskip +% The other keys don't give any information necessary during the scan of the +% arrows. However, you try to detect errors and that's why all the keys are +% listed in this keys set. An unknown key will be detected at the point of the +% command |\Arrow| and not at the end of the environment. +% \begin{macrocode} + tikz-code .code:n = \prg_do_nothing: , + tikz-code .value_required:n = true , + tikz .code:n = \prg_do_nothing: , + tikz .value_required:n = true , +% \end{macrocode} +% +% \medskip +% The option |xoffset| is not allowed when the option |group| or the option +% |groups| is used (since it would be meaningless). +% \begin{macrocode} + xoffset .code:n = + \int_compare:nNnT \l_@@_pos_arrow_int > 5 + { \@@_error:n { Option~xoffset~forbidden } } , + xoffset .value_required:n = true , + start-adjust .code:n = \prg_do_nothing: , + start-adjust .value_required:n = true , + end-adjust .code:n = \prg_do_nothing: , + end-adjust .value_required:n = true , + adjust .code:n = \prg_do_nothing: , + adjust .value_required:n = true , + unknown .code:n = + \@@_sort_seq:N \l_@@_options_Arrow_seq + \seq_if_in:NVTF \l_@@_options_WithArrows_seq \l_keys_key_tl + { + \str_set:Nn \l_tmpa_str + { ~However,~this~key~can~be~used~in~the~options~of~\{WithArrows\}. } + } + { \str_clear:N \l_tmpa_str } + \@@_error:n { Unknown~option~in~Arrow } + } +% \end{macrocode} +% +% +% \bigskip +% A sequence of the options available in |\Arrow|. This sequence will be used in +% the error messages and can be modified dynamically. +% \begin{macrocode} +\seq_new:N \l_@@_options_Arrow_seq +\@@_set_seq_of_str_from_clist:Nn \l_@@_options_Arrow_seq + { + adjust, end-adjust, i, jump, ll, lr, rl, rr, start-adjust, tikz, tikz-code, + xoffset + } +% \end{macrocode} +% +% \bigskip +% \begin{macrocode} +\cs_new_protected:Npn \@@_fix_pos_arrow:n #1 + { + \str_if_empty:NT \l_@@_previous_key_str + { + \str_set_eq:NN \l_@@_previous_key_str \l_keys_key_tl + \int_set:Nn \l_@@_pos_arrow_int { #1 } + } + } +% \end{macrocode} +% +% \bigskip +% The options of the individual commands |\Arrows| are scanned twice. The second +% pass is just before the drawing of the arrow. In this set of keys, we don't +% put an item for the unknown keys because an unknown key would have been +% already detected during the first pass. +% +% \begin{macrocode} +\keys_define:nn {WithArrows / Arrow / SecondPass } + { + tikz-code .tl_set:N = \l_@@_tikz_code_tl , + tikz-code .initial:n = \draw~(#1)~to~node{#3}~(#2)~; , + tikz .code:n = \tikzset { WithArrows / arrow / .append~style = { #1 } } , + tikz .initial:n = \c_empty_tl , + rr .code:n = \@@_fix_pos_arrow:n 3 , + ll .code:n = \@@_fix_pos_arrow:n 1 , + rl .code:n = \@@_fix_pos_arrow:n 2 , + lr .code:n = \@@_fix_pos_arrow:n 0 , + i .code:n = \@@_fix_pos_arrow:n 5 , +% \end{macrocode} +% +% \medskip +% The option |xoffset| is not allowed when the option |group| or the option +% |groups| is used (since it would be meaningless). An error has been raised +% during the first pass. Here, we manage to avoid a second error which +% would be redundant. +% \begin{macrocode} + xoffset .code:n = + \int_compare:nNnF \l_@@_pos_arrow_int > 5 + { \dim_set:Nn \l_@@_xoffset_dim { #1 } } , + start-adjust .dim_set:N = \l_@@_start_adjust_dim, + end-adjust .dim_set:N = \l_@@_end_adjust_dim, + adjust .code:n = + \dim_set:Nn \l_@@_start_adjust_dim { #1 } + \dim_set:Nn \l_@@_end_adjust_dim { #1 } , + } +% \end{macrocode} +% +% \bigskip +% |\WithArrowsOptions| is the command of the \pkg{witharrows} package to fix +% options at the document level. It's possible to fix in |\WithArrowsOptions| +% some options specific to |{WithArrows}| (in contrast with |{DispWithArrows}|) +% or specific to |{DispWithArrows}| (in contrast with |{WithArrows}|). That's +% why we have constructed a set of keys specific to |\WithArrowsOptions|. +% \begin{macrocode} +%<*LaTeX> +\NewDocumentCommand \WithArrowsOptions { m } +% +%<*plain-TeX> +\cs_set_protected:Npn \WithArrowsOptions #1 +% + { + \str_clear_new:N \l_@@_previous_key_str + \keys_set:nn { WithArrows / WithArrowsOptions } { #1 } + } +% \end{macrocode} +% +% +% \bigskip +% \subsection{The command \textbackslash 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 |command-name| and the user command for |\@@_Arrow| will be different. +% This mechanism can be useful when the user has already a command named +% |\Arrow| he still wants to use in the environments |{WithArrows}| or +% |{DispWithArrows}|. +% +% \medskip +% \begin{macrocode} +%<*LaTeX> +\NewDocumentCommand \@@_Arrow { O { } m ! O { } } +% +%<*plain-TeX> +\cs_new_protected:Npn \@@_Arrow + { + \peek_meaning:NTF [ + { \@@_Arrow_i } + { \@@_Arrow_i [ ] } + } +\cs_new_protected:Npn \@@_Arrow_i [ #1 ] #2 + { + \peek_meaning:NTF [ + { \@@_Arrow_ii [ #1 ] { #2 } } + { \@@_Arrow_ii [ #1 ] { #2 } [ ] } + } +\cs_new_protected:Npn \@@_Arrow_ii [ #1 ] #2 [ #3 ] +% + { +% \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} +% +% \medskip +% We will construct a global property list to store the informations of the +% considered arrow. The six fields of this property list are ``initial'', +% ``final'', ``status'', ``options'', ``label'' and ``input-line''. In order to +% compute the value of ``final'' (the destination row of the arrow), we have to +% take into account a potential option |jump|. In order to compute the value of +% the field ``status'', we have to take into account options as |ll|, |rl|, +% |rr|, |lr|, etc. or |new-group|. +% +% We will do that job with a first analyze of the options of the command +% |\Arrow| with a dedicated set of keys called |WithArrows/Arrow/FirstPass|. +% +% \begin{macrocode} + \str_clear_new:N \l_@@_previous_key_str + \keys_set:nn { WithArrows / Arrow / FirstPass } { #1 , #3 } +% \end{macrocode} +% +% \medskip +% We construct now a global property list to store the informations of the +% considered arrow with the six fields ``initial'', ``final'', ``status'', +% ``options'', ``label'' and ``input-line''. +% +% \smallskip +% \begin{enumerate} +% \item First, the row from which the arrow starts: +% \begin{macrocode} + \prop_put:NnV \l_tmpa_prop { initial } \g_@@_line_int +% \end{macrocode} +% +% \item The row where the arrow ends (that's why it was necessary to analyze 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 The ``status'' of the arrow, with 3 possible values: empty, +% |independent|, or |new-group|. +% \begin{macrocode} + \prop_put:NnV \l_tmpa_prop { status } \l_@@_status_arrow_str +% \end{macrocode} +% +% \item 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} +% +% \item The number of the line where the command |\Arrow| is issued in the TeX +% source (as of now, this is only useful for an error message). +% \begin{macrocode} + \prop_put:Nnx \l_tmpa_prop { input-line } \msg_line_number: +% \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_str _ \int_use:N \g_@@_arrow_int _ prop } + \prop_gset_eq:cN + { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \g_@@_arrow_int _ prop } + \l_tmpa_prop + } +% \end{macrocode} +% +% \medskip +% The command |\Arrow| (or the corresponding command with a name given by the +% user with the option |command-name|) will be available only in the last column of +% the environments |{WithArrows}| and |{DispWithArrows}|. In the other columns, +% the command will be linked to the following command |\@@_Arrow_first_columns:| +% which will raise an error. +% \begin{macrocode} +\cs_new_protected:Npn \@@_Arrow_first_columns: + { \@@_error:n { Arrow~not~in~last~column } \@@_Arrow } +% \end{macrocode} +% +% +% \bigskip +% \subsection{The environments \{WithArrows\} and \{DispWithArrows\}} +% +% \subsubsection{Code before the \textbackslash halign} +% +% The command |\@@_pre_halign:n| is a code common to the environments +% |{WithArrows}| and |{DispWithArrows}|. The argument is the list of options +% given to the environment. +% \begin{macrocode} +\cs_new_protected:Npn \@@_pre_halign:n #1 +% \end{macrocode} +% +% First, the initialisation of |\l_@@_type_env_str| which is the name of the +% encompassing environment. In fact, this token list is used only in the error +% messages. +% \begin{macrocode} + { +%<*LaTeX> + \str_clear_new:N \l_@@_type_env_str + \str_set:NV \l_@@_type_env_str \@currenvir +% +% \end{macrocode} +% +% \bigskip +% We deactivate the potential externalization of Tikz. The Tikz elements created +% by \pkg{witharrows} can't be externalized since they are created in Tikz +% pictures with |overlay| and |remember picture|. +% \begin{macrocode} + \cs_if_exist:NT \tikz@library@external@loaded + { \tikzset { external / export = false } } +% \end{macrocode} +% +% \bigskip +% The token list |\l_@@_name_str| will contain the potential name of the +% environment (given with the option |name|). This name will be used to create +% aliases for the names of the nodes. +% \begin{macrocode} + \str_clear_new:N \l_@@_name_str +% \end{macrocode} +% +% \bigskip +% The parameter |\l_@@_status_arrow_str| will be used to store the ``status'' of +% an individual arrow. It will be used to fill the field ``status'' in the +% property list describing an arrow. +% \begin{macrocode} + \str_clear_new:N \l_@@_status_arrow_str +% \end{macrocode} +% +% \bigskip +% The dimension |\l_@@_x_dim| will be used to compute the $x$-value for some +% vertical arrows when one of the options |i|, |group| and |groups| (values 5, 6 +% and 7 of |\l_@@_pos_arrow_int|) is used. +% \begin{macrocode} + \dim_zero_new:N \l_@@_x_dim +% \end{macrocode} +% +% \medskip +% The variable |\l_@@_input_line_str| will be used only to store, for each +% command |\Arrow| the line (in the TeX file) where the command is issued. This +% information will be stored in the field ``input-line'' of the arrow. As of +% now, this information is used only in the error message of a arrow impossible +% to draw (because it arrives after the last row of the environment). +% \begin{macrocode} + \str_clear_new:N \l_@@_input_line_str +% \end{macrocode} +% +% +% The initialisation of the counters |\g_@@_arrow_int|, |\g_@@_line_int| and +% |\g_@@_col_int|. However, we have to save their previous values with the +% stacks created for this end. +% \begin{macrocode} + \seq_gput_right:NV \g_@@_arrow_int_seq \g_@@_arrow_int + \int_gzero:N \g_@@_arrow_int + \seq_gput_right:NV \g_@@_line_int_seq \g_@@_line_int + \int_gzero:N \g_@@_line_int + \seq_gput_right:NV \g_@@_col_int_seq \g_@@_col_int + \int_gzero:N \g_@@_col_int +% \end{macrocode} +% +% In the preamble of the |\halign|, there will be \emph{two} counters of the +% columns. The aim of this programmation is to detect the utilisation of a +% command |\omit| in a cell of the |\halign| (it should be forbidden). +% For example, in the part of the preamble concerning the third column (if there +% is a third column in the environment), we will have the following instructions : +% \begin{Verbatim} +% \int_gincr:N \g_~@~@_col_int +% \int_gset:Nn \g_~@~@_static_col_int 3 +% \end{Verbatim} +% The counter |\g_@@_col_int| is incremented dynamically and the second is +% static. If the user has used a command |\omit|, the dynamic incrementation is +% not done in the cell and, at this end of the row, the difference between the +% counters may infer the presence of |\omit| at least once. +% \begin{macrocode} + \int_gzero_new:N \g_@@_static_col_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 six 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 + \str_clear_new:N \l_@@_prefix_str + \str_set:Nx \l_@@_prefix_str { \seq_use:Nnnn \l_tmpa_seq - - - } +% \end{macrocode} +% +% \bigskip +% We define the command |\\| to be the command |\@@_cr:| (defined below). +% \begin{macrocode} + \cs_set_eq:NN \\ \@@_cr: + \dim_zero:N \mathsurround +% \end{macrocode} +% +% \bigskip +% These 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 + \int_zero_new:N \l_@@_pos_of_arrow_int + \int_zero_new:N \l_@@_jump_int +% \end{macrocode} +% +% \medskip +% The counter |\l_@@_jump_int| corresponds to the option |jump|. Now, we set the +% default value for this option. +% \begin{macrocode} + \int_set:Nn \l_@@_jump_int \c_one_int +% \end{macrocode} +% +% \medskip +% The string |\l_@@_format_str| corresponds to the option |format|. Now, we set +% the default value for this option. +% \begin{macrocode} + \str_set:Nn \l_@@_format_str { rl } +% \end{macrocode} +% +% +% +% \bigskip +% In (the last column of) |{DispWithArrows}|, it's possible to put several +% labels (for the same number of equation). That's why these labels will be +% stored in a sequence |\l_@@_labels_seq|. +% \begin{macrocode} +%<*LaTeX> + \seq_clear_new:N \l_@@_labels_seq +% \end{macrocode} +% +% \begin{macrocode} + \bool_set_false:N \l_@@_tag_next_line_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 |interline| of an environment doesn't apply in the nested +% environments.} +% \begin{macrocode} + \skip_zero:N \l_@@_interline_skip +% \end{macrocode} +% +% \bigskip +% The value corresponding to the key |code-before| is put to nil before the +% treatment of the options of the environment, because, of course, we don't want +% the code executed at the beginning of all the nested +% environments~|{WithArrows}|. Idem for |code-after|. +% \begin{macrocode} + \tl_clear_new:N \l_@@_code_before_tl + \tl_clear_new:N \l_@@_code_after_tl +% \end{macrocode} +% +% \bigskip +% We process the options given to the environment |{WithArrows}| or +% |{DispWithArrows}|. +% \begin{macrocode} + \str_clear_new:N \l_@@_previous_key_str + \bool_if:NT \l_@@_in_WithArrows_bool + { \keys_set:nn { WithArrows / WithArrows } { #1 } } + \bool_if:NT \l_@@_in_DispWithArrows_bool + { \keys_set:nn { WithArrows / DispWithArrows } { #1 } } +% \end{macrocode} +% +% \medskip +% Now we link the command |\Arrow| (or the corresponding command with a name +% given by the user with the option |command-name|: that's why the following line +% must be after the loading of the options) to the command +% |\@@_Arrow_first_columns:| which will raise an error. +% \begin{macrocode} + \cs_set_eq:cN \l_@@_command_name_str \@@_Arrow_first_columns: +% \end{macrocode} +% It's only in the last column of the environment that it will be linked to the +% command |\@@_Arrow:|. +% +% \medskip +% The counter |\l_@@_nb_cols_int| is the number of columns in the +% |\halign| (excepted the column for the labels of equations in +% |{DispWithArrows}| and excepted eventuals other columns in |{WithArrows}| allowed +% by the option |more-columns|). +% \begin{macrocode} + \int_set:Nn \l_@@_nb_cols_int { \str_count:N \l_@@_format_str } +% \end{macrocode} +% +% \medskip +% Be careful! The following counter |\g_@@_col_int| will be used for two usages: +% \begin{itemize} +% \item during, the construction of the preamble of the |\halign|, it will be +% used as counter for the number of the column under construction in the +% preamble (since the preamble is constructed backwards, |\g_@@_col_int| will go +% decreasing from |\l_@@_nb_cols_int| to $1$) ; +% \item once the preamble constructed, the primitive |\halign| is executed, and, +% in each row of the |\halign|, the counter |\g_@@_col_int| will be increased +% from column to column. +% \end{itemize} +% +% \begin{macrocode} + \int_gset_eq:NN \g_@@_col_int \l_@@_nb_cols_int +% \end{macrocode} +% +% \medskip +% We convert the format in a sequence because we use it as a stack (with the top +% of the stack at the end of the sequence) in the construction of the preamble. +% \begin{macrocode} + \seq_clear_new:N \l_@@_format_seq + \seq_set_split:NnV \l_@@_format_seq { } \l_@@_format_str +% \end{macrocode} +% +% \bigskip +% If the option |footnote| or the option |footnotehyper| is used, then we +% extract the footnotes with an environment |{savenotes}| (of the package +% \pkg{footnote} or the package \pkg{footnotehyper}). +% \begin{macrocode} +%<*LaTeX> + \bool_if:NT \g_@@_footnote_bool { \begin { savenotes } } +% +% \end{macrocode} +% +% \bigskip +% We execute the code |\l_@@_code_before_tl| of the option |code-before| of the +% environment after the eventual |\begin{savenotes}| and, symetrically, we will +% execute the |\l_@@_code_after_tl| before the eventual |\end{savenotes}| (we +% have a good reason for the last point: we want to extract the footnotes of the +% arrows executed in the |code-after|). +% \begin{macrocode} + \l_@@_code_before_tl +% \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} +% +% +% \begin{macrocode} +%<*LaTeX> + \cs_set_eq:NN \notag \@@_notag: + \cs_set_eq:NN \nonumber \@@_nonumber: + \cs_set_eq:NN \tag \@@_tag + \cs_set_eq:NN \@@_old_label \label + \cs_set_eq:NN \label \@@_label:n + \cs_set_eq:NN \tagnextline \@@_tagnextline: +% + } +% \end{macrocode} +% This is the end of |\@@_pre_halign:n|. +% +% \bigskip +% \subsubsection{The construction of the preamble of the \textbackslash halign} +% +% The control sequence |\@@_construct_halign:| will ``start'' the |\halign| and +% the preamble. In fact, it constructs all the preamble excepted the end of +% the last column (more precisely: except the part concerning the construction +% of the left node and the right node). +% +% The same function |\@@_construct_halign:| will be used both for the +% environment |{WithArrows}| and the environment |{DispWithArrows}|. +% +% Several important points must be noted concerning that construction of the +% preamble. +% \begin{itemize} +% \item The construction of the preamble is done by reading backwards the +% format |\l_@@_format_str| and adding the corresponding tokens in the input +% stream of TeX. That means that the part of the preamble concerning the last +% cell will be constructed first. +% \item The function |\@@_construct_halign:| is recursive in order to treat +% succesively all the letters of the preamble. +% \item Each part of the preamble is created with a |\use:x| function. This +% expansion of the preamble gives the ability of controlling which parts of the +% code will be expanded during the construction of the preamble (other parts +% will be expanded and executed only during the execution of the |\halign|). +% \item The counter |\g_@@_col_int| is used during the loop of the construction +% of the preamble but, it will also appears in the preamble (we could have +% chosen two differents counters but this way saves a counter). +% \end{itemize} +% +% \begin{macrocode} +\cs_new_protected:Npn \@@_construct_halign: + { + \seq_pop_right:NNTF \l_@@_format_seq \l_@@_type_col_str + { +% \end{macrocode} +% Here is the |\use:x| which is fundamental: it will really construct the part +% of the preamble corresponding to a column by expanding only some parts of the +% following code. +% \begin{macrocode} + \use:x + { +% \end{macrocode} +% Before the recursive call of |\@@_construct_halign:|, we decrease the integer +% |\g_@@_col_bool|. But, during the construction of the column which is +% constructed first (that is to say which is the last column of the |\halign|), +% it is \emph{not} lowered because |\int_decr:N|, which is protected, won't be +% expanded by the |\use:x|. +% +% We begin the construction of a generic column. +% \begin{macrocode} + \int_gdecr:N \g_@@_col_int + \@@_construct_halign: + \int_compare:nNnT \g_@@_col_int = \l_@@_nb_cols_int + { +% \end{macrocode} +% We redefine the command |\Arrow| (or the name given to the corresponding +% command by the option |command-name|) in each cell of the last column. +% The braces around |\l_@@_command_name_str| are mandatory because +% |\l_@@_command_name_str| will be expanded by the |\use:x| and the command +% |\cs_set_eq:cN| must still be efficient during the execution of the |\halign|. +% \begin{macrocode} + \cs_set_eq:cN { \l_@@_command_name_str } \@@_Arrow +%<*LaTeX> + \bool_if:NT \l_@@_in_DispWithArrows_bool + { +% \end{macrocode} +% The command |\@@_test_if_to_tag:| (which is protected and, thus, will not be +% expanded during the construction of the preamble) will test, at each row, +% whether the current row must be tagged (and the tag will be put in the very +% last column). +% \begin{macrocode} + \@@_test_if_to_tag: +% \end{macrocode} +% The command |\@@_set_qedhere:| will do a redefinition of |\qedhere| in each +% cell of the last column. +% \begin{macrocode} + \bool_if:NT \c_@@_amsthm_loaded_bool \@@_set_qedhere: + } +% + } + \str_if_eq:VnT \l_@@_type_col_str { c } \hfil + \str_if_eq:VnT \l_@@_type_col_str { r } \hfill + \int_gincr:N \g_@@_col_int + \int_gset:Nn \g_@@_static_col_int { \int_use:N \g_@@_col_int } + \c_math_toggle_token + { + { } + \bool_if:NT \l_@@_displaystyle_bool \displaystyle + #### + } + \c_math_toggle_token + \int_compare:nNnTF \g_@@_col_int = \l_@@_nb_cols_int + { \@@_construct_nodes: } + { +% \end{macrocode} +% The following glue (|\hfil|) will be added only if we are not in the last cell +% because, in the last cell, a glue (=skip) is added between the nodes (in +% |\@@_construct_nodes:|). +% \begin{macrocode} + \str_if_eq:VnT \l_@@_type_col_str { l } \hfil + \str_if_eq:VnT \l_@@_type_col_str { c } \hfil + \bool_if:NT \l_@@_in_DispWithArrows_bool { \tabskip = \c_zero_skip } + & + } + } + } +% \end{macrocode} +% Now the tokens that will be inserted after the analyze of all the tokens of +% the format: here is the token |\halign|. +% \begin{macrocode} + { + \bool_if:NTF \l_@@_in_WithArrows_bool + { + \ialign + \bgroup + } + { + \halign to \l_@@_linewidth_dim + \bgroup + \bool_if:NT \l_@@_fleqn_bool + { \skip_horizontal:N \l_@@_mathindent_dim } + } + \int_gincr:N \g_@@_line_int + \int_gzero:N \g_@@_col_int + \tl_if_eq:NNF \l_@@_left_brace_tl \c_novalue_tl + { + \skip_horizontal:n + { \box_wd:N \l_@@_left_brace_box + \l_@@_delim_wd_dim } + } + \strut + } + } +% \end{macrocode} +% +% +% \bigskip +% The command |\@@_construct_nodes:| is only for the lisibility of the code +% because, in fact, it is used only once. It constructs the ``left node'' and +% the ``right node'' at the end of each row of the arrow. +% \begin{macrocode} +\cs_new_protected:Npn \@@_construct_nodes: + { +% \end{macrocode} +% We create the ``left node'' of the line (when using macros in Tikz node names, +% the macros have to be fully expandable: here, |\int_use:N| is fully +% expandable). +% \begin{macrocode} + \tikz [ remember~picture , overlay ] + \node + [ + node~contents = { } , + @@_node_style , + name = wa - \l_@@_prefix_str - \int_use:N \g_@@_line_int - l , + alias = + { + \str_if_empty:NF \l_@@_name_str + { \l_@@_name_str - \int_use:N \g_@@_line_int - l } + } + ] + ; + \hfil +% \end{macrocode} +% +% \bigskip +% Now, after the |\hfil|, we create the ``right node'' and, if the option +% |show-node-names| is raised, the name of the node is written in the document +% (useful for debugging). +% \begin{macrocode} + \tikz [ remember~picture , overlay ] + \node + [ + node~contents = { } , + @@_node_style , + name = wa - \l_@@_prefix_str - \int_use:N \g_@@_line_int - r , + alias = + { + \str_if_empty:NF \l_@@_name_str + { \l_@@_name_str - \int_use:N \g_@@_line_int - r } + } + ] + ; + \bool_if:NT \l_@@_show_node_names_bool + { + \hbox_overlap_right:n + { \small wa - \l_@@_prefix_str - \int_use:N \g_@@_line_int - r } + } + } +% \end{macrocode} +% +% +% +% \bigskip +% \subsubsection{The environment \{WithArrows\}} +% +% +% \begin{macrocode} +%<*LaTeX> +\NewDocumentEnvironment { WithArrows } { ! O { } } +% +%<*plain-TeX> +\cs_new_protected:Npn \WithArrows + { + \group_begin: + \peek_meaning:NTF [ + { \WithArrows_i } + { \WithArrows_i [ ] } + } +\cs_new_protected:Npn \WithArrows_i [ #1 ] +% + { + \bool_set_true:N \l_@@_in_WithArrows_bool + \bool_set_false:N \l_@@_in_DispWithArrows_bool +%<*plain-TeX> + \str_clear_new:N \l_@@_type_env_str + \str_set:Nn \l_@@_type_env_str { WithArrows } +% + \@@_pre_halign:n { #1 } + \if_mode_math: \else: + \@@_error:n { WithArrows~outside~math~mode } + \fi: +% \end{macrocode} +% +% \bigskip +% The environment begins with a |\vtop|, a |\vcenter| or a +% |\vbox|\footnote{Notice that the use of |\vtop| seems color-safe here...} +% depending of the value of |\l_@@_pos_env_int| (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_env_int { 0 \vtop 1 \vcenter 2 \vbox } + \bgroup +% \end{macrocode} +% +% \bigskip +% We begin the |\halign| and the preamble. During the construction of the +% preamble, |\l_tmpa_int| will be incremented during each column constructed. +% \begin{macrocode} + \@@_construct_halign: +% \end{macrocode} +% +% +% \medskip +% In fact, the construction of the preamble is not finished. We add a little more. +% +% \medskip +% An environmemnt |{WithArrows}| should have a number of columns equal to the +% length of its format (by default, 2 since the default format is |rl|). +% Nevertheless, if the user wants to use more columns (without arrows) +% it's possible with the option |more-columns|. +% \begin{macrocode} + && + \@@_error:n { Too~much~columns~in~WithArrows } + \c_math_toggle_token + \bool_if:NT \l_@@_displaystyle_bool \displaystyle + { ## } + \c_math_toggle_token + \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} +%<*plain-TeX> +\cs_new_protected:Npn \endWithArrows +% + { + \\ + \egroup + \egroup + \@@_post_halign: +% \end{macrocode} +% +% \bigskip +% If the option |footnote| or the option |footnotehyper| is used, then we +% extract the footnotes with an environment |{footnote}| (of the package +% \pkg{footnote} or the package \pkg{footnotehyper}). +% \begin{macrocode} +%<*LaTeX> + \bool_if:NT \g_@@_footnote_bool { \end { savenotes } } +% +%<*plain-TeX> + \group_end: +% + } +% \end{macrocode} +% This is the end of the environment |{WithArrows}|. +% +% +% \bigskip +% \subsubsection{After the construction of the \textbackslash halign} +% +% The command |\@@_post_halign:| is a code common to the second part of the +% environment |{WithArrows}| and the environment |{DispWithArrows}|. +% \begin{macrocode} +\cs_new_protected:Npn \@@_post_halign: +% \end{macrocode} +% +% \bigskip +% The command |\WithArrowsRightX| is not used by \pkg{witharrows}. It's only a +% convenience given to the user. +% \begin{macrocode} + { + \cs_set:Npn \WithArrowsRightX { \g_@@_right_x_dim } +% \end{macrocode} +% +% \bigskip +% It there is really arrows in the environment, we draw the arrows. +% \begin{macrocode} + \int_compare:nNnT \g_@@_arrow_int > 0 \@@_scan_arrows: +% \end{macrocode} +% +% \bigskip +% We will execute the code specified in the option |code-after|, after some +% settings. +% \begin{macrocode} + \group_begin: + \tikzset { every~picture / .style = @@_standard } +% \end{macrocode} +% The command |\WithArrowsNbLines| is not used by \pkg{witharrows}. It's only a +% convenience given to the user. +% \begin{macrocode} + \cs_set:Npn \WithArrowsNbLines { \int_use:N \g_@@_line_int } +% \end{macrocode} +% The command |\MultiArrow| is available in |code-after|, and we have a special +% version of |\Arrow|, called ``|\Arrow| in |code-after|'' in the +% documentation.\footnote{As for now, |\MultiArrow| has no option, and that's +% why its internal name is a name of \pkg{expl3} with the signature |:nn| +% whereas |\Arrow| in |code-after| provides options and has the name of a +% function defined with |\NewDocumentCommand|.} +% \begin{macrocode} + \cs_set_eq:NN \MultiArrow \@@_MultiArrow:nn + \cs_set_eq:cN \l_@@_command_name_str \@@_Arrow_code_after + \bool_set_true:N \l_@@_in_code_after_bool + \l_@@_code_after_tl + \group_end: +% \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 user function |\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 counters |\g_@@_arrow_int|, +% |\g_@@_line_int| and |\g_@@_col_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_@@_arrow_int_seq \l_tmpa_tl + \int_gset:Nn \g_@@_arrow_int \l_tmpa_tl + \seq_gpop_right:NN \g_@@_line_int_seq \l_tmpa_tl + \int_gset:Nn \g_@@_line_int \l_tmpa_tl + \seq_gpop_right:NN \g_@@_col_int_seq \l_tmpa_tl + \int_gset:Nn \g_@@_col_int \l_tmpa_tl + } +% \end{macrocode} +% That's the end of the command |\@@_post_halign:|. +% +% \bigskip +% \subsubsection{The command of end of row} +% +% 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 an |\halign| +% structure. +% +% First, we remove an eventual token |*| (just after the |\\|: there should not +% be space between the two) 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_new_protected:Npn \@@_cr: + { + \scan_stop: +% \end{macrocode} +% We try to detect some |\omit| (as of now, an |\omit| in the last column is +% not detected). +% \begin{macrocode} + \int_compare:nNnF \g_@@_col_int = \g_@@_static_col_int + { \@@_error:n { omit~probably~used } } + \prg_replicate:nn { \l_@@_nb_cols_int - \g_@@_static_col_int } { & { } } + \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_new_protected:Npn \@@_cr_i: + { \peek_meaning:NTF [ \@@_cr_ii: { \@@_cr_ii: [ \c_zero_dim ] } } +% \end{macrocode} +% +% \bigskip +% Now, we test if the next token is the token |\end|. Indeed, we want to test if +% the following tokens are |\end{WithArrows}| (or |\end{DispWithArrows}|, etc). +% In this case, we raise an error because the user must not put "\\" at the end +% of its alignment. +% \begin{macrocode} +%<*LaTeX> +\cs_new_protected:Npn \@@_cr_ii: [ #1 ] + { + \peek_meaning_ignore_spaces:NTF \end + { + \@@_cr_iii:n { #1 } +% \end{macrocode} +% The analyse of the argument of the token |\end| must be after the +% |\group_align_safe_end:| which is the beginning of |\@@_cr_iii:n|. +% \begin{macrocode} + \@@_analyze_end:Nn + } + { \@@_cr_iii:n { #1 } } + } +% \end{macrocode} +% +% \begin{macrocode} +\cs_new_protected:Npn \@@_cr_iii:n #1 +% +%<*plain-TeX> +\cs_new_protected:Npn \@@_cr_ii: [ #1 ] +% + { + \group_align_safe_end: +% \end{macrocode} +% For the environment |{DispWithArrows}|, the behaviour of |\\| is different +% because we add the last column which is the column for the tag (number of the +% equation). Even if there is no tag, this column is used for the +% |v|-nodes.\footnote{The |v|-nodes are used to compute the abscissa of the +% right margin, used by the option |wrap-lines|.} +% \begin{macrocode} + \bool_if:NT \l_@@_in_DispWithArrows_bool +% \end{macrocode} +% At this stage, we know that we have a tag to put if (and only if) the value of +% |\l_@@_tags_clist| is the comma list |all| (only one element). Maybe, +% previously, the value of |\l_@@_tags_clist| was, for example, |1,last| (which +% means that only the first line and the last line must be tagged). However, in +% this case, the comparison with the number of line has be done before and, now, +% if we are in a line to tag, the value of |\l_@@_tags_clist| is |all|. +% \begin{macrocode} + { +%<*LaTeX> + \clist_if_in:NnTF \l_@@_tags_clist { all } + { +% \end{macrocode} +% Here, we can't use |\refstepcounter{equation}| because if the user has issued +% a |\tag| command, we have to use |\l_@@_tag_tl| and not |\theequation|. That's +% why we have to do the job done by |\refstepcounter| manually. +% +% First, the incrementation of the counter (potentially). +% \begin{macrocode} + \tl_if_empty:NT \l_@@_tag_tl { \int_gincr:N \c@equation } +% \end{macrocode} +% +% We store in |\g_tmpa_tl| the tag we will have to compose at the end of the +% line. We use a global variable because we will use it in the \emph{next} cell +% (after the |&|). +% \begin{macrocode} + \cs_gset:Npx \g_tmpa_tl + { \tl_if_empty:NTF \l_@@_tag_tl \theequation \l_@@_tag_tl } +% \end{macrocode} +% It's possible to put several labels for the same line (it's not possible in +% the environments of \pkg{amsmath}). That's why the differents labels of a same +% line are stored in a sequence |\l_@@_labels_seq|. +% \begin{macrocode} + \seq_if_empty:NF \l_@@_labels_seq + { +% \end{macrocode} +% Now, we do the job done by |\refstepcounter| and by the redefinitions of +% |\refstepcounter| done by some packages (the incrementation of the counter has +% been done yet). +% +% First an action which is in the definition of |\refstepcounter|. The command +% |\p@equation| is redefined by some extensions like \pkg{fncylab}. +% \begin{macrocode} + \cs_set:Npx \@currentlabel { \p@equation \g_tmpa_tl } +% \end{macrocode} +% Then, an action done by \pkg{hyperref} in its redefinition of +% |\refstepcounter|. +% \begin{macrocode} + \bool_if:NT \c_@@_hyperref_loaded_bool + { + \str_set:Nn \This@name { equation } + \hyper@refstepcounter { equation } + } +% \end{macrocode} +% Then, an action done by \pkg{cleveref} in its redefinition of +% |\refstepcounter|. The package \pkg{cleveref} creates in the |aux| file a +% command |\cref@currentlabel| similar to |\@currentlabel| but with more +% informations. +% \begin{macrocode} + \bool_if:NT \c_@@_cleveref_loaded_bool + { + \cref@constructprefix { equation } \cref@result + \protected@edef \cref@currentlabel + { + [ + \cs_if_exist:NTF \cref@equation@alias + \cref@equation@alias + { equation } + ] + [ \arabic { equation } ] [ \cref@result ] + \p@equation \g_tmpa_tl + } + } +% \end{macrocode} +% Now, we can issue the command |\label| (some packages may have redefined +% |\label|, for example \pkg{typedref}) for each item in the sequence of the +% labels (it's possible with \pkg{witharrows} to put several labels to the same +% line and that's why the labels are in the sequence |\l_@@_labels_seq|). +% \begin{macrocode} + \seq_map_function:NN \l_@@_labels_seq \@@_old_label + } +% \end{macrocode} +% We save the booleans |\l_@@_tag_star_bool| and |\l_@@_qedhere_bool| because +% they will be used in the \emph{next} cell (after the |&|). We recall that the +% cells of a |\halign| are TeX groups. +% \begin{macrocode} + \@@_save:N \l_@@_tag_star_bool + \@@_save:N \l_@@_qedhere_bool + \bool_if:NT \l_@@_tag_next_line_bool + { + \openup -\jot + \bool_set_false:N \l_@@_tag_next_line_bool + \notag \\ & + } + & + \@@_restore:N \l_@@_tag_star_bool + \@@_restore:N \l_@@_qedhere_bool + \bool_if:NT \l_@@_qedhere_bool + { \hbox_overlap_left:n \@@_qedhere_i: } + \cs_set_eq:NN \theequation \g_tmpa_tl + \bool_if:NT \l_@@_tag_star_bool + { \cs_set_eq:NN \tagform@ \prg_do_nothing: } +% \end{macrocode} +% We use |\@eqnnum| (we recall that there are two definitions of |\@eqnnum|, a +% standard definition and another, loaded if the class option |leqno| is used). +% However, of course, the position of the |v|-node is not the same whether the +% option |leqno| is used or not. That's here that we use the flag +% |\c_@@_leqno_bool|. +% \begin{macrocode} + \hbox_overlap_left:n + { + \bool_if:NF \c_@@_leqno_bool + { + \tikz [ @@_standard ] + \coordinate ( \int_use:N \g_@@_line_int - v ) ; + } + \quad + \@eqnnum + } + \bool_if:NT \c_@@_leqno_bool + { + \tikz [ @@_standard ] + \coordinate ( \int_use:N \g_@@_line_int - v ) ; + } + } + { + \@@_save:N \l_@@_qedhere_bool +% + & +%<*LaTeX> + \@@_restore:N \l_@@_qedhere_bool + \bool_if:NT \l_@@_qedhere_bool + { \hbox_overlap_left:n \@@_qedhere_i: } +% + \tikz [ @@_standard ] + \coordinate ( \int_use:N \g_@@_line_int - v ) ; +%<*LaTeX> + } +% + } + \dim_compare:nNnT { #1 } < \c_zero_dim + { \@@_error:n { option~of~cr~negative } } + + \cr + \noalign + { + \dim_set:Nn \l_tmpa_dim { \dim_max:nn { #1 } \c_zero_dim } + \skip_vertical:n { \l_tmpa_dim + \l_@@_interline_skip } + \scan_stop: + } + } +% \end{macrocode} +% According to the documentation of \pkg{expl3}, the previous addition in +% ``|#1 + \l_@@_interline_skip|'' is really an addition of skips (=glues). +% +% +% The following command will be used when, after a |\\| (and its optional +% arguments) there is a |\end|. You want to known if this is the end of the +% environment |{WithArrows}| (or |{DispWithArrows}|, etc.) because, in this +% case, we will explain that the environment must not be ended by |\\|. If it is +% not the case, that means it's a classical situation of LaTeX environments not +% correctly imbricated and there will be a LaTeX error. +% \begin{macrocode} +%<*LaTeX> +\cs_new_protected:Npn \@@_analyze_end:Nn #1 #2 + { + \exp_args:NV \str_if_eq:nnT \l_@@_type_env_str { #2 } + { \@@_warning:n { newline~at~the~end~of~env } } +% \end{macrocode} +% We reput in the stream the |\end{...}| we have extracted. +% \begin{macrocode} + \end { #2 } + } +% +% \end{macrocode} +% +% \bigskip +% \subsubsection{The environment \{DispWithArrows\}} +% +% For the environment |{DispWithArrows}|, the general form of the construction +% is of the type: +% +% |\[\vtop{\halign to \displaywidth {...}}\]| +% +% The purpose of the |\vtop| is to have an environment unbreakable. +% +% However, if we are juste after an item of a LaTeX list or at the beginning of +% a |{minipage}|, the construction is slightly different: +% +% |\[\vtop{\halign to \linewidth {...}}\]| +% +% +% \bigskip +% The boolean |\l_@@_in_label_or_minipage_bool| will be raised if we are just after a |\item| +% of a list of LaTeX or at the beginning of a |{minipage}|. +% \begin{macrocode} +%<*LaTeX> +\bool_new:N \l_@@_in_label_or_minipage_bool +% +% \end{macrocode} +% +% +% \begin{macrocode} +%<*LaTeX> +\NewDocumentEnvironment { DispWithArrows } { ! d < > ! O { } } +% +%<*plain-TeX> +\cs_new_protected:Npn \DispWithArrows + { + \group_begin: + \peek_meaning:NTF < + { \DispWithArrows_i } + { \DispWithArrows_i < \c_novalue_tl > } + } +\cs_new_protected:Npn \DispWithArrows_i < #1 > + { + \peek_meaning:NTF [ + { \DispWithArrows_ii < #1 > } + { \DispWithArrows_ii < #1 > [ ] } + } +\cs_new_protected:Npn \DispWithArrows_ii < #1 > [ #2 ] +% + { + \bool_set_true:N \l_@@_in_DispWithArrows_bool +%<*plain-TeX> + \str_clear_new:N \l_@@_type_env_str + \str_set:Nn \l_@@_type_env_str { DispWithArrows } +% +% \end{macrocode} +% If \pkg{mathtools} has been loaded with the option |showonlyrefs|, we disable +% the code of \pkg{mathtools} for the option |showonlyrefs| with the command +% |\MT_showonlyrefs_false:| (it will be reactivated at the end of the +% environment). +% \begin{macrocode} +%<*LaTeX> + \bool_if:nT \c_@@_mathtools_loaded_bool + { + \MH_if_boolean:nT { show_only_refs } + { + \MT_showonlyrefs_false: +% \end{macrocode} +% However, we have to re-raise the flag |{show_only_refs}| of \pkg{mhsetup} +% because it has been switched off by |\MT_showonlyrefs_false:| and we will use +% it in the code of the new version of |\label|. +% \begin{macrocode} + \MH_set_boolean_T:n { show_only_refs } + } + } +% \end{macrocode} +% +% An action done by \pkg{typedref} in its redefinition of |\refstepcounter|. The +% command |\sr@name| is a prefix added to the name of the label by the +% redefinition of |\label| done by \pkg{typedref}. +% \begin{macrocode} + \bool_if:NT \c_@@_typedref_loaded_bool { \str_set:Nn \sr@name { equation } } +% \end{macrocode} +% +% The command |\intertext@| is a command of \pkg{amsmath} which loads the +% definition of |\intertext|. +% \begin{macrocode} + \bool_if:NT \c_@@_amsmath_loaded_bool \intertext@ +% + \exp_args:No \tl_if_novalue:nF { #1 } { \tl_set:Nn \l_@@_left_brace_tl { #1 } } + \@@_pre_halign:n { #2 } +% \end{macrocode} +% +% If |subequations| is used, we encapsulate the environment in an +% environment |{subequations}| of \pkg{amsmath}. +% \begin{macrocode} +%<*LaTeX> + \bool_if:NT \l_@@_subequations_bool { \begin { subequations } } +% +% \end{macrocode} +% Since the version 1.16 of \pkg{witharrows}, no space is added between an +% |\item| of a LaTeX list and an environment |{DispWithArrows}| except with the +% option |standard-behaviour-with-items| stored in the boolean +% |\l_@@_sbwi_bool|. We have to know if we are just after an |\item| and this +% information will be stored in |\l_@@_in_label_or_minipage_bool|. +% \begin{macrocode} +%<*LaTeX> + \bool_if:NF \l_@@_sbwi_bool + { + \if@inlabel + \bool_set_true:N \l_@@_in_label_or_minipage_bool + \fi + \if@minipage + \bool_set_true:N \l_@@_in_label_or_minipage_bool + \fi + } +% +% \end{macrocode} +% +% +% \begin{macrocode} + \tl_if_eq:NNF \l_@@_left_brace_tl \c_novalue_tl + { +% \end{macrocode} +% We compute the value of the width of the left delimiter. +% \begin{macrocode} + \hbox_set:Nn \l_tmpa_box + { +% \end{macrocode} +% Even if the default value of |\nulldelimiterspace| is 1.2~pt, we take it into account. +% \begin{macrocode} + \group_begin: + \dim_set_eq:NN \nulldelimiterspace \c_zero_dim + \c_math_toggle_token + \left \l_@@_replace_left_brace_by_tl \vcenter to 1 cm { } \right. + \c_math_toggle_token + \group_end: + } + \dim_zero_new:N \l_@@_delim_wd_dim + \dim_set:Nn \l_@@_delim_wd_dim { \box_wd:N \l_tmpa_box } + \box_clear_new:N \l_@@_left_brace_box + \hbox_set:Nn \l_@@_left_brace_box + { + \group_begin: + \cs_set_eq:NN \label \@@_old_label + \c_math_toggle_token + \bool_if:NT \l_@@_displaystyle_bool \displaystyle + \l_@@_left_brace_tl + { } + \c_math_toggle_token + \group_end: + } + } +% \end{macrocode} +% +% \bigskip +% The token list |\l_@@_tag_tl| will contain the argument of the command |\tag|. +% \begin{macrocode} +%<*LaTeX> + \tl_clear_new:N \l_@@_tag_tl +% \end{macrocode} +% +% \bigskip +% \begin{macrocode} + \bool_set_false:N \l_@@_qedhere_bool +% \end{macrocode} +% +% \bigskip +% The boolean |\l_@@_tag_star_bool| will be raised if the user uses the command +% |\tag| with a star. +% \begin{macrocode} + \bool_set_false:N \l_@@_tag_star_bool +% +% \end{macrocode} +% +% \begin{macrocode} + \if_mode_math: + \@@_fatal:n { DispWithArrows~in~math~mode } + \fi: +% \end{macrocode} +% +% \bigskip +% The construction is not exactly the same whether we are just after an |\item| +% of a LaTeX list or not. We know if we are after an |\item| thanks to the +% boolean |\l_@@_in_label_or_minipage_bool|. +% \begin{macrocode} +%<*plain-TeX> + \dim_zero_new:N \linewidth + \dim_set_eq:NN \linewidth \displaywidth +% +%<*LaTeX> + \bool_if:NTF \l_@@_in_label_or_minipage_bool + { \c_math_toggle_token } + { +% +% \end{macrocode} +% We don't use |\[| of LaTeX because some extensions, like \pkg{autonum}, do a +% redefinition of |\[|. However, we put the following lines which are in the +% definition of |\[| even though they are in case of misuse. +% \begin{macrocode} + \if_mode_vertical: + \nointerlineskip + \hbox_to_wd:nn { .6 \linewidth } { } + \fi: + \c_math_toggle_token \c_math_toggle_token +%<*LaTeX> + } +% +% \end{macrocode} +% +% \begin{macrocode} + \dim_zero_new:N \l_@@_linewidth_dim +%<*LaTeX> + \bool_if:NTF \l_@@_in_label_or_minipage_bool + { \dim_set_eq:NN \l_@@_linewidth_dim \linewidth } + { \dim_set_eq:NN \l_@@_linewidth_dim \displaywidth } +% +%<*plain-TeX> + \dim_set_eq:NN \l_@@_linewidth_dim \displaywidth +% +% \end{macrocode} +% +% +% \begin{macrocode} + \box_clear_new:N \l_@@_halign_box + \setbox \l_@@_halign_box \vtop \bgroup + \tabskip = + \bool_if:NTF \l_@@_fleqn_bool + \c_zero_skip + { 0 pt plus 1000 pt minus 1000 pt } +% \end{macrocode} +% +% +% \begin{macrocode} + \@@_construct_halign: + \tabskip = 0 pt plus 1000 pt minus 1000 pt + & +% \end{macrocode} +% +% If the user tries to use more columns than the length of the format, we have to +% raise an error. However, the error won't be in the next column which is the +% columns for the labels of the equations. The error will be after... and it +% must be after. That means that we must not have an error in the next column +% simply because we are not in math mode. That's why this column, even if it is +% for the labels, is in math mode. +% \begin{macrocode} + $ ## $ + \tabskip = \c_zero_skip + && + \@@_fatal:n { Too~much~columns~in~DispWithArrows } + \bool_if:nT \c_false_bool { ## } + \cr + } +% \end{macrocode} +% +% \bigskip +% We begin the second part of the environment |{DispWithArrows}|. +% \begin{macrocode} +%<*plain-TeX> +\cs_new_protected:Npn \endDispWithArrows +% + { +%<*LaTeX> + \clist_if_in:NnT \l_@@_tags_clist { last } + { \clist_set:Nn \l_@@_tags_clist { all } } +% + \\ +% \end{macrocode} +% The following |\egroup| is for the |\halign|. +% \begin{macrocode} + \egroup + \unskip \unpenalty \unskip \unpenalty + \box_set_to_last:N \l_tmpa_box + \nointerlineskip + \box_use:N \l_tmpa_box + \dim_gzero_new:N \g_@@_alignment_dim + \dim_gset:Nn \g_@@_alignment_dim { \box_wd:N \l_tmpa_box } + \box_clear_new:N \l_@@_new_box + \hbox_set:Nn \l_@@_new_box { \hbox_unpack_clear:N \l_tmpa_box } + \dim_compare:nNnT + { \box_wd:N \l_@@_new_box } < \g_@@_alignment_dim + { \dim_gset:Nn \g_@@_alignment_dim { \box_wd:N \l_@@_new_box } } +% \end{macrocode} +% The |\egroup| is for the box |\l_@@_halign_box|. +% \begin{macrocode} + \egroup +% \end{macrocode} +% +% \begin{macrocode} + \tl_if_eq:NNTF \l_@@_left_brace_tl \c_novalue_tl + { \box_use_drop:N \l_@@_halign_box } + { + \hbox_to_wd:nn \l_@@_linewidth_dim + { + \bool_if:NTF \l_@@_fleqn_bool + { \skip_horizontal:n \l_@@_mathindent_dim } + \hfil + \hbox_to_wd:nn \g_@@_alignment_dim + { + \box_use_drop:N \l_@@_left_brace_box + \dim_set:Nn \l_tmpa_dim + { + \box_ht:N \l_@@_halign_box + + \box_dp:N \l_@@_halign_box + } + \group_begin: + \dim_set_eq:NN \nulldelimiterspace \c_zero_dim + \c_math_toggle_token + \left \l_@@_replace_left_brace_by_tl + \vcenter to \l_tmpa_dim { \vfil } + \right. + \c_math_toggle_token + \group_end: + \hfil + } + \hfil + } + \skip_horizontal:n { - \l_@@_linewidth_dim } + \vcenter { \box_use_drop:N \l_@@_halign_box } + } +% \end{macrocode} +% +% We compute the dimension |\g_@@_right_x_dim|. As a first approximation, +% |\g_@@_right_x_dim| is the $x$-value of the right side of the current +% composition box. In fact, we must take into account the potential labels of +% the equations. That's why we compute |\g_@@_right_x_dim| with the |v|-nodes of +% each row specifically built in this goal. |\g_@@_right_x_dim| is the minimal +% value of the $x$-value of these nodes. +% \begin{macrocode} + \dim_gzero_new:N \g_@@_right_x_dim + \dim_gset_eq:NN \g_@@_right_x_dim \c_max_dim +%<*LaTeX> + \begin { tikzpicture } [ @@_standard ] +% +%<*plain-TeX> + \tikzpicture [ @@_standard ] +% + \int_step_variable:nNn \g_@@_line_int \l_tmpa_int + { + \cs_if_free:cTF + { pgf@sh@ns@wa - \l_@@_prefix_str - \l_tmpa_int - v } + { \@@_fatal:n { Inexistent~v-node } } + { + \tikz@parse@node\pgfutil@firstofone ( \l_tmpa_int - v ) + \dim_set:Nn \l_tmpa_dim \pgf@x + \dim_compare:nNnT \l_tmpa_dim < \g_@@_right_x_dim + { \dim_gset:Nn \g_@@_right_x_dim \l_tmpa_dim } + } + } +%<*LaTeX> + \end { tikzpicture } +% +%<*plain-TeX> + \endtikzpicture +% +% \end{macrocode} +% +% +% \bigskip +% The code in |\@@_post_halign:| is common to |{WithArrows}| and +% |{DispWithArrows}|. +% \begin{macrocode} + \@@_post_halign: +% \end{macrocode} +% If \pkg{mathtools} has been loaded with the option |showonlyrefs|, we +% reactivate the code of \pkg{mathtools} for the option |showonlyrefs| with the +% command |\MT_showonlyrefs_true:| (it has been deactivated in the beginning of +% the environment). +% \begin{macrocode} +%<*LaTeX> + \bool_if:nT \c_@@_mathtools_loaded_bool + { \MH_if_boolean:nT { show_only_refs } \MT_showonlyrefs_true: } + \bool_if:NTF \l_@@_in_label_or_minipage_bool + { + \c_math_toggle_token + \skip_vertical:N \belowdisplayskip + } + { \c_math_toggle_token \c_math_toggle_token } +% +%<*plain-TeX> + \c_math_toggle_token \c_math_toggle_token +% +% \end{macrocode} +% +% \begin{macrocode} +%<*LaTeX> + \bool_if:NT \l_@@_subequations_bool { \end { subequations } } +% \end{macrocode} +% +% \bigskip +% If the option |footnote| or the option |footnotehyper| is used, then we +% extract the footnotes with an environment |{savenotes}| (of the package +% \pkg{footnote} or the package \pkg{footnotehyper}). +% \begin{macrocode} + \bool_if:NT \g_@@_footnote_bool { \end { savenotes } } +% +%<*plain-TeX> + \group_end: +% +%<*LaTeX> + \ignorespacesafterend +% + } +% \end{macrocode} +% +% \bigskip +% With the environment |{DispWithArrows*}|, the equations are not numbered. We +% don't put |\begin{DispWithArrows}| and |\end{DispWithArrows}| because there is +% a |\@currenvir| in some error messages. +% \begin{macrocode} +%<*LaTeX> +\NewDocumentEnvironment { DispWithArrows* } { } + { + \WithArrowsOptions { notag } + \DispWithArrows + } + \endDispWithArrows +% +% \end{macrocode} +% +% +% \bigskip +% \subsection{The commands \textbackslash tag, \textbackslash notag, +% \textbackslash label, \textbackslash tagnextline and \textbackslash qedhere for +% \{DispWithArrows\}} +% +% Some commands are allowed only in the last column of the environment +% |{DispWithArrows}|. We write a command |\@@_if_in_last_col_of_disp:Nn| to +% execute this command only if we are in the last column. If we are in +% another column, an error is raised. The first argument of +% |\@@_if_in_last_col_of_disp:Nn| is the name of the command used in the error +% message and the second is the code to execute. +% \begin{macrocode} +\cs_new_protected:Npn \@@_if_in_last_col_of_disp:Nn #1 #2 + { + \bool_if:NTF \l_@@_in_WithArrows_bool + { \@@_error:nn { Not~allowed~in~WithArrows } { #1 } } + { + \int_compare:nNnTF \g_@@_col_int < \l_@@_nb_cols_int + { \@@_error:nn { Not~allowed~in~DispWithArrows } { #1 } } + { #2 } + } + } +% \end{macrocode} +% +% \bigskip +% The command |\@@_notag:| will be linked to the command |\notag| and also to +% in the environments |{WithArrows}| and |{DispWithArrows}|. +% \begin{macrocode} +%<*LaTeX> +\cs_new_protected:Npn \@@_notag: + { \@@_if_in_last_col_of_disp:Nn \notag { \clist_clear:N \l_@@_tags_clist } } +% \end{macrocode} +% +% \bigskip +% The command |\@@_nonumber:| will be linked to the command |\nonumber| and also to +% in the environments |{WithArrows}| and |{DispWithArrows}|. +% \begin{macrocode} +\cs_new_protected:Npn \@@_nonumber: + { \@@_if_in_last_col_of_disp:Nn \nonumber { \clist_clear:N \l_@@_tags_clist } } +% \end{macrocode} +% +% \bigskip +% The command |\@@_tag| will be linked to |\tag| in |{WithArrows}| and +% |{DispWithArrows}|. We do the definition with |\NewDocumentCommand| because this +% command has a starred version. +% \begin{macrocode} +\NewDocumentCommand \@@_tag { s m } + { + \@@_if_in_last_col_of_disp:Nn \tag + { + \tl_if_empty:NF \l_@@_tag_tl + { \@@_error:nn { Multiple~tags } { #2 } } + \clist_set:Nn \l_@@_tags_clist { all } + \bool_if:nT \c_@@_mathtools_loaded_bool + { + \MH_if_boolean:nT { show_only_refs } + { + \MH_if_boolean:nF { show_manual_tags } + { \clist_clear:N \l_@@_tags_clist } + } + } + \tl_set:Nn \l_@@_tag_tl { #2 } + \bool_set:Nn \l_@@_tag_star_bool { #1 } +% \end{macrocode} +% The starred version |\tag*| can't be used if \pkg{amsmath} has not been loaded +% because this version does the job by deactivating the command |\tagform@| +% inserted by \pkg{amsmath} in the (two versions of the) command +% |\@eqnnum|.\footnote{There are two versions of |@eqnnum|, a standard version +% and a version for the option |leqno|.} +% \begin{macrocode} + \bool_if:nT { #1 && ! \bool_if_p:N \c_@@_amsmath_loaded_bool } + { \@@_error:n { tag*~without~amsmath } } + } + } +% \end{macrocode} +% +% \bigskip +% The command |\@@_label:n| will be linked to |\label| in the environments +% |{WithArrows}| and |{DispWithArrows}|. In these environments, it's possible to +% put several labels for the same line (it's not possible in the environments of +% \pkg{amsmath}). That's why we store the differents labels of a same line in a +% sequence |\l_@@_labels_seq|. +% \begin{macrocode} +\cs_new_protected:Npn \@@_label:n #1 + { + \@@_if_in_last_col_of_disp:Nn \label + { + \seq_if_empty:NF \l_@@_labels_seq + { + \bool_if:NTF \c_@@_cleveref_loaded_bool + { \@@_error:n { Multiple~labels~with~cleveref } } + { \@@_error:n { Multiple~labels } } + } + \seq_put_right:Nn \l_@@_labels_seq { #1 } + \bool_if:nT \c_@@_mathtools_loaded_bool + { + \MH_if_boolean:nT { show_only_refs } + { + \cs_if_exist:cTF { MT_r_#1 } + { \clist_set:Nn \l_@@_tags_clist { all } } + { \clist_clear:N \l_@@_tags_clist } + } + } + \bool_if:nT \c_@@_autonum_loaded_bool + { + \cs_if_exist:cTF { autonum@#1Referenced } + { \clist_set:Nn \l_@@_tags_clist { all } } + { \clist_clear:N \l_@@_tags_clist } + } + } + } +% \end{macrocode} +% +% \bigskip +% The command |\@@_tagnextline:| will be linked to |\tagnextline| in +% |{DispWithArrows}|. +% \begin{macrocode} +\cs_new_protected:Npn \@@_tagnextline: + { + \@@_if_in_last_col_of_disp:Nn \tagnextline + { \bool_set_true:N \l_@@_tag_next_line_bool } + } +% \end{macrocode} +% +% +% \bigskip +% The environments |{DispWithArrows}| and |{DispWithArrows*}| are compliant with +% the command |\qedhere| of \pkg{amsthm}. However, this compatibility requires a +% special version of |\qedhere|. +% +% This special version is called |\@@_qedhere:| and will be linked with +% |\qedhere| in the last column of the environment |{DispWithArrows}| (only if +% the package \pkg{amsthm} has been loaded). |\@@_qedhere:| raises the boolean +% |\l_@@_qedhere_bool|. +% \begin{macrocode} +\cs_new_protected:Npn \@@_qedhere: { \bool_set_true:N \l_@@_qedhere_bool } +\cs_new_protected:Npn \@@_set_qedhere: { \cs_set_eq:NN \qedhere \@@_qedhere: } +% \end{macrocode} +% +% In the last column of the |\halign| of |{DispWithArrows}| (column of the +% labels, that is to say the numbers of the equations), a command +% |\@@_qedhere_i:| will be issued if the flag |\l_@@_qedhere_bool| has been +% raised. The code of this command is an adaptation of the code of |\qedhere| in +% \pkg{amsthm}. +% \begin{macrocode} +\cs_new_protected:Npn \@@_qedhere_i: + { + \group_begin: + \cs_set_eq:NN \qed \qedsymbol +% \end{macrocode} +% The line |\cs_set_eq:NN \qed@elt \setQED@elt| is a preparation for an action +% on the \textsc{qed} stack. Despite its form, the instruction |\QED@stack| +% executes an operation on the stack. This operation prints the \textsc{qed} +% symbol and nullify the top of the stack. +% \begin{macrocode} + \cs_set_eq:NN \qed@elt \setQED@elt + \QED@stack \relax \relax + \group_end: + } +% +% \end{macrocode} +% +% +% +% +% \subsection{We draw the arrows} +% +% \bigskip +% The arrows are divided in groups. There is two reasons for this division. +% \begin{itemize} +% \item If the option |group| or the option |groups| is used, all the arrows of +% a group are drawn on a same vertical at an abscissa of |\l_@@_x_dim|. +% \item For aesthetic reasons, the starting point of all the starting arrows of +% a group is raised upwards by the value |\l_@@_start_adjust_dim|. Idem for the +% ending arrows. +% \end{itemize} +% +% \medskip +% If the option |group| is used (|\l_@@_pos_arrow_int| = 7), we scan the arrows +% twice: in the first step we only compute the value of |\l_@@_x_dim| for the +% whole group, and, in the second step (|\l_@@_pos_arrow_int| is set to 8), we +% divide the arrows in groups (for the vertical adjustement) and we actually +% draw the arrows. +% \begin{macrocode} +\cs_new_protected:Npn \@@_scan_arrows: + { + \group_begin: + \int_compare:nNnT \l_@@_pos_arrow_int = 7 + { + \@@_scan_arrows_i: + \int_set:Nn \l_@@_pos_arrow_int 8 + } + \@@_scan_arrows_i: + \group_end: + } +% \end{macrocode} +% +% \bigskip +% \begin{macrocode} +\cs_new_protected:Npn \@@_scan_arrows_i: + { +% \end{macrocode} +% +% \bigskip +% |\l_@@_first_arrow_of_group_int| will be the first arrow of the current group. +% +% |\l_@@_first_line_of_group_int| will be the first line involved in the group +% of arrows (equal to the initial line of the first arrow of the group because +% the option |jump| is always positive). +% +% |\l_@@_first_arrows_seq| will be the list the arrows of the group starting at +% the first line of the group (we may have several arrows starting from the same +% line). We have to know all these arrows because of the adjustement by +% |\l_@@_start_adjust_dim|. +% +% |\l_@@_last_line_of_group_int| will be the last line involved in the group +% (impossible to guess in advance). +% +% |\l_@@_last_arrows_seq| will be the list of all the arrows of the group +% ending at the last line of the group (impossible to guess in advance). +% \begin{macrocode} + \int_zero_new:N \l_@@_first_arrow_of_group_int + \int_zero_new:N \l_@@_first_line_of_group_int + \int_zero_new:N \l_@@_last_line_of_group_int + \seq_clear_new:N \l_@@_first_arrows_seq + \seq_clear_new:N \l_@@_last_arrows_seq +% \end{macrocode} +% +% \medskip +% The boolean |\l_@@_new_group_bool| is a switch that we will use the indicate +% that a group is finished (and the lines of that group have to be drawn). This +% boolean is not directed connected to the option |new-group| of an individual +% arrow. +% \begin{macrocode} + \bool_set_true:N \l_@@_new_group_bool +% \end{macrocode} +% +% \bigskip +% We begin a loop over all the arrows of the environment. Inside this loop, if a +% group is finished, we will draw the arrows of that group. +% \begin{macrocode} + \int_set:Nn \l_@@_arrow_int \c_one_int + \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'', +% ``final'', ``status'' and ``input-line''. For the two former, we have to do +% conversions to integers. +% \begin{macrocode} + \prop_get:cnN + { g_@@_arrow _ \l_@@_prefix_str _ \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_str _ \int_use:N \l_@@_arrow_int _ prop } + { final } \l_tmpa_tl + \int_set:Nn \l_@@_final_int \l_tmpa_tl + \prop_get:cnN + { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop } + { status } \l_@@_status_arrow_str + \prop_get:cnN + { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop } + { input-line } \l_@@_input_line_str +% \end{macrocode} +% +% \bigskip +% We recall that, after the construction of the |\halign|, |\g_@@_line_int| is +% the total number of lines of the environment. Therefore, the conditionnal +% |\l_@@_final_int > \g_@@_line_int| tests whether an arrow arrives after the +% last line of the environment. In this case, we raise an error (except in the +% second step of treatment for the option |group|). The arrow will be completely +% ignored, even for the computation of |\l_@@_x_dim|. +% \begin{macrocode} + \int_compare:nNnTF \l_@@_final_int > \g_@@_line_int + { + \int_compare:nNnF \l_@@_pos_arrow_int = 8 + { \@@_error:n { Too~few~lines~for~an~arrow } } + } + \@@_code_for_possible_arrow: +% \end{macrocode} +% +% \bigskip +% Incrementation of the index of the loop (and end of the loop). +% \begin{macrocode} + \int_incr:N \l_@@_arrow_int + } +% \end{macrocode} +% +% \bigskip +% After the last arrow of the environment, we have to draw the last group of +% arrows. If we are in option |group| and in the first step of treatment +% (|\l_@@_pos_arrow_int| = 7), we don't draw because, in the first step, we +% don't draw anything. If there is no arrow in the group, we don't draw (this +% situation occurs when all the arrows of the potential group arrive after the +% last line of the environment). +% \begin{macrocode} + \bool_if:nT + { + \int_compare_p:n { \l_@@_pos_arrow_int != 7 } + && + \int_compare_p:nNn \l_@@_first_arrow_of_group_int > 0 + } + { \@@_draw_arrows:nn \l_@@_first_arrow_of_group_int \g_@@_arrow_int } + } +% \end{macrocode} +% +% \bigskip +% \begin{macrocode} +\cs_new_protected:Npn \@@_code_for_possible_arrow: + { +% \end{macrocode} +% We test whether the previous arrow was in fact the last arrow of a group. In +% this case, we have to draw all the arrows of that group, except if we are with +% the option |group| and in the first step of treatment (|\l_@@_pos_arrow_int| = +% 7). +% \begin{macrocode} + \bool_if:nT + { + \int_compare_p:nNn \l_@@_arrow_int > \c_one_int + && + ( \int_compare_p:n { \l_@@_initial_int > \l_@@_last_line_of_group_int } + && + \int_compare_p:n { \l_@@_pos_arrow_int != 7 } + || + \str_if_eq_p:Vn \l_@@_status_arrow_str { new-group } + ) + } + { + \int_compare:nNnF \l_@@_first_arrow_of_group_int = \c_zero_int + { + \@@_draw_arrows:nn + \l_@@_first_arrow_of_group_int + { \l_@@_arrow_int - 1 } + } + \bool_set_true:N \l_@@_new_group_bool + } +% \end{macrocode} +% +% \bigskip +% The flag |\l_@@_new_group_bool| indicates if we have to begin a new group of +% arrows. In fact, we have to begin a new group in three circonstancies: if we +% are at the first arrow of the environment (that's why the flag is raised +% before the beginning of the loop), if we have just finished a group (that's +% why the flag is raised in the previous conditionnal, for topological reasons +% or if the previous arrows had the status ``new-group''). At the beginning of a +% group, we have to initialize the following variables: |\l_@@_first_arrow_int|, +% |\l_@@_first_line_of_group_int|, |\l_@@_last_line_of_group|, +% |\l_@@_first_arrows_seq|, |\l_@@_last_arrows_seq|. +% +% \begin{macrocode} + \bool_if:nTF \l_@@_new_group_bool + { + \bool_set_false:N \l_@@_new_group_bool + \int_set_eq:NN \l_@@_first_arrow_of_group_int \l_@@_arrow_int + \int_set_eq:NN \l_@@_first_line_of_group_int \l_@@_initial_int + \int_set_eq:NN \l_@@_last_line_of_group_int \l_@@_final_int + \seq_clear:N \l_@@_first_arrows_seq + \seq_put_left:NV \l_@@_first_arrows_seq \l_@@_arrow_int + \seq_clear:N \l_@@_last_arrows_seq + \seq_put_left:NV \l_@@_last_arrows_seq \l_@@_arrow_int +% \end{macrocode} +% +% If we are in option |group| and in the second step of treatment +% (|\l_@@_pos_arrow_int| = 8), we don't initialize |\l_@@_x_dim| because we want +% to use the same value of |\l_@@_x_dim| (computed during the first step) for +% all the groups. +% \begin{macrocode} + \int_compare:nT { \l_@@_pos_arrow_int != 8 } + { \dim_set:Nn \l_@@_x_dim { - \c_max_dim } } + } +% \end{macrocode} +% +% \bigskip +% If we are not at the beginning of a new group. +% \begin{macrocode} + { +% \end{macrocode} +% +% If the arrow is independent, we don't take into account this arrow for the +% detection of the end of the group. +% \begin{macrocode} + \bool_if:nF + { \str_if_eq_p:Vn \l_@@_status_arrow_str { independent } } + { +% \end{macrocode} +% If the arrow is not independant, the arrow belongs to the current group and we +% have to take it into account in some variables. +% \begin{macrocode} + \int_compare:nT + { \l_@@_initial_int = \l_@@_first_line_of_group_int } + { \seq_put_left:NV \l_@@_first_arrows_seq \l_@@_arrow_int } + \int_compare:nNnTF \l_@@_final_int > \l_@@_last_line_of_group_int + { + \int_set_eq:NN \l_@@_last_line_of_group_int \l_@@_final_int + \seq_clear:N \l_@@_last_arrows_seq + \seq_put_left:NV \l_@@_last_arrows_seq \l_@@_arrow_int + } + { + \int_compare:nNnT \l_@@_final_int = \l_@@_last_line_of_group_int + { \seq_put_left:NV \l_@@_last_arrows_seq \l_@@_arrow_int } + } + } + } +% \end{macrocode} +% +% \bigskip +% If the arrow is not independent, we update the current $x$-value (in +% |\l_@@_x_dim|) with the dedicated command |\@@_update_x:nn|. If we are +% in option |group| and in the second step of treatment (|\l_@@_pos_arrow_int| = +% 8), we don't initialize |\l_@@_x_dim| because we want to use the same value of +% |\l_@@_x_dim| (computed during the first step) for all the groups. +% \begin{macrocode} + \bool_if:nF { \str_if_eq_p:Vn \l_@@_status_arrow_str { independent } } + { + \int_compare:nT { \l_@@_pos_arrow_int != 8 } + { \@@_update_x:nn \l_@@_initial_int \l_@@_final_int } + } + } +% \end{macrocode} +% +% +% \bigskip +% The following code is necessary because we will have to expand an argument +% exactly 3 times. +% \begin{macrocode} +\cs_generate_variant:Nn \keys_set:nn { n o } +\cs_new_protected:Npn \@@_keys_set: + { \keys_set_known:no { WithArrows / Arrow / SecondPass } } +% \end{macrocode} +% +% \bigskip +% The macro |\@@_draw_arrows:nn| draws all the arrows whose numbers are between +% |#1| and |#2|. |#1| and |#2| must be expressions that expands to an integer +% (they are expanded in the beginning of the macro). This macro is nullified by +% the option |no-arrows|. +% \begin{macrocode} +\cs_new_protected:Npn \@@_draw_arrows:nn #1 #2 + { + \group_begin: + \int_zero_new:N \l_@@_first_arrow_int + \int_set:Nn \l_@@_first_arrow_int { #1 } + \int_zero_new:N \l_@@_last_arrow_int + \int_set:Nn \l_@@_last_arrow_int { #2 } +% \end{macrocode} +% +% \bigskip +% We begin a loop over the arrows we have to draw. The variable +% |\l_@@_arrow_int| (local in the environment |{WithArrows}|) will be used as +% index for the loop. +% \begin{macrocode} + \int_set:Nn \l_@@_arrow_int \l_@@_first_arrow_int + \int_until_do:nNnn \l_@@_arrow_int > \l_@@_last_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. +% \begin{macrocode} + \prop_get:cnN + { g_@@_arrow _ \l_@@_prefix_str _ \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_str _ \int_use:N \l_@@_arrow_int _ prop } + { final } \l_tmpa_tl + \int_set:Nn \l_@@_final_int \l_tmpa_tl +% \end{macrocode} +% +% \bigskip +% If the arrow ends after the last line of the environment, we don't draw the +% arrow (an error has already been raised in |\@@_scan_arrows:|). We recall +% that, after the construction of the |\halign|, |\g_@@_line_int| is the total +% number of lines of the environment). +% \begin{macrocode} + \int_compare:nT { \l_@@_final_int <= \g_@@_line_int } \@@_draw_arrows_i: + \int_incr:N \l_@@_arrow_int + } + \group_end: + } +% \end{macrocode} +% +% \bigskip +% The macro |\@@_draw_arrows_i:| is only for the lisibility of the code. The +% first |\group_begin:| is for the options of the arrows (but we remind that the +% options |ll|, |rr|, |rl|, |lr|, |i| and |jump| have already been extracted and +% are not present in the field |options| of the property list of the arrow). +% \begin{macrocode} +\cs_new_protected:Npn \@@_draw_arrows_i: + { + \group_begin: +% \end{macrocode} +% +% \bigskip +% We process the options of the current arrow. The second argument of +% |\keys_set:nn| 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_str _ \int_use:N \l_@@_arrow_int _ prop } + { options } \l_tmpa_tl + \str_clear_new:N \l_@@_previous_key_str + \exp_args:NNo \exp_args:No + \@@_keys_set: { \l_tmpa_tl , tikz = { xshift = \l_@@_xoffset_dim } } +% \end{macrocode} +% +% We create two booleans to indicate the position of the initial node and final +% node of the arrow in cases of options |rr|, |rl|, |lr| or |ll|: +% \begin{macrocode} + \bool_set_false:N \l_@@_initial_r_bool + \bool_set_false:N \l_@@_final_r_bool + \int_case:nn \l_@@_pos_arrow_int + { + 0 { \bool_set_true:N \l_@@_final_r_bool } + 2 { \bool_set_true:N \l_@@_initial_r_bool } + 3 + { + \bool_set_true:N \l_@@_initial_r_bool + \bool_set_true:N \l_@@_final_r_bool + } + } +% \end{macrocode} +% +% \bigskip +% \begin{center} +% \begin{tabular}{l} +% \begin{tabular}{@{}l*8c@{}} +% \toprule +% option & |lr| & |ll| & |rl| & |rr| & |v| & |i| & |groups| & |group| \\ +% \midrule +% |\l_@@_pos_arrow_int| & $0$ & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ \\ +% \bottomrule +% \end{tabular} \\ +% \footnotesize The option |v| can be used only in |\Arrow| in |code-after| (see +% below). +% \end{tabular} +% \end{center} +% +% \bigskip +% In case of option |i| at a local or global level (|\l_@@_pos_arrow_int| = 5), +% we have to compute the $x$-value of the arrow (which is vertical). The +% computed $x$-value is stored in |\l_@@_x_dim| (the same variable used when the +% option |group| or the option |groups| is used). +% \begin{macrocode} + \int_compare:nNnT \l_@@_pos_arrow_int = 5 + { + \dim_set:Nn \l_@@_x_dim { - \c_max_dim } + \@@_update_x:nn \l_@@_initial_int \l_@@_final_int + } +% \end{macrocode} +% +% \bigskip +% |\l_@@_initial_tl| contains the name of the Tikz node from which the arrow +% starts (in normal cases... because with the option |i|, |group| and |groups|, +% the point will perhaps have another +% $x$-value --- but always the same $y$-value). Idem for |\l_@@_final_tl|. +% \begin{macrocode} + \tl_set:Nx \l_@@_initial_tl + { + \int_use:N \l_@@_initial_int - \bool_if:NTF \l_@@_initial_r_bool rl + .south + } + \tl_set:Nx \l_@@_final_tl + { \int_use:N \l_@@_final_int - \bool_if:NTF \l_@@_final_r_bool rl .north } +% \end{macrocode} +% We use ``|.south|'' and ``|.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 |show-nodes| to visualize the nodes). +% +% \bigskip +% The label of the arrow will be stored in |\l_tmpa_tl|. +% \begin{macrocode} + \prop_get:cnN + { g_@@_arrow _ \l_@@_prefix_str _ \int_use:N \l_@@_arrow_int _ prop } + { label } + \l_tmpa_tl +% \end{macrocode} +% +% \bigskip +% Now, we have to know if the arrow starts at the first line of the group and/or +% ends at the last line of the group. That's the reason why we have stored in +% |\l_@@_first_arrows_seq| the list of all the arrows starting at the +% first line of the group and in |\l_@@_last_arrows_seq| the list of +% all the arrows ending at the last line of the group. We compute these values +% in the booleans |\l_tmpa_bool| and |\l_tmpb_bool|. These computations can't be +% done in the following |{tikzpicture}| because the command |\seq_if_in:NnTF| +% which is \emph{not} expandable. +% \begin{macrocode} + \seq_if_in:NxTF \l_@@_first_arrows_seq + { \int_use:N \l_@@_arrow_int } + { \bool_set_true:N \l_tmpa_bool } + { \bool_set_false:N \l_tmpa_bool } + \seq_if_in:NxTF \l_@@_last_arrows_seq + { \int_use:N \l_@@_arrow_int } + { \bool_set_true:N \l_tmpb_bool } + { \bool_set_false:N \l_tmpb_bool } + \int_compare:nNnT \l_@@_pos_arrow_int = 5 + { + \bool_set_true:N \l_tmpa_bool + \bool_set_true:N \l_tmpb_bool + } +% \end{macrocode} +% +% \bigskip +% We compute and store in |\g_tmpa_tl| and |\g_tmpb_tl| the exact coordinates of +% the extremities of the arrow. +% \begin{itemize} +% \item Concerning the +% $x$-values, the abscissa computed in |\l_@@_x_dim| will be used if the option +% of position is |i|, |group| or |groups|. +% \item Concerning the +% $y$-values, an adjustement is done for each arrow starting at the first line +% of the group and each arrow ending at the last line of the group (with the +% values of |\l_@@_start_adjust_dim| and |\l_@@_end_adjust_dim|). +% \end{itemize} +% +% \begin{macrocode} +%<*LaTeX> + \begin { tikzpicture } [ @@_standard ] +% +%<*plain-TeX> + \tikzpicture [ @@_standard ] +% + \tikz@scan@one@point \pgfutil@firstofone ( \l_@@_initial_tl ) + \tl_gset:Nx \g_tmpa_tl + { + \int_compare:nNnTF \l_@@_pos_arrow_int < 5 + { \dim_use:N \pgf@x } + { \dim_use:N \l_@@_x_dim } , + \bool_if:NTF \l_tmpa_bool + { \dim_eval:n { \pgf@y + \l_@@_start_adjust_dim } } + { \dim_use:N \pgf@y } + } + \tikz@scan@one@point \pgfutil@firstofone ( \l_@@_final_tl ) + \tl_gset:Nx \g_tmpb_tl + { + \int_compare:nNnTF \l_@@_pos_arrow_int < 5 + { \dim_use:N \pgf@x } + { \dim_use:N \l_@@_x_dim } , + \bool_if:NTF \l_tmpb_bool + { \dim_eval:n { \pgf@y - \l_@@_end_adjust_dim } } + { \dim_use:N \pgf@y } + } +%<*LaTeX> + \end { tikzpicture } +% +%<*plain-TeX> + \endtikzpicture +% +% \end{macrocode} +% +% \bigskip +% Eventually, we can draw the arrow with the code in |\l_@@_tikz_code_tl|. We +% recall that the value by default for this token list is :\enskip +% ``\verb|\draw (#1) to node {#3} (#2) ;|''. This value can be modified with the +% option |tikz-code|. We use the variant |\@@_draw_arrow:nno| of the macro +% |\@@_draw_arrow:nnn| because of the characters \emph{underscore} in the name +% |\l_tmpa_tl|: if the user uses the Tikz library |babel|, the third argument of +% the command |\@@_draw_arrow:nno| will be rescanned because this third argument +% will be in the argument of a command |node| of an instruction |\draw| of +% Tikz... and we will have an error because of the characters +% \emph{underscore}.\footnote{There were other solutions: use another name +% without \emph{underscore} (like \Verb|\ltmpatl|) or use the package +% \pkg{underscore} (with this package, the characters \emph{underscore} will be +% rescanned without errors, even in text mode).} +% \begin{macrocode} + \@@_draw_arrow:nno \g_tmpa_tl \g_tmpb_tl \l_tmpa_tl +% \end{macrocode} +% +% \smallskip +% We close the TeX group opened for the options given to |\Arrow[...]| (local +% level of the options). +% \begin{macrocode} + \group_end: + } +% \end{macrocode} +% +% +% \bigskip +% The function |@@_tmpa:nnn| will draw the arrow. It's merely an environment +% |{tikzpicture}|. However, the Tikz instruction in this environment must be +% inserted from |\l_@@_tikz_code_tl| with the markers |#1|, |#2| and |#3|. +% That's why we create a function |\@@_def_function_tmpa:n| which will create +% the function |\@@_tmpa:nnn|. +% \begin{macrocode} +\cs_new_protected:Npn \@@_def_function_tmpa:n #1 + { + \cs_set:Npn \@@_tmpa:nnn ##1 ##2 ##3 + { +%<*LaTeX> + \begin{tikzpicture} +% +%<*plain-TeX> + \tikzpicture +% + [ + @@_standard , + every~path / .style = WithArrows / arrow + ] + #1 +%<*LaTeX> + \end{tikzpicture} +% +%<*plain-TeX> + \endtikzpicture +% + } + } +% \end{macrocode} +% +% \medskip +% When we draw the arrow (with |\@@_draw_arrow:nnn|), we first create the +% function |\@@_tmpa:nnn| and, then, we use the function |\@@_tmpa:nnn| : +% \begin{macrocode} +\cs_new_protected:Npn \@@_draw_arrow:nnn #1 #2 #3 + { +% \end{macrocode} +% +% \medskip +% If the option |wrap-lines| is used, we have to use a special version of +% |\l_@@_tikz_code_tl| (which corresponds to the option |tikz-code|). +% \begin{macrocode} + \bool_if:nT { \l_@@_wrap_lines_bool && \l_@@_in_DispWithArrows_bool } + { \tl_set_eq:NN \l_@@_tikz_code_tl \c_@@_tikz_code_wrap_lines_tl } +% \end{macrocode} +% +% \medskip +% Now, the main lines of this function |\@@_draw_arrow:nnn|. +% \begin{macrocode} + \exp_args:NV \@@_def_function_tmpa:n \l_@@_tikz_code_tl + \@@_tmpa:nnn { #1 } { #2 } { #3 } + } +\cs_generate_variant:Nn \@@_draw_arrow:nnn { n n o } +% \end{macrocode} +% +% \bigskip +% If the option |wrap-lines| is used, we have to use a special version of +% |\l_@@_tikz_code_tl| (which corresponds to the option |tikz-code|). +% \begin{macrocode} +\tl_const:Nn \c_@@_tikz_code_wrap_lines_tl + { +% \end{macrocode} +% First, we draw the arrow without the label. +% \begin{macrocode} + \draw ( #1 ) to node ( @@_label ) { } ( #2 ) ; +% \end{macrocode} +% We retrieve in |\pgf@x| the abscissa of the left-side of the label we will +% put. +% \begin{macrocode} + \tikz@parse@node \pgfutil@firstofone ( @@_label.west ) +% \end{macrocode} +% We compute in |\l_tmpa_dim| the maximal width possible for the label. +% Here is the use of |\g_@@_right_x_dim| which has been computed previously with +% the |v|-nodes. +% \begin{macrocode} + \dim_set:Nn \l_tmpa_dim + { \g_@@_right_x_dim - \pgf@x - \pgfkeysvalueof { / pgf / inner~xsep } } +% \end{macrocode} +% We retrieve in |\g_tmpa_tl| the current value of the Tikz parameter +% ``|text width|''.\footnote{In fact, it's not the current value of +% ``|text width|'': it's the value of ``|text width|'' set in the option |tikz| +% provided by \pkg{witharrows}. These options are given to Tikz in a +% ``|every path|''. That's why we have to retrieve it in a path.} +% \begin{macrocode} + \path \pgfextra { \tl_gset:Nx \g_tmpa_tl \tikz@text@width } ; +% \end{macrocode} +% Maybe the current value of the parameter ``|text width|'' is shorter than +% |\l_tmpa_dim|. In this case, we must use ``|text width|'' (we update +% |\l_tmpa_dim|). +% \begin{macrocode} + \tl_if_empty:NF \g_tmpa_tl + { + \dim_set:Nn \l_tmpb_dim \g_tmpa_tl + \dim_compare:nNnT \l_tmpb_dim < \l_tmpa_dim + { \dim_set_eq:NN \l_tmpa_dim \l_tmpb_dim } + } +% \end{macrocode} +% Now, we can put the label with the right value for ``|text width|''. +% \begin{macrocode} + \dim_compare:nNnT \l_tmpa_dim > \c_zero_dim + { + \path ( @@_label.west ) + node [ anchor = west , text~width = \dim_use:N \l_tmpa_dim ] + { #3 } ; + } + } +% \end{macrocode} +% +% \bigskip +% The command |\@@_update_x:nn| will analyze the lines between |#1| and +% |#2| in order to modify |\l_@@_x_dim| in consequence. More precisely, +% |\l_@@_x_dim| is increased if a line longer than the current value of +% |\l_@@_x_dim| is found. |\@@_update_x:nn| is used in |\@@_scan_arrows:| +% (for options |group| and |groups|) and in |\@@_draw_arrows:nn| (for option +% |i|). +% \begin{macrocode} +\cs_new_protected:Npn \@@_update_x:nn #1 #2 + { + \int_step_inline:nnn { #1 } { #2 } + { +%<*LaTeX> + \begin { tikzpicture } [ @@_standard ] +% +%<*plain-TeX> + \tikzpicture [ @@_standard ] +% + \tikz@scan@one@point \pgfutil@firstofone ( ##1 - l ) + \dim_gset:Nn \g_tmpa_dim { \dim_max:nn \l_@@_x_dim \pgf@x } +%<*LaTeX> + \end { tikzpicture } +% +%<*plain-TeX> + \endtikzpicture +% + \dim_set_eq:NN \l_@@_x_dim \g_tmpa_dim + } + } +% \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~$0$ (to the sense of the nested environments). This macro is fully +% expandable and, thus, can be used directly in the name of a Tikz node. +% \begin{macrocode} +\cs_new:Npn \WithArrowsLastEnv { \int_use:N \g_@@_last_env_int } +% \end{macrocode} +% +% \bigskip +% \subsection{The command \textbackslash Arrow in code-after} +% +% The option |code-after| is an option of the environment |{WithArrows}| (this +% option is only available at the environment level). In the option |code-after|, +% one can use the command |Arrow| but it's a special version of the command +% |Arrow|. For this special version (internally called |\@@_Arrow_code_after|), +% we define a special set of keys called |WithArrows/Arrow/code-after|. +% +% \begin{macrocode} +\keys_define:nn { WithArrows / Arrow / code-after } + { + tikz .code:n = + \tikzset { WithArrows / arrow / .append~style = { #1 } } , + tikz .value_required:n = true , + rr .value_forbidden:n = true , + rr .code:n = \@@_fix_pos_option:n 0 , + ll .value_forbidden:n = true, + ll .code:n = \@@_fix_pos_option:n 1 , + rl .value_forbidden:n = true , + rl .code:n = \@@_fix_pos_option:n 2 , + lr .value_forbidden:n = true , + lr .code:n = \@@_fix_pos_option:n 3 , + v .value_forbidden:n = true , + v .code:n = \@@_fix_pos_option:n 4 , + tikz-code .tl_set:N = \l_@@_tikz_code_tl , + tikz-code .value_required:n = true , + xoffset .dim_set:N = \l_@@_xoffset_dim , + xoffset .value_required:n = true , + unknown .code:n = + \@@_sort_seq:N \l_@@_options_Arrow_code_after_seq + \@@_error:n { Unknown~option~Arrow~in~code-after } + } +% \end{macrocode} +% +% \bigskip +% A sequence of the options available in |\Arrow| in |code-after|. This sequence +% will be used in the error messages and can be modified dynamically. +% \begin{macrocode} +\seq_new:N \l_@@_options_Arrow_code_after_seq +\@@_set_seq_of_str_from_clist:Nn \l_@@_options_Arrow_code_after_seq + { ll, lr, rl, rr, tikz, tikz-code, v, x, offset } +% \end{macrocode} +% +% \bigskip +% \begin{macrocode} +%<*LaTeX> +\NewDocumentCommand \@@_Arrow_code_after { O { } m m m ! O { } } +% +%<*plain-TeX> +\cs_new_protected:Npn \@@_Arrow_code_after + { + \peek_meaning:NTF [ + { \@@_Arrow_code_after_i } + { \@@_Arrow_code_after_i [ ] } + } +\cs_new_protected:Npn \@@_Arrow_code_after_i [ #1 ] #2 #3 #4 + { + \peek_meaning:NTF [ + { \@@_Arrow_code_after_ii [ #1 ] { #2 } { #3 } { #4 } } + { \@@_Arrow_code_after_ii [ #1 ] { #2 } { #3 } { #4 } [ ] } + } +\cs_new_protected:Npn \@@_Arrow_code_after_ii [ #1 ] #2 #3 #4 [ #5 ] +% + { + \int_set:Nn \l_@@_pos_arrow_int 1 + \str_clear_new:N \l_@@_previous_key_str + \group_begin: + \keys_set:nn { WithArrows / Arrow / code-after } + { #1, #5, tikz = { xshift = \l_@@_xoffset_dim } } + \bool_set_false:N \l_@@_initial_r_bool + \bool_set_false:N \l_@@_final_r_bool + \int_case:nn \l_@@_pos_arrow_int + { + 0 + { + \bool_set_true:N \l_@@_initial_r_bool + \bool_set_true:N \l_@@_final_r_bool + } + 2 { \bool_set_true:N \l_@@_initial_r_bool } + 3 { \bool_set_true:N \l_@@_final_r_bool } + } +% \end{macrocode} +% We prevent drawing a arrow from a line to itself. +% \begin{macrocode} + \tl_if_eq:nnTF { #2 } { #3 } + { \@@_error:nn { Both~lines~are~equal } { #2 } } +% \end{macrocode} +% We test whether the two Tikz nodes |(#2-l)| and |(#3-l)| really exist. If not, +% the arrow won't be drawn. +% \begin{macrocode} + { + \cs_if_free:cTF { pgf@sh@ns@wa - \l_@@_prefix_str - #2 - l } + { \@@_error:nx { Wrong~line~in~Arrow } { #2 } } + { + \cs_if_free:cTF { pgf@sh@ns@wa - \l_@@_prefix_str - #3 - l } + { \@@_error:nx { Wrong~line~in~Arrow } { #3 } } + { + \int_compare:nNnTF \l_@@_pos_arrow_int = 4 + { +%<*LaTeX> + \begin { tikzpicture } [ @@_standard ] +% +%<*plain-TeX> + \tikzpicture [ @@_standard ] +% + \tikz@scan@one@point \pgfutil@firstofone (#2-l.south) + \dim_set_eq:NN \l_tmpa_dim \pgf@x + \dim_set_eq:NN \l_tmpb_dim \pgf@y + \tikz@scan@one@point \pgfutil@firstofone (#3-l.north) + \dim_set:Nn \l_tmpa_dim + { \dim_max:nn \l_tmpa_dim \pgf@x } + \tl_gset:Nx \g_tmpa_tl + { \dim_use:N \l_tmpa_dim , \dim_use:N \l_tmpb_dim } + \tl_gset:Nx \g_tmpb_tl + { \dim_use:N \l_tmpa_dim , \dim_use:N \pgf@y } +%<*LaTeX> + \end { tikzpicture } +% +%<*plain-TeX> + \endtikzpicture +% + } + { +%<*LaTeX> + \begin { tikzpicture } [ @@_standard ] +% +%<*plain-TeX> + \tikzpicture [ @@_standard ] +% + \tikz@scan@one@point \pgfutil@firstofone + ( #2-\bool_if:NTF\l_@@_initial_r_bool rl .south ) + \tl_gset:Nx \g_tmpa_tl + { \dim_use:N \pgf@x , \dim_use:N \pgf@y } + \tikz@scan@one@point \pgfutil@firstofone + ( #3-\bool_if:NTF\l_@@_final_r_bool rl .north ) + \tl_gset:Nx \g_tmpb_tl + { \dim_use:N \pgf@x , \dim_use:N \pgf@y } +%<*LaTeX> + \end { tikzpicture } +% +%<*plain-TeX> + \endtikzpicture +% + } + \@@_draw_arrow:nnn \g_tmpa_tl \g_tmpb_tl { #4 } + } + } + } + \group_end: + } +% \end{macrocode} +% +% +% \bigskip +% \subsection{The command \textbackslash MultiArrow in code-after} +% The command |\@@_MultiArrow:nn| will be linked to |\MultiArrow| when the +% |code-after| is executed. +% +% \begin{macrocode} +\cs_new_protected:Npn \@@_MultiArrow:nn #1 #2 + { +% \end{macrocode} +% The user of the command |\MultiArrow| (in |code-after|) will be able to specify +% the list of lines with the same syntax as the loop |\foreach| of \pkg{pgffor}. +% That's why we construct a ``clist'' of \pkg{expl3} from the specification of +% list given by the user. The construction of the ``clist'' must be global in +% order to exit the |\foreach| and that's why we construct the list in +% |\g_tmpa_clist|. +% \begin{macrocode} + \foreach \x in { #1 } + { + \cs_if_free:cTF { pgf@sh@ns@wa - \l_@@_prefix_str - \x - l } + { \@@_error:nx { Wrong~line~specification~in~MultiArrow } \x } + { \clist_gput_right:Nx \g_tmpa_clist \x } + } +% \end{macrocode} +% We sort the list |\g_tmpa_clist| because we want to extract the minimum and +% the maximum. +% \begin{macrocode} + \int_compare:nTF { \clist_count:N \g_tmpa_clist < 2 } + { \@@_error:n { Too~small~specification~for~MultiArrow } } + { + \clist_sort:Nn \g_tmpa_clist + { + \int_compare:nTF { ##1 > ##2 } + \sort_return_swapped: + \sort_return_same: + } +% \end{macrocode} +% We extract the minimum in |\l_tmpa_tl| (it must be an integer but we store it +% in a token list of \pkg{expl3}). +% \begin{macrocode} + \clist_pop:NN \g_tmpa_clist \l_tmpa_tl +% \end{macrocode} +% +% We extract the maximum in |\l_tmpb_tl|. The remaining list (in +% |\g_tmpa_clist|) will be sorted in decreasing order but never mind... +% \begin{macrocode} + \clist_reverse:N \g_tmpa_clist + \clist_pop:NN \g_tmpa_clist \l_tmpb_tl +% \end{macrocode} +% +% We draw the teeth of the rak (except the first one and the last one) with the +% auxiliary function |\@@_MultiArrow_i:n|. This auxiliary fonction is necessary +% to expand the specification of the list in the |\foreach| loop. The first and +% the last teeth of the rak can't be drawn the same way as the others (think, +% for example, to the case of the option ``|rounded corners|'' is used). +% \begin{macrocode} + \exp_args:NV \@@_MultiArrow_i:n \g_tmpa_clist +% \end{macrocode} +% +% Now, we draw the rest of the structure. +% \begin{macrocode} +%<*LaTeX> + \begin { tikzpicture } +% +%<*plain-TeX> + \tikzpicture +% + [ + @@_standard , + every~path / .style = { WithArrows / arrow } + ] + \draw [<->] ([xshift = \l_@@_xoffset_dim]\l_tmpa_tl-r.south) + -- ++(5mm,0) + -- node (@@_label) {} + ([xshift = \l_@@_xoffset_dim+5mm]\l_tmpb_tl-r.south) + -- ([xshift = \l_@@_xoffset_dim]\l_tmpb_tl-r.south) ; + \tikz@parse@node \pgfutil@firstofone (@@_label.west) + \dim_set:Nn \l_tmpa_dim { 20 cm } + \path \pgfextra { \tl_gset:Nx \g_tmpa_tl \tikz@text@width } ; + \tl_if_empty:NF \g_tmpa_tl { \dim_set:Nn \l_tmpa_dim \g_tmpa_tl } + \bool_if:nT { \l_@@_wrap_lines_bool && \l_@@_in_DispWithArrows_bool } + { + \dim_set:Nn \l_tmpb_dim + { \g_@@_right_x_dim - \pgf@x - 0.3333 em } + \dim_compare:nNnT \l_tmpb_dim < \l_tmpa_dim + { \dim_set_eq:NN \l_tmpa_dim \l_tmpb_dim } + } + \path (@@_label.west) + node [ anchor = west, text~width = \dim_use:N \l_tmpa_dim ] { #2 } ; +%<*LaTeX> + \end{tikzpicture} +% +%<*plain-TeX> + \endtikzpicture +% + } + } +% \end{macrocode} +% +% \begin{macrocode} +\cs_new_protected:Npn \@@_MultiArrow_i:n #1 + { +%<*LaTeX> + \begin { tikzpicture } +% +%<*plain-TeX> + \tikzpicture +% + [ + @@_standard , + every~path / .style = { WithArrows / arrow } + ] + \foreach \k in { #1 } + { + \draw [ <- ] + ( [xshift = \l_@@_xoffset_dim]\k-r.south ) -- ++(5mm,0) ; + } ; +%<*LaTeX> + \end{tikzpicture} +% +%<*plain-TeX> + \endtikzpicture +% + } +% \end{macrocode} +% +% +% \bigskip +% \subsection{The error messages of the package} +% +% \begin{macrocode} +\str_const:Nn \c_@@_option_ignored_str + { If~you~go~on,~this~option~will~be~ignored. } +\str_const:Nn \c_@@_command_ignored_str + { If~you~go~on,~this~command~will~be~ignored. } +% \end{macrocode} +% +% \begin{macrocode} +%<*LaTeX> +\@@_msg_new:nn { amsmath~not~loaded } + { + You~can't~use~the~option~'\l_keys_key_tl'~because~the~ + package~'amsmath'~has~not~been~loaded.\\ + If~you~go~on,~this~option~will~be~ignored~in~the~rest~ + of~the~document. + } +% +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Bad~value~for~replace~brace~by } + { + Bad~value~for~the~option~'\l_keys_key_tl'.~The~value~must~begin~ + with~an~extensible~left~delimiter.~The~possible~values~are:~., + \token_to_str:N \{,~(,~[,~\token_to_str:N \lbrace,~ + \token_to_str:N \lbrack,~\token_to_str:N \lgroup,~ + \token_to_str:N \langle,~\token_to_str:N \lmoustache,~ + \token_to_str:N \lfloor\ and~\token_to_str:N \lceil\ + (and~\token_to_str:N \lvert\ and~\token_to_str:N \lVert\ + if~amsmath~or~unicode-math~is~loaded~in~LaTeX).\\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { option~of~cr~negative } + { + The~argument~of~the~command~\token_to_str:N\\~ + should~be~positive~in~the~row~\int_use:N \g_@@_line_int\ + of~your~environment~\{\l_@@_type_env_str\}.\\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { omit~probably~used } + { + There~is~a~problem.~Maybe~you~have~used~a~command~ + \token_to_str:N\omit\ in~the~line~\int_use:N \g_@@_line_int\ + (or~another~line)~of~your~environment~\{\l_@@_type_env_str\}.\\ + You~can~go~on~but~you~may~have~others~errors. + } +% \end{macrocode} +% +% \begin{macrocode} +%<*LaTeX> +\@@_msg_new:nn { newline~at~the~end~of~env } + { + Your~environment~\{\l_@@_type_env_str\}~should~not~end~with~ + a~\token_to_str:N \\.\\ + This~warning~might~become~an~error~in~a~future~version. + } +% +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Invalid~option~format } + { + The~key~'format'~should~contain~only~letters~r,~c~and~l~and~ + must~not~be~empty.\\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Value~for~a~key } + { + The~key~'\l_keys_key_tl'~should~be~used~without~value. \\ + However,~you~can~go~on~for~this~time. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nnn { Unknown~option~in~Arrow } + { + The~key~'\l_keys_key_tl'~is~unknown~for~the~command~ + \l_@@_string_Arrow_for_msg_str\ in~the~row~ + \int_use:N \g_@@_line_int\ of~your~environment~ + \{\l_@@_type_env_str\}. \l_tmpa_str \\ + \c_@@_option_ignored_str \\ + For~a~list~of~the~available~keys,~type~H~. + } + { + The~available~keys~are~(in~alphabetic~order):~ + \seq_use:Nnnn \l_@@_options_Arrow_seq {~and~} {,~} {~and~}. + } +% \end{macrocode} +% +% +% \begin{macrocode} +\@@_msg_new:nnn { Unknown~option~WithArrows } + { + The~key~'\l_keys_key_tl'~is~unknown~in~\{\l_@@_type_env_str\}. \\ + \c_@@_option_ignored_str \\ + For~a~list~of~the~available~keys,~type~H~. + } + { + The~available~keys~are~(in~alphabetic~order):~ + \seq_use:Nnnn \l_@@_options_WithArrows_seq {~and~} {,~} {~and~}. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nnn { Unknown~option~DispWithArrows } + { + The~key~'\l_keys_key_tl'~is~unknown~in~\{\l_@@_type_env_str\}. \\ + \c_@@_option_ignored_str \\ + For~a~list~of~the~available~keys,~type~H~. + } + { + The~available~keys~are~(in~alphabetic~order):~ + \seq_use:Nnnn \l_@@_options_DispWithArrows_seq {~and~} {,~} {~and~}. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nnn { Unknown~option~WithArrowsOptions } + { + The~key~'\l_keys_key_tl'~is~unknown~in~ + \token_to_str:N \WithArrowsOptions. \\ + \c_@@_option_ignored_str \\ + For~a~list~of~the~available~keys,~type~H~. + } + { + The~available~keys~are~(in~alphabetic~order):~ + \seq_use:Nnnn \l_@@_options_WithArrowsOptions_seq {~and~} {,~} {~and~}. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nnn { Unknown~option~Arrow~in~code-after } + { + The~key~'\l_keys_key_tl'~is~unknown~in~ + \token_to_str:N \Arrow\ in~code-after. \\ + \c_@@_option_ignored_str \\ + For~a~list~of~the~available~keys,~type~H~. + } + { + The~available~keys~are~(in~alphabetic~order):~ + \seq_use:Nnnn \l_@@_options_Arrow_code_after_seq {~and~} {,~} {~and~}. + } +% \end{macrocode} +% +% +% \begin{macrocode} +\@@_msg_new:nn { Too~much~columns~in~WithArrows } + { + Your~environment~\{\l_@@_type_env_str\}~has~\int_use:N + \l_@@_nb_cols_int\ columns~and~you~try~to~use~one~more.~ + Maybe~you~have~forgotten~a~\c_backslash_str\c_backslash_str.~ + If~you~really~want~to~use~more~columns~(after~the~arrows)~you~should~use~ + the~option~'more-columns'~at~a~global~level~or~for~an~environment. \\ + However,~you~can~go~one~for~this~time. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Too~much~columns~in~DispWithArrows } + { + Your~environment~\{\l_@@_type_env_str\}~has~\int_use:N + \l_@@_nb_cols_int\ columns~and~you~try~to~use~one~more.~ + Maybe~you~have~forgotten~a~\c_backslash_str\c_backslash_str\ + at~the~end~of~row~\int_use:N \g_@@_line_int. \\ + This~error~is~fatal. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Negative~jump } + { + You~can't~use~a~negative~value~for~the~option~'jump'~of~command~ + \l_@@_string_Arrow_for_msg_str\ + in~the~row~\int_use:N \g_@@_line_int\ + of~your~environment~\{\l_@@_type_env_str\}.~ + You~can~create~an~arrow~going~backwards~with~the~option~'<-'~of~Tikz. \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { new-group~without~groups } + { + You~can't~use~the~option~'new-group'~for~the~command~ + \l_@@_string_Arrow_for_msg_str\ + because~you~are~not~in~'groups'~mode.~Try~to~use~the~option~ + 'groups'~in~your~environment~\{\l_@@_type_env_str\}. \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% +% \begin{macrocode} +\@@_msg_new:nn + { Too~few~lines~for~an~arrow } + { + Line~\l_@@_input_line_str\ + :~an~arrow~specified~in~the~row~\int_use:N \l_@@_initial_int\ + of~your~environment~\{\l_@@_type_env_str\}~can't~be~drawn~ + because~it~arrives~after~the~last~row~of~the~environment. \\ + If~you~go~on,~this~arrow~will~be~ignored. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { WithArrows~outside~math~mode } + { + The~environment~\{\l_@@_type_env_str\}~should~be~used~only~in~math~mode~ + like~the~environment~\{aligned\}~of~amsmath. \\ + Nevertheless,~you~can~go~on. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { DispWithArrows~in~math~mode } + { + The~environment~\{\l_@@_type_env_str\}~should~be~used~only~outside~math~ + mode~like~the~environment~\{align\}~of~amsmath. \\ + This~error~is~fatal. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Incompatible~options~in~Arrow } + { + You~try~to~use~the~option~'\l_keys_key_tl'~but~ + this~option~is~incompatible~or~redundant~with~the~option~ + '\l_@@_previous_key_str'~set~in~the~same~command~ + \l_@@_string_Arrow_for_msg_str. \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% +% \begin{macrocode} +\@@_msg_new:nn { Incompatible~options } + { You~try~to~use~the~option~'\l_keys_key_tl'~but~ + this~option~is~incompatible~or~redundant~with~the~option~ + '\l_@@_previous_key_str'~set~in~the~same~command~ + \bool_if:NT \l_@@_in_code_after_bool + { + \l_@@_string_Arrow_for_msg_str\ + in~the~code-after~of~your~environment~\{\l_@@_type_env_str\} + }. \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Arrow~not~in~last~column } + { + You~should~use~the~command~\l_@@_string_Arrow_for_msg_str\ + only~in~the~last~column~(column~\int_use:N\l_@@_nb_cols_int)~ + of~your~environment~\{\l_@@_type_env_str\}.\\ + However~you~can~go~on~for~this~time. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Wrong~line~in~Arrow } + { + The~specification~of~line~'#1'~you~use~in~the~command~ + \l_@@_string_Arrow_for_msg_str\ + in~the~'code-after'~of~\{\l_@@_type_env_str\}~doesn't~exist. \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Both~lines~are~equal } + { + In~the~'code-after'~of~\{\l_@@_type_env_str\}~you~try~to~ + draw~an~arrow~going~to~itself~from~the~line~'#1'.~This~is~not~possible. \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Wrong~line~specification~in~MultiArrow } + { + The~specification~of~line~'#1'~doesn't~exist. \\ + If~you~go~on,~it~will~be~ignored~for~\token_to_str:N \MultiArrow. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Too~small~specification~for~MultiArrow } + { + The~specification~of~lines~you~gave~to~\token_to_str:N \MultiArrow\ + is~too~small:~you~need~at~least~two~lines. \\ + \c_@@_command_ignored_str + } +% \end{macrocode} +% +% +% \begin{macrocode} +\@@_msg_new:nn { Not~allowed~in~DispWithArrows } + { + The~command~\token_to_str:N #1 + is~allowed~only~in~the~last~column~ + (column~\int_use:N\l_@@_nb_cols_int)~of~\{\l_@@_type_env_str\}. \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Not~allowed~in~WithArrows } + { + The~command~\token_to_str:N #1 is~not~allowed~in~\{\l_@@_type_env_str\}~ + (it's~allowed~in~the~last~column~of~\{DispWithArrows\}). \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +%<*LaTeX> +\@@_msg_new:nn { tag*~without~amsmath } + { + We~can't~use~\token_to_str:N\tag*~because~you~haven't~loaded~amsmath~ + (or~mathtools). \\ + If~you~go~on,~the~command~\token_to_str:N\tag\ + will~be~used~instead. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Multiple~tags } + { + You~can't~use~twice~the~command~\token_to_str:N\tag\ + in~a~line~of~the~environment~\{\l_@@_type_env_str\}. \\ + If~you~go~on,~the~tag~'#1'~will~be~used. + } +% \end{macrocode} +% +% +% \begin{macrocode} +\@@_msg_new:nn { Multiple~labels } + { + Normally,~we~can't~use~the~command~\token_to_str:N\label\ + twice~in~a~line~of~the~environment~\{\l_@@_type_env_str\}. \\ + However,~you~can~go~on.~ + \bool_if:NT \c_@@_showlabels_loaded_bool + { However,~only~the~last~label~will~be~shown~by~showlabels.~ } + If~you~don't~want~to~see~this~message~again,~you~can~use~the~option~ + 'allow-multiple-labels'~at~the~global~or~environment~level. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Multiple~labels~with~cleveref } + { + Since~you~use~cleveref,~you~can't~use~the~command~\token_to_str:N\label\ + twice~in~a~line~of~the~environment~\{\l_@@_type_env_str\}. \\ + If~you~go~on,~you~may~have~undefined~references. + } +% +% \end{macrocode} +% +% +% \begin{macrocode} +\@@_msg_new:nn { Inexistent~v-node } + { + There~is~a~problem.~Maybe~you~have~put~a~command~\token_to_str:N\cr\ + instead~of~a~command~\token_to_str:N\\~at~the~end~of~ + the~row~\l_tmpa_int\ + of~your~environment~\{\l_@@_type_env_str\}. \\ + This~error~is~fatal. + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Option~xoffset~forbidden } + { + You~can't~use~the~option~'xoffset'~in~the~command~ + \l_@@_string_Arrow_for_msg_str\ + while~you~are~using~the~option~ + ' \int_compare:nNnTF \l_@@_pos_arrow_int = 7 + { group } + { groups } '. \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nnn { Duplicate~name } + { + The~name~'\l_keys_value_tl'~is~already~used~and~you~shouldn't~use~ + the~same~environment~name~twice.~You~can~go~on,~but,~ + maybe,~you~will~have~incorrect~results. \\ + For~a~list~of~the~names~already~used,~type~H~. \\ + If~you~don't~want~to~see~this~message~again,~use~the~option~ + 'allow-duplicate-names'. + } + { + The~names~already~defined~in~this~document~are:~ + \seq_use:Nnnn \g_@@_names_seq { ,~ } { ,~ } { ~and~ }. + } +% \end{macrocode} +% +% +% +% \subsection{The command \textbackslash WithArrowsNewStyle} +% +% A new key defined with |\WithArrowsNewStyle| will not be available at the +% local level. +% \begin{macrocode} +%<*LaTeX> +\NewDocumentCommand \WithArrowsNewStyle { m m } +% +%<*plain-TeX> +\cs_new_protected:Npn \WithArrowsNewStyle #1 #2 +% + { + \keys_if_exist:nnTF { WithArrows / Global } { #1 } + { \@@_error:nn { Key~already~defined } { #1 } } + { + \keys_define:nn { WithArrows / Global } + { + #1 .code:n = + { \keys_set_known:nn { WithArrows / WithArrowsOptions } { #2 } } + } + \seq_put_right:Nx \l_@@_options_WithArrows_seq { \tl_to_str:n { #1 } } + \seq_put_right:Nx \l_@@_options_DispWithArrows_seq + { \tl_to_str:n { #1 } } + \seq_put_right:Nx \l_@@_options_WithArrowsOptions_seq + { \tl_to_str:N { #1 } } +% \end{macrocode} +% We now set the options in a TeX group in order to detect if some keys in |#2| +% are unknown. If a key is unknown, an error will be raised. However, the key +% will, even so, be stored in the definition of key~|#1|. +% \begin{macrocode} + \group_begin: + \msg_set:nnn { witharrows } { Unknown~option~WithArrowsOptions } + { + The~key~'\l_keys_key_tl'~can't~be~set~in~the~ + definition~of~a~style.~You~can~go~on~for~this~time~ + but~you~should~suppress~this~key. + } + \WithArrowsOptions { #2 } + \group_end: + } + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { Key~already~defined } + { + The~key~'#1'~is~already~defined. \\ + If~you~go~on,~your~instruction~\token_to_str:N\WithArrowsNewStyle\ + will~be~ignored. + } +% \end{macrocode} +% +% +% \subsection{The options up and down} +% +% The options |up| and |down| are available for individual arrows. The +% corresponding code is given here. It is independent of the main code of the +% extension \pkg{witharrows}. +% +% This code is the only part of the code of \pkg{witharrows} which uses the +% package \pkg{varwidth} and also the Tikz library |calc|. That's why we have +% decided not to load this package and this library. If they are not loaded, the +% user will have an error only when using the option |up| or the option |down|. +% +% \medskip +% The token list |\c_@@_tikz_code_up_tl| is the value of |tikz-code| which will +% be used for an option |up|. +% \begin{macrocode} +\tl_const:Nn \c_@@_tikz_code_up_tl + { + \draw [ rounded~corners ] + let \p1 = (#1) , + \p2 = (#2) + in (\p1) -- node { +%<*LaTeX> + \dim_set:Nn \l_tmpa_dim { \x2 - \x1 } + \begin { varwidth } \l_tmpa_dim +% \end{macrocode} +% |\narrowragged| is a command of the package \pkg{varwidth}. +% \begin{macrocode} + \narrowragged + #3 + \end { varwidth } +% +%<*plain-TeX> + #3 +% + } + (\x2,\y1) -- (\p2) ; + } +% \end{macrocode} +% +% +% \medskip +% Idem for the option |down|. +% \begin{macrocode} +\tl_const:Nn \c_@@_tikz_code_down_tl + { + \draw [ rounded~corners ] + let \p1 = (#1) , + \p2 = (#2) + in (\p1) -- (\x1,\y2) -- + node { +%<*LaTeX> + \dim_set:Nn \l_tmpa_dim { \x1 - \x2 } + \begin { varwidth } \l_tmpa_dim + \narrowragged + #3 + \end { varwidth } +% +%<*plain-TeX> + #3 +% + } + (\p2) ; + } +% \end{macrocode} +% +% \begin{macrocode} +\keys_define:nn { WithArrows / Arrow / FirstPass } + { + up .code:n = \@@_set_independent: , + down .code:n = \@@_set_independent: , + up .default:n = NoValue , + down .default:n = NoValue + } +% \end{macrocode} +% +% \bigskip +% \begin{macrocode} +\keys_define:nn { WithArrows / Arrow / SecondPass } + { + up .code:n = + \str_if_empty:NT \l_@@_previous_key_str + { + \str_set:Nn \l_@@_previous_key_str { up } +%<*LaTeX> + \bool_if:NTF \c_@@_varwidth_loaded_bool + { +% + \cs_if_exist:cTF { tikz@library@calc@loaded } + { + \int_set:Nn \l_@@_pos_arrow_int \c_one_int +% \end{macrocode} +% We have to set |\l_@@_wrap_lines_bool| to |false| because, otherwise, if the +% option |wrap_lines| is used at a higher level (global or environment), we will +% have a special affectation to |tikz-code| that will overwrite our affectation. +% \begin{macrocode} + \bool_set_false:N \l_@@_wrap_lines_bool + \tl_set_eq:NN \l_@@_tikz_code_tl + \c_@@_tikz_code_up_tl + } + { \@@_error:n { calc~not~loaded } } +%<*LaTeX> + } + { \@@_error:n { varwidth~not~loaded } } +% + } , + down .code:n = + \str_if_empty:NT \l_@@_previous_key_str + { + \str_set:Nn \l_@@_previous_key_str { down } +%<*LaTeX> + \bool_if:NTF \c_@@_varwidth_loaded_bool + { +% + \cs_if_exist:cTF { tikz@library@calc@loaded } + { + \int_set:Nn \l_@@_pos_arrow_int \c_one_int + \bool_set_false:N \l_@@_wrap_lines_bool + \tl_set_eq:NN \l_@@_tikz_code_tl + \c_@@_tikz_code_down_tl + } + { \@@_error:n { calc~not~loaded } } +%<*LaTeX> + } + { \@@_error:n { varwidth~not~loaded } } +% + } + } +% \end{macrocode} +% +% +% +% \begin{macrocode} +\seq_put_right:Nn \l_@@_options_Arrow_seq { down } +\seq_put_right:Nn \l_@@_options_Arrow_seq { up } +% \end{macrocode} +% +% +% \begin{macrocode} +\@@_msg_new:nn { varwidth~not~loaded } + { + You~can't~use~the~option~'\l_keys_key_tl'~because~ + you~don't~have~loaded~the~package~'varwidth'. \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +\@@_msg_new:nn { calc~not~loaded } + { + You~can't~use~the~option~'\l_keys_key_tl'~because~you~don't~have~loaded~the~ + Tikz~library~'calc'.You~should~add~'\token_to_str:N\usetikzlibrary{calc}'~ + ~in~the~preamble~of~your~document. \\ + \c_@@_option_ignored_str + } +% \end{macrocode} +% +% \begin{macrocode} +%<*plain-TeX> +\catcode `\@ = 12 +\ExplSyntaxOff +% +% \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}| +% +% +% \subsection*{Changes between versions 1.1 and 1.2} +% +% The package \pkg{witharrows} can now be loaded without having loaded +% previously \pkg{tikz} and the libraries |arrow.meta| and |bending| (this +% extension and these libraries are loaded silently by \pkg{witharrows}). +% +% New option |groups| (with a \emph{s}) +% +% +% \subsection*{Changes between versions 1.2 and 1.3} +% +% New options |ygap| and |ystart| for fine tuning. +% +% \subsection*{Changes between versions 1.3 and 1.4} +% +% The package \pkg{footnote} is no longer loaded by default. Instead, two +% options |footnote| and |footnotehyper| have been added. In particular, +% \pkg{witharrows} becomes compatible with \cls{beamer}. +% +% \subsection*{Changes between versions 1.4 and 1.5} +% +% The Tikz code used to draw the arrows can be changed with the option +% |tikz-code|. +% +% Two new options |code-before| and |code-after| have been added at the +% environment level. +% +% A special version of |\Arrow| is available in |code-after| in order to draw +% arrows in nested environments. +% +% A command |\MultiArrow| is available in |code-after| to draw arrows of other +% shapes. +% +% \subsection*{Changes between versions 1.5 and 1.6} +% +% The code has been improved to be faster and the Tikz library |calc| is no +% longer required. +% +% A new option |name| is available for the environments |{WithArrows}|. +% +% \subsection*{Changes between 1.6 and 1.7} +% +% New environments |{DispWithArrows}| and |{DispWithArrows*}|. +% +% \subsection*{Changes between 1.7 and 1.8} +% +% The numbers and tags of the environment |{DispWithArrows}| are now compatible +% with all the major LaTeX packages concerning references (\pkg{autonum}, +% \pkg{cleveref}, \pkg{fancyref}, \pkg{hyperref}, \pkg{prettyref}, +% \pkg{refstyle}, \pkg{typedref} and \pkg{varioref}) and with the options +% |showonlyrefs| and |showmanualtags| of \pkg{mathtools}. +% +% \subsection*{Changes between 1.8 and 1.9} +% +% New option |wrap-lines| for the environments |{DispWithArrows}| and +% |{DispWithArrows*}|. +% +% \subsection*{Changes between 1.9 and 1.10} +% +% If the option |wrap-lines| is used, the option ``|text width|'' of Tikz is +% still active: if the value given to ``|text width|'' is lower than the width +% computed by |wrap-lines|, this value is used to wrap the lines. +% +% The option |wrap-lines| is now fully compatible with the class option |leqno|. +% +% Correction of a bug: |\nointerlineskip| and |\makebox[.6\linewidth]{}| should +% be inserted in |{DispWithArrows}| only in vertical mode. +% +% \subsection*{Changes between 1.10 and 1.11} +% +% New commands |\WithArrowsNewStyle| and |\WithArrowsRightX|. +% +% \subsection*{Changes between 1.11 and 1.12} +% +% New command |\tagnextline|. +% +% New option |tagged-lines|. +% +% An option of position (|ll|, |lr|, |rl|, |rr| or |i|) is now allowed at the +% local level even if the option |group| or the option |groups| is used at the +% global or environment level. +% +% Compatibility of |{DispWithArrows}| with |\qedhere| of \pkg{amsthm}. +% +% Compatibility with the packages \pkg{refcheck}, \pkg{showlabels} and +% \pkg{listlbls}. +% +% The option |\AllowLineWithoutAmpersand| is deprecated because lines without +% ampersands are now always allowed. +% +% \subsection*{Changes between 1.12 and 1.13} +% +% Options |start-adjust|, |end-adjust| and |adjust|. +% +% This version is not stricty compatible with previous ones. To restore the +% behaviour of the previous versions, one has to use the option |adjust| with +% the value $0$~pt: +% +% \begin{Verbatim} +% \WithArrowsOptions{adjust = 0pt} +% \end{Verbatim} +% +% \subsection*{Changes between 1.13 and 1.14} +% +% New options |up| and |down| for the arrows. +% +% \smallskip +% Replacement of some options |O { }| in commands and environments defined with +% \pkg{xparse} by |! O { }| (a recent version of \pkg{xparse} introduced +% the specifier |!| and modified the default behaviour of the last optional +% arguments: +% |//www.texdev.net/2018/04/21/xparse-optional-arguments-at-the-end|). +% +% \smallskip +% Modification of the code of |\WithArrowsNewStyle| following a correction of a +% bug in \pkg{l3keys} in the version of \pkg{l3kernel} of 2019/01/28. +% +% New error message |Inexistent~v-node| to avoid a \pkg{pgf} error. +% +% The error |Option incompatible with 'group(s)'| was suppressed in the version +% 1.12 but this was a mistake since this error is used with the option |xoffset| +% at the local level. The error is put back. +% +% \subsection*{Changes between 1.14 and 1.15} +% +% Option |new-group| to start a new group of arrows (only available when the +% environment is composed with the option |groups|). +% +% Tikz externalization is now deactivated in the environments of the +% extension \pkg{witharrows}.\footnote{Before this version, there was an error +% when using \pkg{witharrows} with Tikz externalization. In any case, it's not +% possible to externalize the Tikz elements constructed by \pkg{witharrows} +% because they use the options |overlay| and |remember picture|.} +% +% \subsection*{Changes between 1.15 and 1.16} +% +% Option |no-arrows| +% +% The behaviour of |{DispWithArrows}| after an |\item| of a LaTeX list has been +% changed : no vertical is added. The previous behaviour can be restored with +% the option |standard-behaviour-with-items|. +% +% A given name can no longer be used for two distinct environments. However, +% it's possible to deactivate this control with the option +% |allow-duplicate-names|. +% +% +% \subsection*{Changes between 1.16 and 1.17} +% +% Option |format| +% +% \subsection*{Changes between 1.17 and 1.18} +% +% New option |<...>| for |{DispWithArrows}|. +% +% Option |subequations|. +% +% Warning when |{WithArrows}| or |{DispWithArrows}| ends by "\\". +% +% No space before an environnement |{DispWithArrows}| if we are at the beginning +% of a |{minipage}|. +% +% \subsection*{Changes between 1.18 and 2.0} +% +% A version of \pkg{witharrows} is available for plain-TeX. +% +% \PrintIndex +% +% \tableofcontents +% +% \endinput +% Local Variables: +% TeX-fold-mode: nil +% fill-column: 80 +% End: diff --git a/macros/generic/witharrows/witharrows.ins b/macros/generic/witharrows/witharrows.ins new file mode 100644 index 0000000000..bc0fccc6b3 --- /dev/null +++ b/macros/generic/witharrows/witharrows.ins @@ -0,0 +1,48 @@ +%% +%% Copyright (C) 2017-2019 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) 2017-2019 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}{LaTeX}} + \file{witharrows.tex}{\from{witharrows.dtx}{plain-TeX}}} +\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/macros/generic/witharrows/witharrows.pdf b/macros/generic/witharrows/witharrows.pdf new file mode 100644 index 0000000000..2ee53b5af7 Binary files /dev/null and b/macros/generic/witharrows/witharrows.pdf differ -- cgit v1.2.3