From 9d52a67c4dd12d828f99b735ed4970f3d338cb24 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Thu, 17 Aug 2017 21:17:10 +0000 Subject: witharrows (17aug17) git-svn-id: svn://tug.org/texlive/trunk@45056 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/doc/latex/witharrows/README.md | 9 + .../texmf-dist/doc/latex/witharrows/witharrows.pdf | Bin 0 -> 124003 bytes .../texmf-dist/doc/latex/witharrows/witharrows.tex | 785 +++++++++++++++++++++ 3 files changed, 794 insertions(+) create mode 100644 Master/texmf-dist/doc/latex/witharrows/README.md create mode 100644 Master/texmf-dist/doc/latex/witharrows/witharrows.pdf create mode 100644 Master/texmf-dist/doc/latex/witharrows/witharrows.tex (limited to 'Master/texmf-dist/doc/latex/witharrows') diff --git a/Master/texmf-dist/doc/latex/witharrows/README.md b/Master/texmf-dist/doc/latex/witharrows/README.md new file mode 100644 index 00000000000..10ca27cb4f7 --- /dev/null +++ b/Master/texmf-dist/doc/latex/witharrows/README.md @@ -0,0 +1,9 @@ +The LaTeX extension witharrows is distributed under the LPPL 1.3 license. + +This extension has been written by F. Pantigny (fpantigny at wanadoo point fr). + +This extension is entirely contained in a single file : witharrows.sty + +The extension witharrows gives a LaTeX environment {WithArrows} which is similar +to the environment {aligned} of amsmath but which gives the possibility to draw arrows +on the right side of the equations for explanations. \ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/witharrows/witharrows.pdf b/Master/texmf-dist/doc/latex/witharrows/witharrows.pdf new file mode 100644 index 00000000000..fe3b4175df5 Binary files /dev/null and b/Master/texmf-dist/doc/latex/witharrows/witharrows.pdf differ diff --git a/Master/texmf-dist/doc/latex/witharrows/witharrows.tex b/Master/texmf-dist/doc/latex/witharrows/witharrows.tex new file mode 100644 index 00000000000..675da4518ee --- /dev/null +++ b/Master/texmf-dist/doc/latex/witharrows/witharrows.tex @@ -0,0 +1,785 @@ +% This document is compatible with the following workflows : +% pdflatex, +% xelatex (with xdvipdfmx), +% latex --> dvips --> ps2pdf (or Adobe Distiller). +\documentclass{article} + +\usepackage{ifxetex} + +\ifxetex + \usepackage{xltxtra} +\else + \usepackage{expl3} + \usepackage{xparse} + \usepackage[T1]{fontenc} +\fi + +\usepackage{xspace} + + +\usepackage[dvipsnames]{xcolor} + +\usepackage{lmodern} + +\ifxetex + \usepackage[xetex]{geometry} +\else + \usepackage{geometry} +\fi + +\geometry{papersize={16.5cm,24cm},total={12.5cm,21cm},headheight=13.2pt,includeheadfoot,twoside,centering} + + +\usepackage{tikz} +\usetikzlibrary{calc} +\usetikzlibrary{arrows.meta} +\usetikzlibrary{bending} +\usetikzlibrary{decorations.pathreplacing} + + +\usepackage{footnote} + +\usepackage{witharrows} + +\usepackage{fancyvrb} +\usepackage{mathtools} + + +% this following lines only for this document + +\usepackage{amsfonts} + +\def\interitem{\vskip 7mm plus 2 mm minus 3mm} +\def\emphase#1{{\color{RoyalPurple}#1}} +\fvset{commandchars=\~\#\@,formatcom={\color{gray}}} +\DeclareMathOperator{\re}{Re} +\let\group\begingroup + + +\begin{document} + + +\parindent0pt + +\title{Extension witharrows, v. 1.0} + +\author{Fran\c cois Pantigny} + +\date{2017/08/17} + +\maketitle + + + +\begin{abstract} +The LaTeX package \verb|witharrows| gives an environment \verb|{WithArrows}| which is similar to environment +\verb|{aligned}| of \verb|amsmath| (and \verb|mathtools|) but gives the possibility to draw arrows on the right +side of the alignment. These arrows are usually used to give explanations concerning the mathematical calculus presented. +\end{abstract} + + +\vskip1cm + +This package uses Tikz to draw the arrows. It can be used with \verb|xelatex|, \verb|pdflatex| but also by the +classical workflow \verb|latex|-\verb|dvips|-\verb|ps2pdf| (or Distiller). Two compilations may be necessary. + +\medskip +This package gives an environment \verb|{WithArrows}| to construct alignments of equations with +arrows for the explanations on the right side : +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 ~emphase#\Arrow{we expand}@ \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{we expand} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + + + +\medskip +The arrow has been drawn with the command \verb|\Arrow| on the ligne from which it starts. The command \verb|\Arrow| +can be used anywhere on the line but the best way is to put it at the end. + + +\medskip +The ends of the lines of the tabular can be coded by \verb|\\| but also by \verb|\cr| (like in the command +\verb|\halign| of TeX). In fact, in an environment \verb|{WithArrows}|, the command \verb|\\| has no option for the +spacing between rows like in many environments of LaTeX. + + + + +\section{Options for the shape of the arrows} + +The commande \verb|\Arrow| has several options. These options can be put between square brackets, before, or after +the mandatory argument. + +The option \verb|jump| gives the number of lines the arrow must jump (the default value is, of course,~$1$) +\footnote{It's not possible to give a non-positive value to \texttt{jump}. See below the way to draw an arrow which +goes backwards.} +% +\begin{Verbatim} +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 \Arrow~emphase#[jump=2]@{we expand} \\ + & = (a+b)^2 + 2(a+b) +1 \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 \\ +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 \Arrow[jump=2]{we expand} \\ + & = (a+b)^2 + 2(a+b) +1 \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 \\ +\end{WithArrows}$ + + + + +\interitem +It's possible to put several arrows which start from the same line. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 ~emphase#\Arrow{}\Arrow{}[jump=2]@ \\ + & = (a+b)^2 + 2(a+b) +1 \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 \Arrow{}\Arrow{}[jump=2] \\ + & = (a+b)^2 + 2(a+b) +1 \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ + + +\interitem +The option \verb|xoffset| shift the arrows to the right (we usually don't want the arrows to be stucked +on the text). The default value of \verb|xoffset| is $3$~mm. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 +\Arrow[~emphase#xoffset=1cm@]{with \texttt{xoffset=1cm}} \\ + & = (a+b)^2 + 2(a+b) +1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 +\Arrow[xoffset=1cm]{with \texttt{xoffset=1cm}} \\ + & = (a+b)^2 + 2(a+b) +1 \\ +\end{WithArrows}$ + + + + +\interitem +The arrows are drawn with Tikz. That's why the command \verb|\Arrow| has an option +\verb|tikz| which can be used to give to the arrow (in fact, the command \verb|\path| of Tikz) the options +proposed by Tikz for such an arrow. The following example gives an blue thick arrow. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[~emphase#tikz={blue,thick}@]{we expand} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[tikz={blue,thick}]{we expand} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + + + +\interitem +It's also possible to change the arrowheadss. For example, we can draw an arrow which goes backwards +with the Tikz option~\verb|<-|. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow~emphase#[tikz=<-]@{we factorize} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[tikz=<-]{we factorize} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + + + +\interitem +It's also possible to suppress both tips of the arrow with the Tikz option \verb|-|. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[~emphase#tikz=-@]{very classical} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[tikz=-]{very classical} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + + + +\interitem +In order to have straight arrows instead of curved ones, we must use the Tikz option ``\verb|bend left = 0|''. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow~emphase#[tikz={bend left=0}]@{we expand} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[tikz={bend left=0}]{we expand} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + + + +\interitem +One of the most useful options is ``\verb|text width|'' to control the with of the text associated to the arrow. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 +\Arrow[jump=2,~emphase#tikz={text width=5.3cm}@]{We have done...} \\ + & = (a+b)^2 + 2(a+b) +1 \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = \bigl((a+b)+1\bigr)^2 +\Arrow[jump=2,tikz={text width=5.3cm}]{We have done a two-stages expansion but it would have been clever +to expand with the multinomial theorem.} \\ + & = (a+b)^2 + 2(a+b) +1 \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ + + +\interitem +If we want to change the font of the text associated to the arrow, we can, of course, put a command like +\verb|\bfseries|, \verb|\large| or \verb|\sffamily| at the beginning of the text. But, by default, the texts +are composed with a combination of \verb|\small| and \verb|\itshape|. When adding \verb|\bfseries| at the beginning +of the text, we won't suppress the \verb|\small| and the \verb|\itshape| and we will consequently have a text in a +bold, italic and small font. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{~emphase#\bfseries@ we expand} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{\bfseries we expand} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + + +\interitem +If we put commands \verb|\\| in the text to force newlines, a command of font placed in the beginning of the +text will have effect only until the first command \verb|\\| (like in a environment \verb|{tabular}|). That's why +Tikz gives a option \verb|font| to modify the font of the whole text. Nevertheless, if we use the option +\verb|tikz={font={\bfseries}}|, the default specification of \verb|\small| and \verb|\itshape| will be overwritten. +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[~emphase#tikz={font={\bfseries}}@]{we expand} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow[tikz={font={\bfseries}}]{we expand} \\ + & = a^2 + 2a + 1 +\end{WithArrows}$ + +\medskip +If we want exactly the same result as previously, we have to give to the option \verb|font| the value +\verb|{\itshape\small\bfseries}|. + + + + +\interitem +Almost all the options can be given directly to the environment \verb|WithArrows| (between square brackets). +In this case, they apply to all the arrows of the environment. +% +\begin{Verbatim} +$\begin{WithArrows}~emphase#[tikz=blue]@ +A & = \bigl((a+b)+1\bigr)^2 \Arrow{First expansion.} \\ + & = (a+b)^2 + 2(a+b) +1 \Arrow{Second expansion.} \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows}[tikz=blue] +A & = \bigl((a+b)+1\bigr)^2 \Arrow{First expansion.} \\ + & = (a+b)^2 + 2(a+b) +1 \Arrow{Second expansion.} \\ + & = a^2 + 2ab + b^2 + 2a + 2b +1 +\end{WithArrows}$ + + +\interitem +The environment \verb|{WithArrows}| has an option \verb|displaystyle|. With this option, all the elements are +composed in \verb|\displaystyle| (like in an environment \verb|{aligned}| of \verb|amsmath|). + +\medskip +Without the option \verb|displaystyle| : +% +\begin{Verbatim} +$\begin{WithArrows} +\int_0^1 (x+1)^2 dx +& = \int_0^1 (x^2+2x+1) dx +\Arrow{linearity of integration} \\ +& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\ +& = \frac13 + 2\frac12 + 1 \\ +& = \frac73 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +\int_0^1 (x+1)^2 dx +& = \int_0^1 (x^2+2x+1) dx +\Arrow{linearity of integration} \\ +& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\ +& = \frac13 + 2\frac12 + 1 \\ +& = \frac73 +\end{WithArrows}$ + + +\medskip +The same example with the option \verb|displaystyle| :\par\nobreak + +$\begin{WithArrows}[displaystyle] +\int_0^1 (x+1)^2 dx +& = \int_0^1 (x^2+2x+1) dx +\Arrow{linearity of integration} \\ +& = \int_0^1 x^2 dx + 2 \int_0^1 x dx + \int_0^1 dx \\ +& = \frac13 + 2\frac12 + 1 \\ +& = \frac73 +\end{WithArrows}$ + + +\interitem +Almost all the options can also be set at the document level with the command \verb|\WithArrowsOptions|. +In this case, the scope of the declarations is the current TeX group (these declarations are ``semi-global''). +For example, if we want all the environments \verb|{WithArrows}| composed in \verb|\displaystyle| with blue +arrows, we can write \verb|\WithArrowsOptions{displaystyle,tikz=blue}|.\footnote{It's also possible to give the + options directly when loading the package, \emph{i.e.} with the command \texttt{\string\usepackage} in the preamble.} +% +\begin{Verbatim} +~emphase#\WithArrowsOptions{displaystyle,tikz=blue}@ +$\begin{WithArrows} +\sum_{i=1}^n (x_i+1)^2 +& = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{by linearity}\\ +& = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n +\end{WithArrows}$ +\end{Verbatim} + +\begin{group} +\WithArrowsOptions{displaystyle,tikz=blue} +$\begin{WithArrows} +\sum_{i=1}^n (x_i+1)^2 +& = \sum_{i=1}^n (x_i^2+2x_i+1) \Arrow{by linearity}\\ +& = \sum_{i=1}^n x_i^2 + 2\sum_{i=1}^nx_i+ n +\end{WithArrows}$ +\end{group} + + +\interitem +The command \verb|\Arrow| is recognized only in the environments \verb|{WithArrows}|. If we have a command +\verb|\Arrow| previously defined, it's possible to go on using it outside the environments \verb|{WithArrows}|. + +However, a previouly defined command \verb|\Arrow| may still be useful in a environment \verb|{WithArrows}|. If we +want to use it in such an environment, it's possible to change the name of the command \verb|\Arrow| of the package +\verb|witharrows| : there is an option \verb|CommandName| for this purpose. The new name of the command must be +given to the option \emph{without} the leading backslash. +% +\begin{Verbatim} +\def\Arrow{\longmapsto} +$\begin{WithArrows}~emphase#[CommandName=Explanation]@ +f & = \bigl(x \Arrow (x+1)^2\bigr) +~emphase#\Explanation{we work directly on fonctions}@\\ +& = \bigl(x \Arrow x^2+2x+1\bigr) +\end{WithArrows}$ +\end{Verbatim} +% +\begin{group} +\def\Arrow{\longmapsto} +$\begin{WithArrows}[CommandName=Explanation] +f & = \bigl(x \Arrow (x+1)^2\bigr) +\Explanation{we work directly on fonctions}\\ +& = \bigl(x \Arrow x^2+2x+1\bigr) +\end{WithArrows}$ +\end{group} + + +\interitem +It's possible to use directly the nodes created by \verb|{WithArrows}| (see below) with explicit Tikz instructions +(in order, for example, to draw something that can't be drawn with the command \verb|\Arrow|). That's why a style +for the tips of the arrows has be created : \verb|TipsOfWithArrows|. By using this style, we will have homogeneous +tips for the arrows of the document. + +Therefore, if we want to modify the tips of the arrows of \verb|{WithArrows}|, we have to modify the style +\verb|TipsOfWithArrows|. +% +\begin{Verbatim} +\tikzset{TipsOfWithArrows/.style= { > = {Latex[scale=1.2,bend]}} } +\end{Verbatim} + + + + +\section{Precise positioning of the arrows} + + +The environment \verb|{WithArrows}| defines, during the composition of the array, two series of nodes materialized in +red in the following example.\footnote{The option \texttt{shownodes} can be used to materialize the nodes.} + +\smallskip +$\begin{WithArrows}[displaystyle,shownodes] +I +& = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) \\ +& = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\ +& = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\ +& =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u \\ +& =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\ +& =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\ +& =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u \\ +& =\frac{\pi}4\ln2-I +\end{WithArrows}$ + +\bigskip +The nodes of the left are at the end of each line of text. These nodes will be called \emph{left nodes}. +The nodes of the right side are aligned vertically on the right side of the array. These nodes will be called +\emph{right nodes}.\footnote{The names of the Tikz nodes created by \texttt{\{WithArrows\}} are \texttt{wa-}$n$\texttt{-l} and + \texttt{wa-}$n$\texttt{-r} where $n$~is the number of the line. It's possible to refer to these Tikz nodes after the + environment (one should use the options \texttt{remember picture} and \texttt{overlay} and also + \texttt{TipsOfWithArrows} and \texttt{->} in order to have the same arrowheads).} + +By default, the arrows use the right nodes. We will say that they are in \verb|rr| mode ($r$ for \emph{right}). +These arrows are \verb|vertical| (we will say that an arrow is \emph{vertical} when its two ends have the +same abscissa). + + +\smallskip +However, it's possible to use the left nodes, or a combination of left and right nodes, with one of the options +\verb|lr|, \verb|rl| and \verb|ll| ($l$ for \emph{left}). Those arrows are, usually, not vertical. + + +Therefore +$\begin{WithArrows}[displaystyle] +I +& = \int_{\frac{\pi}4}^0 \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)(-d u) +\Arrow[lr]{This arrow uses the \texttt{lr} option.}\\ +& = \int_0^{\frac{\pi}4} \ln\Bigl(1+\tan\left(\tfrac{\pi}4-u\right)\Bigr)d u \\ +& = \int_0^{\frac{\pi}4}\ln\left(1+\frac{1-\tan u}{1+\tan u}\right)\, d u \\ +& =\int_0^{\frac{\pi}4}\ln\left(\frac{1+\tan u+1-\tan u}{1+\tan u}\right) d u +\Arrow[ll,jump=2,tikz={text width = 5cm}]{This arrow uses a \texttt{ll} option and a \texttt{jump} equal to $2$}\\ +& =\int_0^{\frac{\pi}4} \ln\left(\frac2{1+\tan u}\right)\, d u\\ +& =\int_0^{\frac{\pi}4}\bigl(\ln2-\ln(1+\tan u)\bigr)\, d u \\ +& =\frac{\pi}4\ln2-\int_0^{\frac{\pi}4}\ln(1+\tan u)\, d u \\ +& =\frac{\pi}4\ln2-I +\end{WithArrows}$ + + + +\interitem +There is also an option called \texttt{i} ($i$ for \emph{intermediate}). With this option, the arrow is vertical +and at the leftmost position. + +% +\begin{Verbatim} +$\begin{WithArrows} +(a+b)(a+ib)(a-b)(a-ib) +& = (a+b)(a-b)\cdot(a+ib)(a-ib) \\ +& = (a^2-b^2)(a^2+b^2) \Arrow~emphase#[i]@{because $(x-y)(x+y)=x^2-y^2$}\\ +& = a^4-b^4 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +(a+b)(a+ib)(a-b)(a-ib) +& = (a+b)(a-b)\cdot(a+ib)(a-ib) \\ +& = (a^2-b^2)(a^2+b^2) \Arrow[i]{because $(x-y)(x+y)=x^2-y^2$}\\ +& = a^4-b^4 +\end{WithArrows}$ + + +\interitem +The environment \verb|{WithArrows}| gives also a \verb|group| option. With this option, \emph{all} the +arrows of the environment are grouped on a same vertical line and at a leftmost position. +% +\begin{Verbatim}[formatcom=\small\color{gray}] +$\begin{WithArrows}~emphase#[displaystyle,group]@ +2xy'-3y=\sqrt x +& \Longleftrightarrow 2x(K'y_0+Ky_0')-3Ky_0 = \sqrt x \\ +& \Longleftrightarrow 2xK'y_0 + K(2xy_0'-3y_0) = \sqrt x \\ +& \Longleftrightarrow 2x K'y_0 = \sqrt x \Arrow{...}\\ +... +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows}[displaystyle,group] +2xy'-3y=\sqrt x +& \Longleftrightarrow 2x(K'y_0+Ky_0')-3Ky_0 = \sqrt x \\ +& \Longleftrightarrow 2xK'y_0 + K(2xy_0'-3y_0) = \sqrt x \\ +& \Longleftrightarrow 2x K'y_0 = \sqrt x \Arrow{We remplace $y_0$ by its value.}\\ +& \Longleftrightarrow 2xK'x^{\frac32} = x^{\frac12} \Arrow{simplification of the $x$}\\ +& \Longleftrightarrow K' = \tfrac1{2x²} \Arrow{antiderivation}\\ +& \Longleftrightarrow K = -\tfrac1{2x} +\end{WithArrows}$ + + +\bigskip +If desired, the option \verb|group| can be given to the command \verb|WithArrowsOptions| so that it will become the +default value. + + +\section{Comparison with the environment \{aligned\}} + + + +\verb|{WithArrows}| bears similarities with the environment \verb|{aligned}| of the extension +\verb|amsmath|. These are only similarities because \verb|{WithArrows}| has not been written upon the environment +\verb|{aligned}|. + +In paticular, the command \verb|\\| of the end of line has no option to change the row spacings. In fact, this +command \verb|\\| can be replaced, in a environment \verb|{WithArrows}| by a \verb|\cr| of TeX. That's what we will +do in the balance of this document. + + + + +\interitem +If desired, it's possible to change the spacing between two given lines by putting a command +\verb|\vspace| in a \verb|\noalign| (which is a low level command of TeX to insert extraordinary elements between +the lines of an array). +% +\begin{Verbatim} +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{we expand} \cr +~emphase#\noalign{\vspace{3mm}}@ + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{we expand} \cr +\noalign{\vspace{3mm}} + & = a^2 + 2a + 1 +\end{WithArrows}$ + + +\interitem +In the environments of \verb|amsmath|, the spacing between lines is fixed by a parameter called +\verb|\jot| and that's also the case for the environment \verb|{WithArrows}|. An option \verb|jot| has been given +to the environment \verb|{WithArrows}| in order to change the value of this parameter \verb|\jot| for an given environment. +% +\begin{Verbatim} +$\begin{WithArrows}[displaystyle,~emphase#jot=2mm@] +F & = \frac12G \Arrow{we expand}\cr + & = H + \frac12K \Arrow{we go on}\cr + & = K +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows}[displaystyle,jot=2mm] +F & = \frac12G \Arrow{we expand}\cr + & = H + \frac12K \Arrow{we go on}\cr + & = K +\end{WithArrows}$ + + +\interitem +Like the environment \verb|{aligned}|, \verb|{WithArrows}| has an option of placement which can assume the values +\verb|t|, \verb|c| or \verb|b|. However, the default value is not \verb|c| but \verb|t|. If desired, it's possible +to have the \verb|c| value as the default with the command \verb|WithArrowsOptions{c}| at the beginning of the document. +% +\begin{Verbatim} +~emphase#Et donc\enskip@ +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{we expand} \cr + & = a^2 + 2a + 1 +\end{WithArrows}$ +\end{Verbatim} + +Et donc\enskip +$\begin{WithArrows} +A & = (a+1)^2 \Arrow{we expand} \cr + & = a^2 + 2a + 1 +\end{WithArrows}$ + +\bigskip +The value \verb|c| may be useful, for example, if we want to add curly braces : + +\smallskip +\begin{Verbatim} +On pose\enskip $~emphase#\left\{@ +\begin{WithArrows}~emphase#[c]@ +f(x) & = 3x^3+2x^2-x+4 +\Arrow[tikz=-]{both are polynoms}\cr +g(x) & = 5x^2-5x+6 +\end{WithArrows} +~emphase#\right.@$ +\end{Verbatim} + + + + +On pose\enskip $\left\{ +\begin{WithArrows}[c] +f(x) & = 3x^3+2x^2-x+4 +\Arrow[tikz=-]{both are polynoms}\cr +g(x) & = 5x^2-5x+6 +\end{WithArrows} +\right.$ + + +\interitem +Unlike \verb|{aligned}|, the environment \verb|{WithArrows}| uses \verb|\textstyle| by default. + +Once again, it's possible to change this behaviour with \verb|WithArrowsOptions| : + +\quad \verb|WithArrowsOptions{displaystyle}|. + + +\smallskip +The following example is composed with \verb|{aligned}| :\par\nobreak + +\smallskip +$\left\{ +\begin{aligned} +\sum_{i=1}^n (x_i+1)^2 +& = \sum_{i=1}^n (x_i^2 + 2x_i+1) \\ +& = \sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^nx_i + n +\end{aligned} +\right.$% + + +\medskip +The following is composed with \verb|{WithArrows}[c,displaystyle]|. The results are stricly identical.\par\nobreak + +\smallskip +$\left\{ +\begin{WithArrows}[c,displaystyle] +\sum_{i=1}^n (x_i+1)^2 +& = \sum_{i=1}^n (x_i^2 + 2x_i+1) \\ +& = \sum_{i=1}^n x_i^2 + 2 \sum_{i=1}^nx_i + n +\end{WithArrows} +\right.$% + + + + +\section{Examples} + +It's possible to use the environment \verb|{WithArrows}| with making use of the left column only, or the right +column only. +% +\begin{Verbatim} +$\begin{WithArrows} +&f(x) \ge g(x) \Arrow{by squaring both sides} \cr +& f(x)^2 \ge g(x)^2 \Arrow{by moving to left side} \cr +& f(x)^2 - g(x)^2 \ge 0 +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows} +&f(x) \ge g(x) \Arrow{by squaring both sides} \cr +& f(x)^2 \ge g(x)^2 \Arrow{by moving to left side} \cr +& f(x)^2 - g(x)^2 \ge 0 +\end{WithArrows}$ + + +\interitem +Here is an example with a loop flow. +% +\begin{Verbatim}[formatcom=\small\color{gray}] +$\begin{WithArrows}[tikz={font={\tiny}}] +a.\;& f \text{ est continuous on } E +\Arrow{(1)}\Arrow[tikz=<-,jump=4,xoffset=1cm]{(5)}\cr +b.\;& f \text{ est continuous in } 0 +\Arrow{(2)}\cr +c.\;& f \text{ is bounded on the unit sphere} +\Arrow{(3)}\cr +d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| +\Arrow{(4)}\cr +e.\;& f \text{ is lipschitzian} +\end{WithArrows}$ +\end{Verbatim} + +$\begin{WithArrows}[tikz={font={\tiny}}] +a.\;& f \text{ est continuous on } E +\Arrow{(1)}\Arrow[tikz=<-,jump=4,xoffset=1cm]{(5)}\cr +b.\;& f \text{ est continuous in } 0 +\Arrow{(2)}\cr +c.\;& f \text{ is bounded on the unit sphere} +\Arrow{(3)}\cr +d.\;& \exists K > 0\quad \forall x \in E\quad \|f(x)\| \le K \|x\| +\Arrow{(4)}\cr +e.\;& f \text{ is lipschitzian} +\end{WithArrows}$ + +\interitem +The option \verb|font| of Tikz contains in fact a list of tokens which will be placed at the beginning of the text. + +These tokens can be true commands for a changement of font (like \verb|\bfseries| or \verb|\sffamily|) but can also +be, in fact, any TeX command. + +In the following example, the argument of \verb|font| is the token list \verb|\tiny\counter| where +\verb|\counter| is a command which increment a counter previously defined and display its new value. Thus, the +arrows are automatically numbered. +% +\begin{Verbatim}[formatcom=\small\color{gray}] +\newcounter{MyCounter} +\newcommand{\counter}{\stepcounter{MyCounter}\theMyCounter.} +$\begin{WithArrows}[tikz={~emphase#font={\tiny\counter}@}] +A(x) +& = B(x) \Arrow{} \cr +& = C(x) \Arrow{} \cr +& = C(x) \Arrow{} \cr +& = E(x) \Arrow{} \cr +& = F(x) \Arrow{} \cr +& = G(x) +\end{WithArrows}$ +\end{Verbatim} + +\begin{group} +\newcounter{MyCounter} +\newcommand{\counter}{\stepcounter{MyCounter}\theMyCounter.} +$\begin{WithArrows}[tikz={font={\tiny\counter}}] +A(x) +& = B(x) \Arrow{} \cr +& = C(x) \Arrow{} \cr +& = C(x) \Arrow{} \cr +& = E(x) \Arrow{} \cr +& = F(x) \Arrow{} \cr +& = G(x) +\end{WithArrows}$ +\end{group} + + + +\end{document} + + + + + -- cgit v1.2.3