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diff --git a/macros/latex/contrib/cases/cases.tex b/macros/latex/contrib/cases/cases.tex index 93311c2b1d..f2bb343590 100644 --- a/macros/latex/contrib/cases/cases.tex +++ b/macros/latex/contrib/cases/cases.tex @@ -1,148 +1,210 @@ \documentclass[DIV=9, pagesize=auto]{scrartcl} -\usepackage{fixltx2e} \usepackage{lmodern} \usepackage[T1]{fontenc} \usepackage{textcomp} \usepackage{amsmath} \usepackage{cases} \usepackage{microtype} -\usepackage{hyperref} - +\usepackage{shortvrb} +\usepackage[colorlinks]{hyperref} +\MakeShortVerb" +\newcommand*\kp[1]{\kern#1pt} \newcommand*{\fancybreak}{% - \par - \nopagebreak\medskip\nopagebreak - \noindent\null\hfill$*\quad*\quad*\quad$\hfill\null\par - \nopagebreak\medskip\pagebreak[0]% + \par \medbreak \vspace{0pt plus 1cm}\penalty 500 \vspace{0pt plus -1cm}% } \newcommand*{\mail}[1]{\href{mailto:#1}{\texttt{#1}}} \newcommand*{\pkg}[1]{\textsf{#1}} \newcommand*{\cmd}[1]{\texttt{\string#1}} \newcommand*{\env}[1]{\texttt{#1}} \newcommand*{\meta}[1]{\textlangle\textsl{#1}\textrangle} +\newcommand*{\opt}[1]{\texttt{[#1]}} -\addtokomafont{title}{\rmfamily} +%\addtokomafont{title}{\rmfamily} -\title{The \pkg{cases} package\thanks{This manual corresponds to \pkg{cases}~v2.5, dated~May 2002.}} +\title{The \pkg{cases} package% + \textnormal{\thanks{~~This manual corresponds to \pkg{cases}~v3.0, dated 2020/02/22.}}} \author{Donald Arseneau\\\mail{asnd@triumf.ca}} -\date{May 2002} +\date{Feb 2020} \begin{document} \maketitle -\begingroup -\small +\begin{small} \noindent -Copyright \textcopyright~1993, 1994, 1995, 2000, 2002 by Donald Arseneau, \mail{asnd@triumf.ca}. +Copyright \textcopyright~1993, 1994, 1995, 2000, 2002, 2020 by Donald Arseneau, \mail{asnd@triumf.ca}. These macros may be freely transmitted, reproduced, or modified provided that this notice is left intact. Sub-equation numbering -is based on \pkg{subeqn.sty} by Stephen Gildea; most of the rest is based -on \LaTeX's \cmd{\eqnarray} by Leslie Lamport and the \LaTeX3 team. +is based on \pkg{subeqn.sty} by Stephen Gildea; parts are based +on \LaTeX's \env{eqnarray} by Leslie Lamport and the \LaTeX3 team; +and some on amsmath.sty by the American Mathematical Society. \par -\endgroup +\end{small} -\fancybreak +\section*{Description} -This provides a \LaTeX\ environment \verb+{numcases}+ to produce multi-case -equations with a separate equation number for each case. There is -also \verb+{subnumcases}+ which numbers each case with the overall equation +The \pkg{cases} package provides a \LaTeX\ environment \env{numcases} to produce +multi-case equations with a separate equation number for each case. There is +also \env{subnumcases} which numbers each case with the overall equation number plus a letter [8a, 8b, etc.]. The syntax is % -\begin{verbatim} -\begin{numcases}{left_side} - case_1 & explanation_1 \\ - case_2 & explanation_2 \\ - ... - case_n & explanation_n -\end{numcases} -\end{verbatim} +\begin{flushleft} +"\begin{numcases}{"~\meta{left side}~"}"\\ +\quad \meta{case 1\kp1} "&" \meta{explanation 1\kp1} "\\" \\ +\quad \meta{case 2\kp2} "&" \meta{explanation 2\kp2} "\\" \\ +\quad .~.~.\\ +\quad \meta{case $n$} "&" \meta{explanation $n$} \\ +"\end{numcases}" +\end{flushleft} % -Each \meta{case} is a math formula, and each \meta{explanation} is a piece of lr mode -text (which may contain math mode in \verb+\(...\)+ or \verb+$...$+). The explanations +Each \meta{case} is a math formula, to be typeset in display-math mode, like +in a regular numbered equation. Each \meta{explanation} is a piece of lr-mode +text (which may contain math mode in "\("\,\dots"\)" or "$"\,\dots"$"). The explanations are optional. Equation numbers are inserted automatically, just as for the \env{eqnarray} environment. In particular, the \cmd{\nonumber} command suppresses an equation number and the \cmd{\label} command allows reference to a particular -case. In a \env{subnumcases} environment, a \cmd{\label} in the \meta{left\_side} of the +case. In a \env{subnumcases} environment, a \cmd{\label} in the \meta{left side} of the equation gives the overall equation number, without any letter. To use this package, -include ``\verb+\usepackage{cases}+'' after ``\cmd{\documentclass}''. You may also -specify ``\verb+\usepackage[subnum]{cases}+'' to force \emph{all} \env{numcases} -environments to be treated as \env{subnumcases}. - -\emph{Question:} Is there a \verb+{numcases*}+ environment for -unnumbered cases?\\ -\emph{Answer:} There is a \verb+{cases}+ -environment in \AmS-\LaTeX, but it is just as convenient to stick -with the canonical \LaTeX\ array: -% -\begin{verbatim} -\[ left side = \left\{ \begin{array}...\end{array} \right. \] -\end{verbatim} -% -Speaking of \pkg{\AmS-math}, they use an entirely different system -of equation numbering, and this package uses ordinary \LaTeX\ % -numbering. +include "\usepackage{cases}" after \cmd{\documentclass}, and also after +"\usepackage{amsmath}" if you are using that. \fancybreak -\noindent +\noindent \emph{Question:} Is there a \env{numcases*} environment for +unnumbered cases?\\ +\emph{Answer:} That would have the natural name \env{cases}, and it is +provided by \AmS-\LaTeX\ (\pkg{amsmath} package), or by this package given +the \opt{cases} option. It can also be achieved by using an ordinary \LaTeX\ array +between `"\left\lbrace\ "' and `"\right."'. + +Speaking of \pkg{amsmath} and package options, there are differences between the +style used for this package and the cases done by \pkg{amsmath} (see below), but cases.sty +has options to increase compatibility. Here is the full list of options for +this package. +\begin{description} +\item[\opt{subnum}] Force all \env{numcases} environments to be treated as + \env{subnumcases}. +\item[\opt{amsstyle}] For compatibility with \pkg{amsmath}'s \env{cases}, make \env{numcases} + use cramped math style ("\textstyle"), and put explanations in the same math style. +\item[\opt{casesstyle}] Change \pkg{amsmath}'s \env{cases} environment to work in the text/math style + of \env{numcases}. +\item[\opt{cases}] Define a \env{cases} environment for use without \pkg{amsmath}. (This + is actually the same as the \opt{casesstyle} option.) +\item[\opt{fleqn}] Flush-left equation alignment, indented by \cmd{\mathindent} + or \cmd{\mathmargin}. (Usually inherited from the \cmd{\documentclass} options.) +\item[\opt{leqno}] Left-side equation numbering (usually inherited from the \cmd{\documentclass} + options). This looks silly with numbered cases! +\end{description} + +\section*{Examples} + A simple example is: % \begin{verbatim} -\begin{numcases}{|x|=} - x, & for $x \geq 0$\\ - -x, & for $x < 0$ -\end{numcases} + \begin{numcases} {|x|=} + x, & for $x \geq 0$\\ + -x, & for $x < 0$ + \end{numcases} \end{verbatim} % Giving: % -\begin{numcases}{|x|=} +\begin{numcases} {|x|=} x, & for $x \geq 0$\\ -x, & for $x < 0$ \end{numcases} \fancybreak - \noindent -Another example is calculating the square root of $c+id$. First compute -\phantomsection -\begin{subnumcases}{\label{w} w\equiv} - 0 & $c = d = 0$\label{wzero}\\ - \sqrt{|c|}\,\sqrt{\frac{1 + \sqrt{1+(d/c)^2}}{2}} & $|c| \geq |d|$ \\ - \sqrt{|d|}\,\sqrt{\frac{|c/d| + \sqrt{1+(c/d)^2}}{2}} & $|c| < |d|$ +Another example, employing sub-numbering, is calculating the square root +of a complex number $c+id$. First compute +\begin{subnumcases} {\label{weqn} w\equiv} + 0 & for $c = d = 0$\label{wzero}\\ + \sqrt{|c|}\,\sqrt{\frac{1 + \sqrt{1+(d/c)^2}}{2}} & for $|c| \geq |d|$ \\ + \sqrt{|d|}\,\sqrt{\frac{|c/d| + \sqrt{1+(c/d)^2}}{2}} & for $|c| < |d|$ \end{subnumcases} -Then, using $w$ from eq.~(\ref{w}), the square root is -\begin{subnumcases}{\sqrt{c+id}=} - 0 & $w=0$ (case \ref{wzero})\\ - w+i\frac{d}{2w} & $w \neq 0$, $c \geq 0$ \\ - \frac{|d|}{2w} + iw & $w \neq 0$, $c < 0$, $d \geq 0$ \\ - \frac{|d|}{2w} - iw & $w \neq 0$, $c < 0$, $d < 0$ +Then, using $w$ from eq.~(\ref{weqn}), the square root is +\begin{subnumcases}{\label{sqrteqn} \sqrt{c+id}=} + 0\,, \label{aaa} & $w=0$ (case \ref{wzero})\\ + w+i\frac{d}{2w}\,, & $w \neq 0$, $c \geq 0$ \\ + \frac{|d|}{2w} + iw\,, & $w \neq 0$, $c < 0$, $d \geq 0$ \\ + \frac{|d|}{2w} - iw\,,\label{ddd} & $w \neq 0$, $c < 0$, $d < 0$ \end{subnumcases} - -\pagebreak[2] - -\noindent -This was produced by: -% -\small +These equations, eq.~(\ref{weqn}) and (\ref{sqrteqn}), were produced by: +\begin{small} \begin{verbatim} -Another example is calculating the square root of $c+id$. First compute -\begin{subnumcases}{\label{w} w\equiv} - 0 & $c = d = 0$\label{wzero}\\ -\sqrt{|c|}\,\sqrt{\frac{1 + \sqrt{1+(d/c)^2}}{2}} & $|c| \geq |d|$ \\ -\sqrt{|d|}\,\sqrt{\frac{|c/d| + \sqrt{1+(c/d)^2}}{2}} & $|c| < |d|$ +Another example, employing sub-numbering, is calculating the square root +of a complex number $c+id$. First compute +\begin{subnumcases} {\label{weqn} w\equiv} + 0 & for $c = d = 0$\label{wzero}\\ + \sqrt{|c|}\,\sqrt{\frac{1 + \sqrt{1+(d/c)^2}}{2}} & for $|c| \geq |d|$ \\ + \sqrt{|d|}\,\sqrt{\frac{|c/d| + \sqrt{1+(c/d)^2}}{2}} & for $|c| < |d|$ \end{subnumcases} -Then, using $w$ from eq.~(\ref{w}), the square root is -\begin{subnumcases}{\sqrt{c+id}=} -0 & $w=0$ (case \ref{wzero})\\ -w+i\frac{d}{2w} & $w \neq 0$, $c \geq 0$ \\ -\frac{|d|}{2w} + iw & $w \neq 0$, $c < 0$, $d \geq 0$ \\ -\frac{|d|}{2w} - iw & $w \neq 0$, $c < 0$, $d < 0$ +Then, using $w$ from eq.~(\ref{weqn}), the square root is +\begin{subnumcases}{\label{sqrteqn} \sqrt{c+id}=} + 0\,, & $w=0$ (case \ref{wzero})\\ + w+i\frac{d}{2w}\,, & $w \neq 0$, $c \geq 0$ \\ + \frac{|d|}{2w} + iw\,, & $w \neq 0$, $c < 0$, $d \geq 0$ \\ + \frac{|d|}{2w} - iw\,, & $w \neq 0$, $c < 0$, $d < 0$ \end{subnumcases} \end{verbatim} +\end{small} + +\section*{Compatibilibility with amsmath} + +When used in conjunction with amsmath.sty, the cases package will obey the the variant +commands \cmd{\tag}, \cmd{\notag}, and \cmd{\mathmargin}, however the formatting details +differ between \pkg{amsmath}'s \env{cases} environment and \env{numcases}. +For comparison, equation~(\ref{weqn}) formatted by \pkg{amsmath} and its \env{cases} environment +may be entered as +\begin{flushleft}\small +\begin{verbatim} +\begin{equation} +\label{wams} w \equiv +\begin{cases} + 0 & \text{for}\ c = d = 0\\ + \sqrt{|c|}\,\sqrt{\frac{1+\sqrt{1+(d/c)^2}}{2}} &\text{for}\ |c| \geq |d|\\ + \sqrt{|d|}\,\sqrt{\frac{|c/d| + \sqrt{1+(c/d)^2}}{2}} &\text{for}\ |c|<|d| +\end{cases} +\end{equation} +\end{verbatim} +\end{flushleft} +which produces +\begin{equation} +\label{wams} w\equiv +\begin{cases} + 0 & \text{for }c = d = 0\\ + \sqrt{|c|}\,\sqrt{\frac{1+\sqrt{1+(d/c)^2}}{2}} & \text{for}\ |c| \geq |d| \\ + \sqrt{|d|}\,\sqrt{\frac{|c/d| + \sqrt{1+(c/d)^2}}{2}} & \text{for}\ |c| < |d| +\end{cases} +\end{equation} +To get this more compact layout with \env{numcases} you can insert "\textstyle" +at the beginning of each case, as needed, or use the \pkg{cases} +package option \opt{amsstyle}. +To have the \env{cases} environment give the more open layout of eq.~(\ref{weqn}) +you can put "\displaystyle" at the beginning of each case, or use the +option \opt{casesstyle} for the \pkg{cases} package. (Yes these go with the cases package, they +are not options for amsmath.) + +For full disclosure, even without any relevant package options, cases.sty will +slightly adjust the \env{cases} environment from \pkg{amsmath}, by adding a little +space after the left brace. + +\section*{Sub-numbering} +For control of the sub-equation-numbering style, see the +\AmS-\LaTeX\ documentation for \env{subequations}, currently +in section 3.11.3. If you are not using amsmath, that documentation +still mostly applies, except the name for regular equation numbers +is then `mainequation' instead of `parentequation'. Also, the +sub-numbering style can be controlled more easily by defining +\cmd{\thesubequation}. An example for capitalized letters is +\begin{verbatim} +\renewcommand\thesubequation{\themainequation.\Alph{equation}} % 13.C +\end{verbatim} + \end{document} |