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\documentclass[DIV=9, pagesize=auto]{scrartcl}
\usepackage{fixltx2e}
\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage{textcomp}
\usepackage{amsmath}
\usepackage{cases}
\usepackage{microtype}
\usepackage{hyperref}
\newcommand*{\fancybreak}{%
\par
\nopagebreak\medskip\nopagebreak
\noindent\null\hfill$*\quad*\quad*\quad$\hfill\null\par
\nopagebreak\medskip\pagebreak[0]%
}
\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}
\addtokomafont{title}{\rmfamily}
\title{The \pkg{cases} package\thanks{This manual corresponds to \pkg{cases}~v2.5, dated~May 2002.}}
\author{Donald Arseneau\\\mail{asnd@triumf.ca}}
\date{May 2002}
\begin{document}
\maketitle
\begingroup
\small
\noindent
Copyright \textcopyright~1993, 1994, 1995, 2000, 2002 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.
\par
\endgroup
\fancybreak
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
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}
%
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
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
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.
\fancybreak
\noindent
A simple example is:
%
\begin{verbatim}
\begin{numcases}{|x|=}
x, & for $x \geq 0$\\
-x, & for $x < 0$
\end{numcases}
\end{verbatim}
%
Giving:
%
\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}} & $|c| < |d|$
\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 & $w \neq 0$, $c < 0$, $d < 0$
\end{subnumcases}
\pagebreak[2]
\noindent
This was produced by:
%
\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}} & $|c| < |d|$
\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 & $w \neq 0$, $c < 0$, $d < 0$
\end{subnumcases}
\end{verbatim}
\end{document}
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