% C A S E S . S T Y ver 2.5 May 2002
%
% Copyright (C) 1993,1994,1995,2000,2002 by Donald Arseneau
% 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 subeqn.sty by Stephen Gildea; most of the rest is based
% on LaTeX's \eqnarray by Leslie Lamport and the LaTeX3 team.
%
% This provides a LaTeX environment {numcases} to produce multi-case
% equations with a separate equation number for each case. There is
% also {subnumcases} which numbers each case with the overall equation
% number plus a letter [8a, 8b, etc.]. The syntax is
%
% \begin{numcases}{left_side}
% case_1 & explanation_1 \\
% case_2 & explanation_2 \\
% ...
% case_n & explanation_n
% \end{numcases}
%
% Each case is a math formula, and each explanation is a piece of lr mode
% text (which may contain math mode in \(...\) or $...$). The explanations
% are optional. Equation numbers are inserted automatically, just as for
% the eqnarray environment. In particular, the \nonumber command suppresses
% an equation number and the \label command allows reference to a particular
% case. In a subnumcases environment, a \label in the left_side of the
% equation gives the overall equation number, without any letter.
%
% To use this package,
% include "\usepackage{cases}" after \documentclass. You may also
% specify "\usepackage[subnum]{cases}" to force *all* numcases
% environments to be treated as subnumcases.
%
% Question: Is there a {numcases*} environment for unnumbered cases?
% Answer: There is a {cases} environment in AMS-LaTeX, but it is just as
% convenient to stick with the canonical LaTeX array:
% \[ left side = \left\{ \begin{array}...\end{array} \right. \]
%
% Speaking of AMS-math, they use an entirely different system of equation
% numbering, and this package uses ordinary LaTeX numbering.
%
% - - - - -
% A simple example is:
% \begin{numcases}{|x|=}
% x, & for $x \geq 0$\\
% -x, & for $x < 0$
% \end{numcases}
%
% Giving:
% / x for x > 0 (1)
% |x| = < -
% \ -x for x < 0 (2)
%
% - - - - -
%
% 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}
%
% - - - begin definitions - - -
\ProvidesPackage{cases}[2002/05/02 ver 2.5 ]
\newenvironment{numcases}[1]%
{$$\numc@opts \setbox\z@\hbox
{\advance\c@equation\@ne\def\@currentlabel{\p@equation\theequation}% local
$\displaystyle {#1\null}\m@th$}%
\numc@setsub
\setbox\tw@\vbox\bgroup
\stepcounter{equation}\def\@currentlabel{\p@equation\theequation}%
\global\@eqnswtrue\m@th \everycr{}\tabskip\numc@left\let\\\@eqncr
\halign to\dimen@ii \bgroup \kern\wd\z@ \kern14\p@ % assume width of brace
\tabskip\z@skip \global\@eqcnt\@ne $\displaystyle{##}$\hfil
&\global\@eqcnt\tw@ \skip@10\p@ \advance\skip@\tw@\arraycolsep \hskip\skip@
##\unskip\hfil\tabskip\@centering% \unskip removes space if no explanations
&\global\@eqcnt\thr@@\hbox to\z@\bgroup\hss##\egroup\tabskip\z@skip\cr
}{\@@eqncr \egroup % end \halign, which does not contain first column or brace
\global\advance\c@equation\m@ne
%Measure the natural width of the alignment
\unskip\unpenalty\unskip\unpenalty \setbox\z@\lastbox % grab last line
\nointerlineskip \copy\z@ % then put it back
\global\dimen@i\wd\z@
\setbox\z@\hbox{\hskip-\numc@left\unhbox\z@}% Measure its natural width
\ifdim \wd\z@<\dimen@i \global\dimen@i\wd\z@ \fi
\egroup% end \vbox (box\tw@, box\z@ is restored to LHS)
\hbox to\dimen@ii{\m@th % assemble the whole equation
\hskip\numc@left
\hbox to\dimen@i{$\displaystyle \box\z@ % parameter #1
\dimen@\ht\tw@ \advance\dimen@\dp\tw@ % get size of brace
\left\{\vcenter to\dimen@{\vfil}\right.\n@space % make brace
$\hfil}\hskip\@centering % finished first part (filled whole line)
\kern-\dimen@ii % backspace the full width
$\vcenter{\box\tw@}$% overlay the alignment
}% end the \hbox to\dimen@ii
\numc@resetsub
$$\global\@ignoretrue}
\let\numc@setsub\relax
\let\numc@resetsub\relax
\def\subnumcases{\let\numc@setsub\subequations
\let\numc@resetsub\endsubequations \numcases}
\let\endsubnumcases\endnumcases
% declare subequations -- either defining them following the style of
% Gildea's subeqn.sty, or using the syntax of AMS-LaTeX if that is loaded.
\@ifundefined{c@parentequation}{% No AMS, define subequations from scratch:
%
% These versions of subequations follow the style of Gildea's subeqn.sty,
% but are thoroughly rewritten.
%
% You can change the labelling by redefining \thesubequation, but the names
% of the counters may be confusing: The sub-number is given by counter
% {equation}, while the overall equation number is given by {mainequation}.
% There are two ways to reference the overall equation number:
% through the value of \c@mainequation, as in \Roman{mainequation}, or
% through \themainequation, which gives the text of the normal \theequation.
% Refer to the local sub-number with \c@equation, as in \alph{equation}.
% The default numbering is like 13c, given by:
%
\def\thesubequation{\themainequation\alph{equation}}
%
% Some alternatives:
% \def\thesubequation{\themainequation.\Alph{equation}} % 13.C
% \def\thesubequation{\themainequation-\roman{equation}} % 13-iii
% \def\thesubequation{(\arabic{mainequation}\alph{equation})} % (13c)
% The third alternative should be used if a document style has
% declared \renewcommand{\@eqnnum}{\theequation} and
% \renewcommand{\theequation}{(\arabic{equation})}, which makes
% \ref put parentheses around regular equation numbers automatically.
%
\def\subequations{\refstepcounter{equation}%
\mathchardef\c@mainequation\c@equation
\let\@tempa\protect % * added protection
\def\protect{\noexpand\protect\noexpand}% *
\edef\themainequation{\theequation}\let\theequation\thesubequation
\let\protect\@tempa % *
\global\c@equation\z@}
%
\def\endsubequations{%
\global\c@equation\c@mainequation
\global\@ignoretrue}
%
% \begin{subeqnarray} works like \begin{subequations}\begin{eqnarray},
% with the added feature that a \label command given given at the very
% beginning of the first entry defines a label for the overall equation
% number.
%
\def\subeqnarray{\subequations\eqnarray\@ifnextchar\label{\@lab@subeqnarray}{}}
\def\endsubeqnarray{\endeqnarray\endsubequations}
\def\@lab@subeqnarray#1#2{\begingroup
\let\@currentlabel\themainequation #1{#2}\endgroup}
%
}{}% AMS \subequations already defined
\def\numc@left{\@centering}
\def\numc@opts{\dimen@ii\displaywidth}
\DeclareOption{subnum}{
\let\numc@setsub\subequations
\let\numc@resetsub\endsubequations }
\DeclareOption{fleqn}{
\def\numc@left{\mathindent}
\def\numc@opts{\displaywidth\linewidth
\dimen@ii\linewidth }
}
\ProcessOptions
\endinput
% Send problem reports to asnd@triumf.ca
Test file integrity: ASCII 32-57, 58-126: !"#$%&'()*+,-./0123456789
:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~