<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%  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 &amp; explanation_1 \\
%   case_2 &amp; explanation_2 \\
%   ...
%   case_n &amp; 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, &amp; for $x \geq 0$\\
%    -x, &amp; for $x &lt; 0$
%    \end{numcases}
%
%  Giving:
%                    / x   for x &gt; 0              (1)
%             |x| = &lt;            -
%                    \ -x  for x &lt; 0              (2)
% 
% - - - - -   
%
% Another example is calculating the square root of $c+id$. First compute
% \begin{subnumcases}{\label{w} w\equiv}
%  0    &amp; $c = d = 0$\label{wzero}\\
% \sqrt{|c|}\,\sqrt{\frac{1 + \sqrt{1+(d/c)^2}}{2}}   &amp; $|c| \geq |d|$ \\
% \sqrt{|d|}\,\sqrt{\frac{|c/d| + \sqrt{1+(c/d)^2}}{2}}   &amp; $|c| &lt; |d|$
% \end{subnumcases}
% Then, using $w$ from eq.~(\ref{w}), the square root is
% \begin{subnumcases}{\sqrt{c+id}=}
% 0                    &amp; $w=0$ (case \ref{wzero})\\
% w+i\frac{d}{2w}      &amp; $w \neq 0$, $c \geq 0$ \\
% \frac{|d|}{2w} + iw  &amp; $w \neq 0$, $c &lt; 0$, $d \geq 0$ \\
% \frac{|d|}{2w} - iw  &amp; $w \neq 0$, $c &lt; 0$, $d &lt; 0$ 
% \end{subnumcases}     
%
%  - - -  begin definitions - - - 
 
\ProvidesPackage{cases}[2002/05/02 ver 2.5 ]

\newenvironment{numcases}[1]%
{$$\numc@opts \setbox\z@\hbox
  {\advance\c@equation\@ne\def\@currentlabel{\p@equation\theequation}% local
  $\displaystyle {#1\null}\m@th$}%
 \numc@setsub 
 \setbox\tw@\vbox\bgroup
  \stepcounter{equation}\def\@currentlabel{\p@equation\theequation}% 
  \global\@eqnswtrue\m@th \everycr{}\tabskip\numc@left\let\\\@eqncr
  \halign to\dimen@ii \bgroup \kern\wd\z@ \kern14\p@ % assume width of brace
    \tabskip\z@skip \global\@eqcnt\@ne $\displaystyle{##}$\hfil 
   &amp;\global\@eqcnt\tw@ \skip@10\p@ \advance\skip@\tw@\arraycolsep \hskip\skip@
    ##\unskip\hfil\tabskip\@centering% \unskip removes space if no explanations
   &amp;\global\@eqcnt\thr@@\hbox to\z@\bgroup\hss##\egroup\tabskip\z@skip\cr
}{\@@eqncr \egroup % end \halign, which does not contain first column or brace
 \global\advance\c@equation\m@ne 
%Measure the natural width of the alignment
 \unskip\unpenalty\unskip\unpenalty \setbox\z@\lastbox % grab last line
 \nointerlineskip \copy\z@ % then put it back
 \global\dimen@i\wd\z@ 
 \setbox\z@\hbox{\hskip-\numc@left\unhbox\z@}% Measure its natural width
 \ifdim \wd\z@&lt;\dimen@i \global\dimen@i\wd\z@ \fi
\egroup% end \vbox (box\tw@, box\z@ is restored to LHS)
\hbox to\dimen@ii{\m@th % assemble the whole equation
  \hskip\numc@left 
  \hbox to\dimen@i{$\displaystyle \box\z@ % parameter #1
    \dimen@\ht\tw@ \advance\dimen@\dp\tw@ % get size of brace
    \left\{\vcenter to\dimen@{\vfil}\right.\n@space % make brace
    $\hfil}\hskip\@centering % finished first part (filled whole line)
  \kern-\dimen@ii % backspace the full width
  $\vcenter{\box\tw@}$% overlay the alignment
 }% end the \hbox to\dimen@ii
\numc@resetsub
$$\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

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