cases doc update, own package (21feb09)

git-svn-id: svn://tug.org/texlive/trunk@17123 c570f23f-e606-0410-a88d-b1316a301751

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-%  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{|}~