%%
%% This is file `uwamaths.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% uwamaths.dtx 
%% 
%%% ===================================================================
%%%  @LaTeX-file{
%%%     filename = "uwamaths.dtx",
%%%     version  = "2.2",
%%%     date     = "1999/08/02",
%%%     time     = "03:40:42 EST",
%%%     checksum = "31454 3960 17407 178032"
%%%     author   = "Greg Gamble",
%%%     address  = "Centre for Discrete Mathematics & Computing,
%%%                 Department of Computer Science
%%%                       & Electrical Engineering,
%%%                 The University of Queensland,
%%%                 Queensland 4072,
%%%                 Australia",
%%%     telephone = "+61 7 336 52425",
%%%     FAX       = "+61 7 336 54999",
%%%     copyright = "Copyright (C) 1996,1997,1998,1999 Greg Gamble,
%%%                  all rights reserved.  Copying of this file is
%%%                  authorised only if either:
%%%                   (1) you make absolutely no changes to your copy,
%%%                       including name; OR
%%%                   (2) if you do make changes, you first rename it
%%%                       to some other name.
%%%                  This file may be distributed under the terms of
%%%                  the LaTeX Project Public License, as described
%%%                  in lppl.txt in the base LaTeX distribution.",
%%%     email     = "gregg@csee.uq.edu.au (Internet)",
%%%     codetable = "ISO/ASCII",
%%%     keywords  = "latex, amslatex, ams-latex, installation",
%%%     supported = "yes",
%%%     abstract  = "This is an installation file that will generate
%%%                  \pkg{uwamaths}. Initially provided to be an update
%%%                  of \fn{maths.tex} for LaTeX 2e.
%%%                  As the name suggests it contains
%%%                  general purpose macros that are used at UWA.
%%%                  It also incorporates the macros of
%%%                  \fn{macros.tex} compiled by various UWA honours
%%%                  students ... most notably: Paul Hanssen and
%%%                  Stuart Allie. A great many additional macros have
%%%                  since been added by the present author."
%%%     docstring = "The checksum field above contains a CRC-16
%%%                  checksum as the first value, followed by the
%%%                  equivalent of the standard UNIX wc (word
%%%                  count) utility output of lines, words, and
%%%                  characters.  This is produced by Robert
%%%                  Solovay's checksum utility.",
%%%  }
%%% ===================================================================
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{uwamaths}[1999/08/02 v2.2]
\typeout{Package: uwamaths 2.2 <1999/08/02>}
\newif\if@autonum
\DeclareOption{autonum}{\@autonumtrue}
\newif\if@savewspace
\newif\if@depttitle
\DeclareOption{savewspace}{\@savewspacetrue}
\DeclareOption{depttitle}{\@depttitletrue\@savewspacetrue}
\newif\if@noepsf
\DeclareOption{noepsf}{\@noepsftrue}
\newif\if@thm
\newif\if@itproof
\newif\if@nosfirst
\newif\if@unsectioned
\DeclareOption{thm}{\@thmtrue}
\DeclareOption{nothm}{\@thmfalse}
\DeclareOption{nosfirst}{\@nosfirsttrue}
\DeclareOption{itproof}{\@itprooftrue}
\DeclareOption{unsectioned}{\@unsectionedtrue}
\newif\if@eref
\DeclareOption{eref}{\@ereftrue}
\DeclareOption{noeref}{\@ereffalse}
\newif\if@addenv
\DeclareOption{addenv}{\@addenvtrue}
\DeclareOption{noaddenv}{\@addenvfalse}
\DeclareOption{noextras}{\@thmfalse\@ereffalse\@addenvfalse}
\DeclareOption{defaults}{\@thmtrue\@ereftrue\@addenvtrue}
\newif\if@danger
\DeclareOption{danger}{\@dangertrue}
\newif\if@gk
\DeclareOption{gkabbrev}{\@gktrue}
\newif\if@strut
\DeclareOption{strut}{\@struttrue}
\newif\if@vec
\DeclareOption{vectors}{\@vectrue}
\ExecuteOptions{defaults}
\ProcessOptions
\RequirePackage{amsmath,amssymb}
\hyphenation{ana-lo-gous}
\hyphenation{ne-cess-ary}
\newif\if@slides
\@ifundefined{slide}{}{\@slidestrue}
\if@slides
  \@unsectionedtrue
  \providecommand\section{%
       \@startsection{section}{1}{\z@}%
                     {.7\baselineskip\@plus\baselineskip}{.5\baselineskip}%
                     {\normalfont\bfseries\centering}}
  \providecommand\subsection{%
       \@startsection{subsection}{2}{\z@}%
                     {.7\baselineskip\@plus\baselineskip}{.5\baselineskip}%
                     {\normalfont\bfseries\centering}}
  \def\thanks{\footnote}
  \newenvironment{abstract}{\section{Abstract}}{}
  \def\bibitem#1{\par}
  \def\thebibliography#1{\section{References}}
  \def\endthebibliography{}
  \def\newblock{}
  \RequirePackage{float}
  \newcounter{figure}
  \providecommand\fps@figure{H}
  \providecommand\ftype@figure{1}
  \providecommand\ext@figure{lof}
  \providecommand\fnum@figure{}
  \newenvironment{figure}{\@float{figure}}{\end@float}
  \newcounter{table}
  \providecommand\fps@table{H}
  \providecommand\ftype@table{2}
  \providecommand\ext@table{lot}
  \providecommand\fnum@table{}
  \newenvironment{table}{\@float{table}}{\end@float}
  \newlength{\abovecaptionskip} \setlength{\abovecaptionskip}{10\p@}
  \newlength{\belowcaptionskip} \setlength{\belowcaptionskip}{0\p@}
  \long\def\@makecaption#1#2{%
    \vskip\abovecaptionskip
    \sbox\@tempboxa{\bfseries #2}%
    \ifdim \wd\@tempboxa >\hsize
      \bfseries #2\par
    \else
      \global \@minipagefalse
      \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}%
    \fi
    \vskip\belowcaptionskip}
  \def\equation{$$\refstepcounter{equation}}
  \def\endequation{\eqno \hbox{\@eqnnum}$$\global\@ignoretrue}
  \def\multline{\addtocounter{equation}{-1}\start@multline\st@rredfalse}
  \if@autonum%
    \pagestyle{slide}
    \AtBeginDocument{\slide}
    \AtEndDocument{\endslide}
    \def\@extraslide{\par\break\stepcounter{slide}\G@slideswtrue}
  \fi%
\fi
\newcommand{\vrD}{\vrule height1.9ex width0.4pt depth0.8ex}
\newcommand{\vrS}{\vrule height1.26ex width0.3pt depth0.56ex}
\newcommand{\vrSS}{\vrule height0.95ex width0.3pt depth0.4ex}
\def\vr{\mathchoice{\vrD}{\vrD}{\vrS}{\vrSS}}
\def\nvr{\!\!\not\,\,\vr}
\def\divides{\mathchoice{\mathrel{\vr}}{\mathrel{\vr}}
                        {\mathrel{\,\vr\,}}{\mathrel{\,\vr\,}}}
\def\ndivides{\mathchoice{\mathrel{\nvr}}{\mathrel{\nvr}}
                         {\mathrel{\,\nvr\,}}{\mathrel{\,\nvr\,}}}
\newcommand{\nimplies}{\DOTSB\;\,\,\not\!\!\Longrightarrow\;}
\newcommand{\nimpliedby}{\DOTSB\;\,\,\,\not\!\!\!\Longleftarrow\;}
\newcommand{\similar}{\mathrel{|||}}
\newcommand{\since}{\text{ since }}
\newcommand{\as}{\text{ as }}
\newcommand{\If}{\text{ if }}
\newcommand{\Or}{\text{ or }}
\newcommand{\AND}{\text{ and }}
\newcommand{\where}{\text{ where }}
\newcommand{\for}{\text{ for }}
\newcommand{\some}{\text{ some }}
\newcommand{\forsome}{\text{ for some }}
\newcommand{\forany}{\text{ for any }}
\ifx\htmlstyloaded\relax
  \def\wrt{with respect to}
  \def\Wlog{without loss of generality}
  \def\corr{corresponding to}
\else
  \def\wrt/{with respect to}
  \def\Wlog/{without loss of generality}
  \def\corr/{corresponding to}
\fi
\ifx\htmlstyloaded\relax
  \def\Divides{\ifmmode\divides\else divides\fi}
  \def\Exists{\ifmmode\,\,\exists\,\else there exists\fi}
  \def\is{\ifmmode\,\,\exists\,\else there is\fi}
  \def\are{\ifmmode\,\,\exists\,\else there are\fi}
  \def\Forall{\ifmmode\,\,\forall\,\else for all\fi}
  \def\Iff{\ifmmode\iff\else if and only if\fi}
  \def\st{\ifmmode\text{ such that }\else such that\fi}
  \def\isomorphic{\ifmmode\cong\else is isomorphic to\fi}
  \def\iso{\ifmmode\cong\else is isomorphic to\fi}
\else
  \def\Divides/{\ifmmode\divides\else divides\fi}
  \def\Exists/{\ifmmode\,\,\exists\,\else there exists\fi}
  \def\is/{\ifmmode\,\,\exists\,\else there is\fi}
  \def\are/{\ifmmode\,\,\exists\,\else there are\fi}
  \def\Forall/{\ifmmode\,\,\forall\,\else for all\fi}
  \def\Iff/{\ifmmode\iff\else if and only if\fi}
  \def\st/{\ifmmode\text{ such that }\else such that\fi}
  \def\isomorphic/{\ifmmode\cong\else is isomorphic to\fi}
  \def\iso/{\ifmmode\cong\else is isomorphic to\fi}
\fi
\newcommand{\N}{{\ensuremath{\mathbb{N}}}}
\newcommand{\Z}{{\ensuremath{\mathbb{Z}}}}
\newcommand{\Q}{{\ensuremath{\mathbb{Q}}}}
\newcommand{\R}{{\ensuremath{\mathbb{R}}}}
\newcommand{\Zplus}{{\ensuremath{\mathbb{Z}^+}}}
\newcommand{\Qplus}{{\ensuremath{\mathbb{Q}^+}}}
\newcommand{\Rplus}{{\ensuremath{\mathbb{R}^+}}}
\newcommand{\C}{{\ensuremath{\mathbb{C}}}}
\newcommand{\F}{{\ensuremath{\mathbb{F}}}}
\newcommand{\D}{{\ensuremath{\mathbb{D}}}}
\newcommand{\E}{{\ensuremath{\mathbb{E}}}}
\newcommand{\K}{{\ensuremath{\mathbb{K}}}}
\newcommand{\M}{{\ensuremath{\mathbb{M}}}}
\newcommand{\Prob}{{\ensuremath{\mathbb{P}}}}
\newcommand{\T}{{\ensuremath{\mathbb{T}}}}
\newcommand{\ab}{{\boldsymbol{a}}}
\newcommand{\bb}{{\boldsymbol{b}}}
\newcommand{\cb}{{\boldsymbol{c}}}
\newcommand{\db}{{\boldsymbol{d}}}
\newcommand{\eb}{{\boldsymbol{e}}}
\newcommand{\fb}{{\boldsymbol{f}}}
\newcommand{\gb}{{\boldsymbol{g}}}
\newcommand{\hb}{{\boldsymbol{h}}}
\newcommand{\ib}{{\boldsymbol{i}}}
\newcommand{\jb}{{\boldsymbol{j}}}
\newcommand{\kb}{{\boldsymbol{k}}}
\newcommand{\ub}{{\boldsymbol{u}}}
\newcommand{\vb}{{\boldsymbol{v}}}
\newcommand{\wb}{{\boldsymbol{w}}}
\newcommand{\xb}{{\boldsymbol{x}}}
\newcommand{\yb}{{\boldsymbol{y}}}
\newcommand{\zb}{{\boldsymbol{z}}}
\newcommand{\zer}{{\boldsymbol{0}}}
\DeclareMathOperator{\re}{\mathcal{R}\!\scriptstyle{\textit{e}}}
\DeclareMathOperator{\im}{\mathcal{I}\!\scriptstyle{\textit{m}}}
\DeclareMathOperator{\cosec}{cosec}
\DeclareMathOperator{\sech}{sech}
\DeclareMathOperator{\cosech}{cosech}
\DeclareMathOperator{\arctanh}{arctanh}
\DeclareMathOperator{\arcsinh}{arcsinh}
\DeclareMathOperator{\arccosh}{arccosh}
\DeclareMathOperator{\arcsec}{arcsec}
\DeclareMathOperator{\arcsech}{arcsech}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator{\lcd}{lcd}
\DeclareMathOperator{\hcf}{hcf}
\DeclareMathOperator{\curl}{curl}
\DeclareMathOperator{\grad}{grad}
\DeclareMathOperator{\divg}{div}
\DeclareMathOperator{\trig}{trig}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\cis}{cis}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\ind}{ind}
\newcommand{\half}{\tfrac{1}{2}}
\newcommand{\third}{\tfrac{1}{3}}
\newcommand{\qtr}{\tfrac{1}{4}}
\newcommand{\fifth}{\tfrac{1}{5}}
\newcommand{\sixth}{\tfrac{1}{6}}
\newcommand{\seventh}{\tfrac{1}{7}}
\newcommand{\eighth}{\tfrac{1}{8}}
\newcommand{\ninth}{\tfrac{1}{9}}
\newcommand{\tenth}{\tfrac{1}{10}}
\newcommand{\floor}[1]{\left\lfloor #1\right\rfloor}
\newcommand{\ceiling}[1]{\left\lceil #1\right\rceil}
\newcommand{\absval}[1]{\lvert #1\rvert}
\newcommand{\modulus}[1]{\lvert #1\rvert}
\newcommand{\norm}[1]{\lvert #1\rvert}
\newcommand{\Norm}[1]{\lVert #1\rVert}
\newcommand{\bigmod}[1]{\big\lvert #1\big\rvert}
\newcommand{\toi}[1]{#1\to\infty}
\newcommand{\toz}[1]{#1\to0}
\newcommand{\limtoi}[1]{\lim_{\toi#1}}
\newcommand{\limtoz}[1]{\lim_{\toz#1}}
\newcommand{\limseq}{\lim_{n\to\infty}}
\newcommand{\la}{\langle}
\newcommand{\ra}{\rangle}
\newcommand{\onto}{\twoheadrightarrow}
\newcommand{\inj}{\rightarrowtail}
\newcommand{\inner}[2]{\la #1 ,\, #2\ra}
\newcommand{\union}{\cup}
\newcommand{\intersection}{\cap}
\def\@vr#1{\vrule height #1ex width 0pt}
\def\dotcup{\DOTSB\mathop{\overset{\textstyle.}\cup}}
\let\disjunion\dotcup
\def\@dotbigcupD{\smash\bigcup\@vr{2.1}}
\def\@dotbigcupT{\smash\bigcup\@vr{1.5}}
\def\dotbigcupD{\DOTSB\mathop{\overset{\textstyle.}\@dotbigcupD%
                              \vphantom{\bigcup}}}
\def\dotbigcupT{\DOTSB\smash{\mathop{\overset{\textstyle.}\@dotbigcupT%
                             \vphantom{\bigcup}}}%
                      \vphantom{\bigcup}\@vr{2.0}}
\def\dotbigcup{\mathop{\mathchoice{\dotbigcupD}{\dotbigcupT}
                                  {\dotbigcupT}{\dotbigcupT}}}
\let\Disjunion\dotbigcup
\newcommand{\dg}{\partial}
\newcommand{\partn}[2]{\genfrac{[}{]}{0pt}{}{#1}{#2}}
\newcommand{\dee}{\mathrm{d}}
\newcommand{\deedee}[2]{{\dee#1 / \dee#2}}
\newcommand{\DeeDee}[2]{\dfrac{\dee#1}{\dee#2}}
\newcommand{\normp}[2]{\norm{#2}\lower1ex\hbox{$\scriptscriptstyle{#1}$}}
\newcommand{\Normp}[2]{\Norm{#2}\lower1ex\hbox{$\scriptscriptstyle{#1}$}}
\newcommand{\normone}[1]{\normp1{#1}}
\newcommand{\normtwo}[1]{\normp2{#1}}
\newcommand{\Normone}[1]{\Normp1{#1}}
\newcommand{\Normtwo}[1]{\Normp2{#1}}
\newcommand{\eqdef}{\mathrel{\widehat{=}}}
\newcommand{\Th}{{\text{th}}}
\newcommand{\normr}[2]{\mathrm{N}_{#1}\left({#2}\right)}
\newcommand{\centr}[2]{\mathrm{C}_{#1}\left({#2}\right)}
\newcommand{\centre}[1]{\mathrm{Z}\left({#1}\right)}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\Inn}{Inn}
\DeclareMathOperator{\Out}{Out}
\DeclareMathOperator{\Alt}{Alt}
\DeclareMathOperator{\Sym}{Sym}
\DeclareMathOperator{\Syl}{Syl}
\DeclareMathOperator{\Wr}{wr}
\DeclareMathOperator{\twr}{twr}
\DeclareMathOperator{\soc}{soc}
\DeclareMathOperator{\fix}{fix}
\DeclareMathOperator{\supp}{supp}
\DeclareMathOperator{\mov}{mov}
\DeclareMathOperator{\val}{val}
\DeclareMathOperator{\Cay}{Cay}
\newcommand{\liso}{\lesssim}
\newcommand{\giso}{\gtrsim}
\newsavebox\@tbox
\newdimen\@raiseamount
\newcommand\lowstackrel[2]{%
     \sbox{\@tbox}{$#2$} \setlength{\@raiseamount}{\ht\@tbox}
     \mathrel{\raisebox{-\@raiseamount}%
                       {$\stackrel{\displaystyle#1}{\usebox{\@tbox}}$}}}
\newcommand{\leiso}{\lowstackrel{\le}{\sim}}
\newcommand{\geiso}{\lowstackrel{\ge}{\sim}}
\newcommand{\conjelt}{%
     \mathrel{\underset{\raisebox{0.4ex}{$\scriptstyle{\sim}$}}{\in}}}
\newcommand{\contconjelt}{%
     \mathrel{\underset{\raisebox{0.4ex}{$\scriptstyle{\sim}$}}{\ni}}}
\newcommand{\norml}{\vartriangleleft}
\newcommand{\normlgt}{\vartriangleright}
\newcommand{\normleq}{\trianglelefteq}
\newcommand{\normlge}{\trianglerighteq}
\DeclareMathOperator{\Var}{Var}
\DeclareMathOperator{\Cov}{Cov}
\DeclareMathOperator{\Ndist}{N}
\DeclareMathOperator{\tdist}{t}
\DeclareMathOperator{\Fdist}{F}
\DeclareMathOperator{\Bern}{Bern}
\DeclareMathOperator{\Bin}{Bin}
\DeclareMathOperator{\Geo}{Geo}
\DeclareMathOperator{\Geom}{Geom}
\DeclareMathOperator{\Exp}{Exp}
\DeclareMathOperator{\Poi}{Poi}
\xdef\Join{\mathrel{\mathchar"0\hexnumber@\symAMSb 6F\mkern-13.8mu%
  \mathchar"0\hexnumber@\symAMSb 6E}}
\providecommand{\singlespacing}{\renewcommand{\baselinestretch}{1}}
\providecommand{\oneandhalfspacing}{\renewcommand{\baselinestretch}{1.24}}
\providecommand{\doublespacing}{\renewcommand{\baselinestretch}{1.66}}
\newcommand{\onespace}{\quad}
\newcommand{\twospace}{\qquad}
\newcommand{\threespace}{\qquad\quad}
\newcommand{\fourspace}{\qquad\qquad}
\chardef\bslchar=`\\
\newcommand{\addbslash}{\expandafter\@addbslash\string}
\def\@addbslash#1{\bslchar\@nobslash#1}
\newcommand{\nobslash}{\expandafter\@nobslash\string}
\def\@nobslash#1{\ifnum`#1=\bslchar\else#1\fi}
\newcommand{\ntt}{\normalfont\ttfamily}
\def\@boxorbreak{\leavevmode
  \ifmmode\hbox\else\ifdim\lastskip=\z@\penalty9999 \fi\fi}
\newcommand{\cn}[1]{\@boxorbreak{\ntt\addbslash#1\@empty}}
\newcommand{\cls}[1]{{\ntt#1}}
\newcommand{\pkg}[1]{{\ntt#1}}
\newcommand{\opt}[1]{{\ntt#1}}
\newcommand{\env}[1]{{\ntt#1}}
\newcommand{\fn}[1]{{\ntt#1}}
\def\allowtthyphens{\input{OT1cmtt.fd}%
  \expandafter\let\csname OT1+cmtt\endcsname\@empty}
\def\AmS{{\protect\usefont{OMS}{cmsy}{m}{n}%
  A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
\ifx\htmlstyloaded\relax
  \def\Latex{{\protect\LaTeX}}
  \def\latexe{{\protect\LaTeXe}}
  \def\amslatex{{\protect\AmS-\protect\LaTeX}}
  \def\tex{{\protect\TeX}}
  \def\amstex{{\protect\AmS-\protect\TeX}}
  \def\bibtex{{Bib\protect\TeX}}
  \def\makeindx{MakeIndex}
  \def\xypic{XY\mbox{-}pic}
\else
  \def\latex/{{\protect\LaTeX}}
  \def\Latex/{{\protect\LaTeX}}
  \def\latexe/{{\protect\LaTeXe}}
  \def\amslatex/{{\protect\AmS-\protect\LaTeX}}
  \def\tex/{{\protect\TeX}}
  \def\amstex/{{\protect\AmS-\protect\TeX}}
  \def\bibtex/{{Bib\protect\TeX}}
  \def\makeindx/{MakeIndex}
  \def\xypic/{XY\mbox{-}pic}
\fi
\providecommand{\indx}[1]{#1\index{#1}}
\providecommand{\gloss}[1]{\emph{#1}\glossary{#1}}
\newcommand{\uwamd}{The University of Western Australia\\
                    DEPARTMENT OF MATHEMATICS \& STATISTICS}
\if@savewspace
  \RequirePackage{anysize}
  \marginsize{2cm}{2cm}{2cm}{2cm}
  \def\obeycrMakeUppercase#1#2{\global\let#1\@empty%
                               \@obeycrUppercase#1#2\\\\\end}
  \def\@obeycrUppercase#1#2\\#3\\\end{%
         \ifx#2\relax\else%
           \ifx#1\@empty\gdef#1{\Makeuppercase{#2}}%
           \else%
             \g@addto@macro#1{\\\Makeuppercase{#2}}%
           \fi%
           \@obeycrUppercase#1#3\\\\\end%
         \fi}
  \let\Makeuppercase\MakeUppercase
  \def\course#1{\obeycrMakeUppercase\@course{#1}}
  \if@depttitle
    \def\@course{\PackageWarning{uwamaths}{No \noexpand\course given}\@empty}
  \else
    \let\@course\@empty
  \fi
  \let\@@course\@course
  \let\@@author\@author
  \let\department\uwamd
  \def\@maketitle{%
    \newpage
    \begin{center}%
    \let \footnote \thanks
      {\normalsize%
       \if@depttitle\department\\[0.7em]%
       \else\fi
       \ifx\@course\@@course\@course\else%
         \bfseries\@course\ \\[0.9em]
       \fi
       \bfseries\large \@title \par}%
       \ifx\@author\@@author\@author\else%
         \vskip 1em%
         \begin{tabular}[t]{c}%
           \@author
         \end{tabular}%
       \fi
       \vskip 1em%
      {\normalsize \@date}%
    \end{center}%
    \par%
    \global\let\@@author\relax%
    \global\let\@@course\relax}
  \@ifundefined{chapter}{}{%
      \def\abstract{\section*{\centering\abstractname}}
      \def\endabstract{\medbreak}
      \providecommand\chaptername{Chapter}
      \def\@makechapterhead#1{%
        \begingroup
        \fontsize{\@xivpt}{18}\bfseries\centering
          \ifnum\c@secnumdepth>\m@ne
            \leavevmode \hskip-\leftskip
            \rlap{\vbox to\z@{\vss
                \centerline{\normalsize\mdseries
                    \uppercase\@xp{\chaptername}\enspace\thechapter}
                \vskip 3pc}}\hskip\leftskip\fi
           #1\par \endgroup
        \skip@34\p@ \advance\skip@-\normalbaselineskip
        \vskip\skip@ }
      \def\@makeschapterhead#1{%
        \begingroup
        \fontsize{\@xivpt}{18}\bfseries\centering
        #1\par \endgroup
        \skip@34\p@ \advance\skip@-\normalbaselineskip
        \vskip\skip@ }
      }
  \def\section{\@startsection {section}{1}{\z@}%
      {-3.5ex \@plus -1ex \@minus -.2ex}{2.3ex \@plus.2ex}%
      {\normalfont\secsize\bfseries}}
  \def\subsection{\@startsection{subsection}{2}{\z@}%
      {-3.25ex\@plus -1ex \@minus -.2ex}{1.5ex \@plus .2ex}%
      {\normalfont\subsecsize\bfseries}}
  \def\subsubsection{\@startsection{subsubsection}{3}{\z@}%
      {-3.25ex\@plus -1ex \@minus -.2ex}{1.5ex \@plus .2ex}%
      {\normalfont\normalsize\bfseries}}
  \def\paragraph{\@startsection{paragraph}{4}{\z@}%
      {3.25ex \@plus1ex \@minus.2ex}{-1em}%
      {\normalfont\normalsize\bfseries}}
  \def\subparagraph{\@startsection{subparagraph}{5}{\parindent}%
      {3.25ex \@plus1ex \@minus .2ex}{-1em}%
      {\normalfont\normalsize\bfseries}}
  \let\secsize\normalsize
  \let\subsecsize\normalsize
\fi
\if@noepsf\else\if@thm\if@eref\if@addenv%
  \RequirePackage{epsf}
\fi\fi\fi\fi
\if@thm%
  \RequirePackage{amsthm}
  \newtheoremstyle{slant}{\topsep}{\topsep}{\slshape}{0pt}%
                  {\bfseries}{.}{ }{}
  \newtheoremstyle{algorithm}{\topsep}{\topsep}{\ttfamily}{0pt}%
                  {\bfseries}{.}{ }{}
  \def\renewtheorem{\@ifstar{\@renewtheorem *}{\@renewtheorem \relax}}
  \def\@renewtheorem#1#2{%
        \@ifundefined{#2}%
          {\@latex@error{Theorem environment #2 undefined}\@ehc}{}%
        \@xp\let\csname#2\endcsname\relax
        \@xp\let\csname end#2\endcsname\relax
        \@xnthm{#1}{#2}}
  \if@nosfirst \swapnumbers \fi
  \edef\@numbered@as{\if@unsectioned theorem\else subsection\fi}
  \theoremstyle{slant}
    \if@unsectioned%
      \newtheorem{theorem}{Theorem}
    \else%
      \newtheorem{theorem}[subsection]{Theorem}
    \fi%
    \newtheorem*{theorem*}{Theorem}
    \newtheorem{lemma}[\@numbered@as]{Lemma}
    \newtheorem*{lemma*}{Lemma}
    \newtheorem{corollary}[\@numbered@as]{Corollary}
    \newtheorem*{corollary*}{Corollary}
    \newtheorem{proposition}[\@numbered@as]{Proposition}
    \newtheorem*{proposition*}{Proposition}
    \newtheorem{conjecture}[\@numbered@as]{Conjecture}
    \newtheorem*{conjecture*}{Conjecture}
    \newtheorem{construction}[\@numbered@as]{Construction}
    \newtheorem*{construction*}{Construction}
    \newtheorem{result}[\@numbered@as]{Result}
    \newtheorem*{result*}{Result}
    \newtheorem{example}[\@numbered@as]{Example}
    \newtheorem*{example*}{Example}
    \newtheorem{axiom}{Axiom}
    \newtheorem*{axiom*}{Axiom}
    \newtheorem{property}{Property}
    \newtheorem*{property*}{Property}
  \theoremstyle{definition}
    \newtheorem{remark}[\@numbered@as]{Remark}
    \newtheorem*{remark*}{Remark}
    \if@slides\else
      \newtheorem{note}[\@numbered@as]{Note}
      \newtheorem*{note*}{Note}
    \fi
    \newtheorem{Note}[\@numbered@as]{Note}
    \newtheorem*{Note*}{Note}
    \newtheorem{definition}[\@numbered@as]{Definition}
    \newtheorem*{definition*}{Definition}
    \newtheorem{exercise}[\@numbered@as]{Exercise}
    \newtheorem*{exercise*}{Exercise}
    \newtheorem{question}[\@numbered@as]{Question}
    \newtheorem*{question*}{Question}
    \newtheorem{problem}[\@numbered@as]{Problem}
    \newtheorem*{problem*}{Problem}
    \newtheorem{case}{Case}
    \newtheorem*{case*}{Case}
    \newtheorem{subcase}{Subcase}[case]
    \newtheorem*{subcase*}{Subcase}
  \theoremstyle{algorithm}
    \newtheorem{algthm}[\@numbered@as]{Algorithm}
    \newtheorem*{algthm*}{Algorithm}
    \newtheorem{proc}[\@numbered@as]{Procedure}
    \newtheorem*{proc*}{Procedure}
  \theoremstyle{remark}
    \newtheorem{plaus}[\@numbered@as]{Plausibility}
    \newtheorem*{plaus*}{Plausibility}
  \if@itproof\else%
   \renewenvironment{proof}[1][\proofname]{\par
     \normalfont
     \topsep6\p@\@plus6\p@ \trivlist
     \item[\hskip\labelsep\bfseries
       #1\@addpunct{.}]\ignorespaces
     }{%
     \qed\endtrivlist
     }%
  \fi
  \newenvironment{smproof}{\small\begin{proof}}{\end{proof}}
  \providecommand{\numberin}[2]{%
     \@addtoreset{#1}{#2}%
     \@xp\@xp\@xp\renewcommand\@xp{\csname the#1\endcsname}{%
                        \csname the#2\endcsname.\arabic{#1}}}
  \if@unsectioned\else
     \numberin{equation}{section}
     \numberin{table}{section}
     \numberin{figure}{section}
  \fi
  \newcommand{\numberallin}[1]{\numberin{theorem}{#1} \numberin{table}{#1}%
                               \numberin{figure}{#1} \numberin{equation}{#1}}
\fi
\if@eref
  \DeclareRobustCommand\eref[1]{\@eref#1\end}
  \def\@eref#1:#2\end{%
        \@xp\ifx\csname pr@#1\endcsname\relax%
              \PackageWarning{uwamaths}{Reference format #1\space undefined}%
              \ref{#1:#2}%
        \else \csname pr@#1\endcsname{\ref{#1:#2}}{\pageref{#1:#2}}{#1:#2}%
        \fi}
  \def\newrefformat#1#2{\@namedef{pr@#1}##1##2##3{%
       \def\onpage{\@xp\@onpage\csname r@##3\endcsname\@secondoftwo{##3}}#2}}
  \def\@onpage#1#2#3{%
        \ifx#1\relax%
              \@latex@warning{Reference `#3' on page \thepage
                              \space undefined}
              on page \textbf{??}%
        \else \@xp\@xp\@xp\@@onpage\@xp#2#1\end%
        \fi}
  \def\@@onpage#1\end{%
        \ifnum\thepage=#1\null\onthispage%
              \typeout{Reference on same page as float (page \thepage)}%
        \else \typeout{Reference on page \thepage, float on page #1}
              on page #1%
        \fi}
  \def\onthispage{ on this page}
  \newrefformat{eq}{\textup{(#1)}}
  \newrefformat{tab}{Table #1\onpage}
  \newrefformat{fig}{Figure #1\onpage}
  \newrefformat{cha}{Chapter #1}
  \newrefformat{apx}{Appendix #1}
  \newrefformat{sec}{Section #1}
  \newrefformat{thm}{Theorem #1}
  \newrefformat{lem}{Lemma #1}
  \newrefformat{cor}{Corollary #1}
  \newrefformat{prn}{Proposition #1}
  \newrefformat{cnj}{Conjecture #1}
  \newrefformat{cns}{Construction #1}
  \newrefformat{res}{Result #1}
  \newrefformat{eg}{Example #1}
  \newrefformat{ax}{Axiom #1}
  \newrefformat{pry}{Property #1}
  \newrefformat{rem}{Remark #1}
  \newrefformat{nte}{Note #1}
  \newrefformat{def}{Definition #1}
  \newrefformat{ex}{Exercise #1}
  \newrefformat{q}{Question #1}
  \newrefformat{prb}{Problem #1}
  \newrefformat{cse}{Case #1}
  \newrefformat{scs}{Subcase #1}
  \newrefformat{alg}{Algorithm #1}
  \newrefformat{prc}{Procedure #1}
  \newrefformat{pls}{Plausibility #1}
\fi
\newif\ifnoq
\newif\ifnoans      \newif\ifIgnoreAnsOpt
\newif\ifnosoln     \newif\ifIgnoreSolnOpt
\if@addenv%
  \newcounter{exno}
  \newenvironment{exercises}[1][\exsname]%
    {\ifx#1\relax\else\medbreak\noindent{\bfseries #1.}\fi%
     \begin{list}{\arabic{exno}.}%
                 {\usecounter{exno}\def\makelabel##1{\hss\llap{##1}}}}
    {\end{list}}
  \newcommand{\exsname}{Exercises}
  \newenvironment{exerciseset}%
    {\begin{exercises}[Exercise Set \thesection]}
    {\end{exercises}}
  \newcommand{\uwa@enum}[2]{%
     \begin{list}{(\csname #2\endcsname{#1})}%
                 {\usecounter{#1}\def\makelabel##1{\hss\llap{##1}}}}
  \newcommand{\newuwa@enumenv}[2]{%
     \newcounter{#1}
     \newenvironment{#1}{\uwa@enum{#1}{#2}}{\end{list}}}
  \newuwa@enumenv{sub}{roman}
  \newuwa@enumenv{subsub}{alph}
  \newuwa@enumenv{Sub}{Roman}
  \newuwa@enumenv{Subsub}{Alph}
  \@ifundefined{acknowledgements}{%
    \newenvironment{acknowledgements}%
       {\renewcommand{\abstractname}{Acknowledgements}%
        \begin{abstract}}
       {\end{abstract}}
    }{}
  \providecommand{\glossaryname}{Glossary}
  \@ifundefined{theglossary}{%
    \newenvironment{theglossary}%
      {\chapter*{\glossaryname}
       \addcontentsline{toc}{chapter}{\glossaryname}
       \thispagestyle{plain}
       \begin{description}}
      {\end{description}}
    }{}
  \def\qonly{\noqfalse\noanstrue\nosolntrue}
  \def\ansonly{\noqtrue\noansfalse\nosolntrue}
  \def\solnonly{\noqtrue\noanstrue\nosolnfalse}
  \RequirePackage{verbatim}
  \newenvironment{exquestion}%
     {\ifnoq\let\@next=\comment\let\endexquestion=\endcomment%
      \else\let\@next=\relax%
      \fi\@next}%
     {}
  \def\ansfontsize{\small}
  \def\anshead{{\bfseries Answer\@addpunct{.}\enspace}}
  \newenvironment{answer}[1][]%
     {\ifnoans\let\@next=\comment\let\endanswer=\endcomment%
        \ifIgnoreAnsOpt\else #1\fi
      \else\let\@next=\relax%
        \ifnoq\else%
          \ansfontsize
          \begin{list}%
            {}{\itemindent\listparindent \parsep 0pt plus 1pt}
          \item[] \anshead
        \fi%
      \fi\@next}
     {\ifnoans\else\ifnoq\else\end{list}\fi\fi}
  \def\solnfontsize{\small}
  \def\solnhead{{\bfseries Solution\@addpunct{.}\enspace}}
  \newenvironment{solution}[1][]%
     {\ifnosoln\let\@next=\comment\let\endsolution=\endcomment%
        \ifIgnoreSolnOpt\else #1\fi
      \else\let\@next=\relax%
        \ifnoq\else%
          \solnfontsize
          \begin{list}%
            {}{\itemindent\listparindent \parsep 0pt plus 1pt}
          \item[] \solnhead
        \fi%
      \fi\@next}
     {\ifnosoln\else\ifnoq\else\end{list}\fi\fi}
  \def\exlist#1{\ifx *#1%
                   \typeout{Requested exitem list: all}%
                   \let\exitem\@exitem
                \else
                   \typeout{Requested exitem list: #1}%
                \fi%
                \AtEndDocument{%
                   \typeout{Available exitem list: \@availexlist.}}%
                \@splitexlist#1,,\end}
  \def\@add@avail#1{\ifx\@empty\@availexlist
                      \gdef\@availexlist{#1}%
                    \else
                      \g@addto@macro\@availexlist{,#1}%
                    \fi}
  \let\@availexlist\@empty
  \def\@splitexlist#1,#2\end{\gdef\@next@ex{#1}\gdef\@exlist{#2\end}}
  \newenvironment{exitem}[1]%
               {\edef\@temp{#1}\@add@avail{#1}\ifx\@temp\@next@ex%
                   \typeout{Including exitem: \@temp.}
                   \@xp\global\@xp\@splitexlist\@exlist
                     \let\@next=\item
                   \else\let\endexitem=\endcomment\let\@next=\comment\fi
                   \@next}{}
  \def\@exitem#1{\@add@avail{#1}\typeout{Including exitem: #1.}\item}
\fi
\if@danger%
  \font\manual=manfnt at 1\@ptsize pt
  \def\dbend{{\manual\char127}}
  \newlength{\dangerwidth}
  \def\@setdangerwidth{%
     \setlength{\dangerwidth}{\textwidth}
     \addtolength{\dangerwidth}{-40pt}}
  \newenvironment{danger}%
     {\begin{center}\@setdangerwidth%
      \begin{minipage}{\dangerwidth}\parindent=20pt%
      \noindent\hangindent\parindent\hangafter=-2%
      \hbox to0pt{\hskip-\hangindent\dbend\hfill}%
      \small\ignorespaces}%
     {\end{minipage}\end{center}}
  \newenvironment{ddanger}%
     {\begin{center}\@setdangerwidth%
      \begin{minipage}{\dangerwidth}\parindent=40pt%
      \noindent\hangindent\parindent\hangafter=-2%
      \hbox to0pt{\hskip-\hangindent\dbend\kern1pt\dbend\hfill}%
      \small\ignorespaces}%
     {\end{minipage}\end{center}}
\fi
\if@gk%
  \newcommand{\al}{\alpha}
  \newcommand{\be}{\beta}
  \newcommand{\ga}{\gamma}
  \newcommand{\de}{\delta}
  \newcommand{\ep}{\varepsilon}
  \newcommand{\ka}{\kappa}
  \newcommand{\ph}{\varphi}
  \newcommand{\lam}{\lambda}
  \newcommand{\si}{\sigma}
  \newcommand{\om}{\omega}
  \newcommand{\alb}{{\boldsymbol{\alpha}}}
  \newcommand{\beb}{{\boldsymbol{\beta}}}
  \newcommand{\gab}{{\boldsymbol{\gamma}}}
  \newcommand{\deb}{{\boldsymbol{\delta}}}
  \newcommand{\epb}{{\boldsymbol{\varepsilon}}}
  \newcommand{\kab}{{\boldsymbol{\kappa}}}
  \newcommand{\phb}{{\boldsymbol{\varphi}}}
  \newcommand{\lamb}{{\boldsymbol{\lambda}}}
  \newcommand{\sib}{{\boldsymbol{\sigma}}}
  \newcommand{\omb}{{\boldsymbol{\omega}}}
  \newcommand{\Ga}{\varGamma}
  \newcommand{\De}{\varDelta}
  \newcommand{\The}{\varTheta}
  \newcommand{\La}{\varLambda}
  \newcommand{\itXi}{\varXi}
  \newcommand{\itPi}{\varPi}
  \newcommand{\Si}{\varSigma}
  \newcommand{\Ups}{\varUpsilon}
  \newcommand{\Ph}{\varPhi}
  \newcommand{\Ps}{\varPsi}
  \newcommand{\Om}{\varOmega}
  \newcommand{\Gab}{{\boldsymbol{\varGamma}}}
  \newcommand{\Deb}{{\boldsymbol{\varDelta}}}
  \newcommand{\Theb}{{\boldsymbol{\varTheta}}}
  \newcommand{\Lab}{{\boldsymbol{\varLambda}}}
  \newcommand{\itXib}{{\boldsymbol{\varXi}}}
  \newcommand{\itPib}{{\boldsymbol{\varPi}}}
  \newcommand{\Sib}{{\boldsymbol{\varSigma}}}
  \newcommand{\Upsb}{{\boldsymbol{\varUpsilon}}}
  \newcommand{\Phb}{{\boldsymbol{\varPhi}}}
  \newcommand{\Psb}{{\boldsymbol{\varPsi}}}
  \newcommand{\Omb}{{\boldsymbol{\varOmega}}}
\fi
\if@strut%
  \newcommand{\hstrut}{\vrule height2.1ex width0pt depth0pt}
  \newcommand{\dstrut}{\vrule height0pt width0pt depth1ex}
  \newcommand{\medhstrut}{\vrule height2.5ex width0pt depth0pt}
  \newcommand{\medstrut}{\vrule height2.5ex width0pt depth1.5ex}
  \newcommand{\meddstrut}{\vrule height0pt width0pt depth1.5ex}
  \newcommand{\highstrut}{\vrule height4.2ex width0pt depth0pt}
  \newcommand{\bigstrut}{\vrule height4.2ex width0pt depth3ex}
  \newcommand{\deepstrut}{\vrule height0pt width0pt depth3ex}
\fi
\if@vec%
  \newcommand{\vectr}[1]{\ensuremath%
      {\oalign{$#1$\crcr\hidewidth
               \vbox to .2ex{\hbox{$\boldsymbol{\mathchar"7E}$}\vss}%
               \hidewidth}}}
  \renewcommand{\vec}[1]{\vectr{{\boldsymbol{#1}}}}
  \newcommand{\unitvec}[1]{\vec{\hat#1}}
  \newcommand{\varvectr}[1]{\ensuremath{\!\vectr{\,#1}}}
  \newcommand{\varvec}[1]{\varvectr{{\boldsymbol{#1}}}}
  \newcommand{\varunitvec}[1]{\varvec{\hat#1}}
  \newcommand{\scdot}{\boldsymbol{\cdot}}
  \newcommand{\cross}{\boldsymbol{\times}}
  \newcommand{\del}{\vec{\nabla}}
  \newcommand{\delsq}{\ensuremath{\nabla^2}}
  \renewcommand{\zer}{\vec{0}}
\fi
\endinput
%%
%% End of file `uwamaths.sty'.