% Load the Fraktur font for Lie algebras
\font\lie=eufm10  %scaled 1000
% Load the AmSTeX blackboard-bold font
%\font\Bbb=msym10 scaled 1200
\font\Bbb=bbm10 scaled 1200
% Load certain symbols
%\font\binary=msxm10

\newenvironment{example}{\begin{exm} \rm}{\end{exm}}
\newtheorem{prop}{Proposition}
\newtheorem{cor}[prop]{Corollary}
\newtheorem{thm}{Theorem}
\newtheorem{exm}{Example}
\newcommand{\be}{\begin{equation}}
\newcommand{\ee}{\end{equation}}
\newcommand{\bea}{\begin{eqnarray*}}
\newcommand{\eea}{\end{eqnarray*}}
\newcommand{\bean}{\begin{eqnarray}}
\newcommand{\eean}{\end{eqnarray}}
\newcommand{\lil}[1]{{\mbox{\scriptsize {#1}}}}
\newcommand{\zed}{\mbox{\Bbb Z}}
\newcommand{\real}{ {\mbox{\Bbb R}} }
\newcommand{\pp}[2]{\frac{\partial {#1}}{\partial {#2}}}
\newcommand{\bigform}[1]{\raisebox{0ex}[2.5ex][1.5ex]{#1}}
\newcommand{\smbox}[1]{\mbox{\small {#1}}}
\newcommand{\proof}{\noindent {\bf Proof: }}
\newcommand{\qed}{\begin{flushright}
           {\mbox{  $\Box$}}\end{flushright}\vspace{1ex}}
\newcommand{\T}{{\cal T}}
\newcommand{\dstool}{\mbox{\bf DsTool}}
\newcommand{\kaos}{\mbox{\bf kaos}}
\newcommand{\newed}[1]{ {\binary I}{\sl #1 \binary J} }
\newcommand{\notimp}[1]{ {\em Not yet implemented. #1} }
\newcommand{\ie}{\mbox{\em i.e.}}
\newcommand{\eg}{\mbox{\em e.g.}}
\newcommand{\code}[1]{{\tt #1}}
\newcommand{\unix}[1]{{\tt #1}}
\newcommand{\csize}{ \footnotesize }
\newcommand{\csmallsize}{ \scriptsize }

\setcounter{secnumdepth}{4}




% Definitions for commutative diagrams, see p 182, 325 of the TeXBook
\def\normalbaselines{\baselineskip20pt
   \lineskip3pt \lineskiplimit3pt }
\def\mapright#1{\smash{
   \mathop{\longrightarrow}\limits^{#1}}}
\def\mapdown#1{\Big\downarrow
   \rlap{$\vcenter{\hbox{$\scriptstyle#1$}}$}}
\def\mapup#1{\Big\uparrow
   \rlap{$\vcenter{\hbox{$\scriptstyle#1$}}$}}


% definition for acknowledgements
\def\acknowledgements{
\typeout{Acknowledgements}
\chapter*{Acknowledgements}
}
\def\endacknowledgements{
\cleardoublepage
}
