% Welcome to Elef's LaTeX macros and goodies
% I hereby place the following file to the public domain.

% Define the margins
\textheight 8.01in
\textwidth 6.5in
\topmargin 0.25in
\oddsidemargin .15in
\evensidemargin .15in
\headheight 0in
\headsep 0in
\parindent .35in
\parskip 0.0in

\begin{document}

% Define a couple of new fonts
\newfont{\smallrm}{cmr10}
\newfont{\smallbf}{cmb10}

% Define environments for definitions, propositions and theorems and proofs
\newtheorem{Def}{Definition}
\newtheorem{Prop}{Proposition}
\newtheorem{Thm}{Theorem}
\newtheorem{Cor}{Corollary}
\newtheorem{Rem}{Remark}
\newtheorem{Axiom}{Axiom}
\newtheorem{Exercise}{Exercise}
\newenvironment{Proof}{{\bf Proof:}\\}{$\Box$\\}

% Define some useful mathematical symbols
\newcommand{\twocases}[4]{\left\{ \begin{array}{ll} #1 &\mbox{if $ #2 $} \\ 
#3 & \mbox{if $ #4 $} \\ 
\end{array} \right. }
\newcommand{\bindtwoleft}[2]{\left\{ \begin{array}{l} #1 \\ #2 \\ \end{array} 
\right. }
\newcommand{\chooz}[2]{\left( \begin{array}{c} #1 \\ #2 \\ \end{array} \right) }

% Some aliases for commonly confusing math macros.
\newcommand{\implies}{\Longrightarrow}
\newcommand{\therefore}{\Rightarrow}
\newcommand{\ifonlyif}{\Longleftrightarrow}
\newcommand{\union}{\cup}
\newcommand{\intersection}{\cap}
\newcommand{\bigunion}{\bigcup}
\newcommand{\bigintersection}{\bigcap}
\newcommand{\del}{\nabla}
\newcommand{\cond}{{\rm cond}}
\newcommand{\rank}{{\rm rank}}
\newcommand{\diag}{{\rm diag}}

% Shortcut for caligraphic letters
\newcommand{\cA}{{\cal A}} \newcommand{\cB}{{\cal B}} \newcommand{\cC}{{\cal C}}
\newcommand{\cD}{{\cal D}} \newcommand{\cE}{{\cal E}} \newcommand{\cF}{{\cal F}}
\newcommand{\cG}{{\cal G}} \newcommand{\cH}{{\cal H}} \newcommand{\cI}{{\cal I}}
\newcommand{\cJ}{{\cal J}} \newcommand{\cK}{{\cal K}} \newcommand{\cL}{{\cal L}}
\newcommand{\cM}{{\cal M}} \newcommand{\cN}{{\cal N}} \newcommand{\cO}{{\cal O}}
\newcommand{\cP}{{\cal P}} \newcommand{\cQ}{{\cal Q}} \newcommand{\cR}{{\cal R}}
\newcommand{\cS}{{\cal S}} \newcommand{\cT}{{\cal T}} \newcommand{\cU}{{\cal U}}
\newcommand{\cV}{{\cal V}} \newcommand{\cW}{{\cal W}} \newcommand{\cX}{{\cal X}}
\newcommand{\cY}{{\cal Y}} \newcommand{\cZ}{{\cal Z}}

% Short cut for bold capital letters
\newcommand{\bfA}{{\bf A}} \newcommand{\bfB}{{\bf B}} \newcommand{\bfC}{{\bf C}}
\newcommand{\bfD}{{\bf D}} \newcommand{\bfE}{{\bf E}} \newcommand{\bfF}{{\bf F}}
\newcommand{\bfG}{{\bf G}} \newcommand{\bfH}{{\bf H}} \newcommand{\bfI}{{\bf I}}
\newcommand{\bfJ}{{\bf J}} \newcommand{\bfK}{{\bf K}} \newcommand{\bfL}{{\bf L}}
\newcommand{\bfM}{{\bf M}} \newcommand{\bfN}{{\bf N}} \newcommand{\bfO}{{\bf O}}
\newcommand{\bfP}{{\bf P}} \newcommand{\bfQ}{{\bf Q}} \newcommand{\bfR}{{\bf R}}
\newcommand{\bfS}{{\bf S}} \newcommand{\bfT}{{\bf T}} \newcommand{\bfU}{{\bf U}}
\newcommand{\bfV}{{\bf V}} \newcommand{\bfW}{{\bf W}} \newcommand{\bfX}{{\bf X}}
\newcommand{\bfY}{{\bf Y}} \newcommand{\bfZ}{{\bf Z}}

% Short cut for bold small letters
\newcommand{\bfa}{{\bf a}} \newcommand{\bfb}{{\bf b}} \newcommand{\bfc}{{\bf c}}
\newcommand{\bfd}{{\bf d}} \newcommand{\bfe}{{\bf e}} \newcommand{\bff}{{\bf f}}
\newcommand{\bfg}{{\bf g}} \newcommand{\bfh}{{\bf h}} \newcommand{\bfi}{{\bf i}}
\newcommand{\bfj}{{\bf j}} \newcommand{\bfk}{{\bf k}} \newcommand{\bfl}{{\bf l}}
\newcommand{\bfm}{{\bf m}} \newcommand{\bfn}{{\bf n}} \newcommand{\bfo}{{\bf o}}
\newcommand{\bfp}{{\bf p}} \newcommand{\bfq}{{\bf q}} \newcommand{\bfr}{{\bf r}}
\newcommand{\bfs}{{\bf s}} \newcommand{\bft}{{\bf t}} \newcommand{\bfu}{{\bf u}}
\newcommand{\bfv}{{\bf v}} \newcommand{\bfw}{{\bf w}} \newcommand{\bfx}{{\bf x}}
\newcommand{\bfy}{{\bf y}} \newcommand{\bfz}{{\bf z}}

% A bold zero is useful thing to have
\newcommand{\bfzero}{{\bf 0}}

% A "shortitem" macro. Use this in itemize and enumerate enviroments where
% you are listing short things and you don't want an entire blank line
% seperating every entry
\newcommand{\shortitem}{\item\vskip -6pt}


% To include an encapsulated postscript on your document do the following:
% --------------------------------------
% \begin{figure}\begin{center}
% \fbox{\ \fsp{3in}{h-bomb.eps}}
% \caption[h-bomb.eps]{How to make an H-bomb} 
% \label{h-bomb.eps}
% \end{center}\end{figure}
% -------------------------------------- 
% This example will put in the file h-bomb.eps in a figure environment,
% center it. fbox will surround it with a box. Note that the 3in means
% 3 inches and you can modify it to resize your image.
% \caption and \label must be put in in this order. Then you can use
% ~\ref{h-bomb.eps} to refer to your figure's number. 'h-bomb.eps' is
% what must appear in both the \label and the first argument of \caption
%
% The following will initialize the capability to insert postscript
% 
%\input{epsf.sty}
%\newcommand{\fsp}[2]{\epsfysize=#1 \epsfbox{#2}}