% std.sty  --The standard definitions.

\def\AmSTeX{$\cal A$\kern-.1667em\lower.5ex\hbox
 {$\cal M$}\kern-.125em{$\cal S$}-\TeX}
\@ifundefined{normalshape}{\def\normalshape{\rm}}{}
\def\refp#1{{\normalshape(\ref{#1})}}
\@ifundefined{dfrac}{
\def\dfrac#1#2{{\displaystyle\frac{#1}{#2}}}
\def\tfrac#1#2{{\textstyle\frac{#1}{#2}}}
\def\binom#1#2{{#1\choose#2}}
\def\dbinom#1#2{{\displaystyle{#1\choose#2}}}
\def\tbinom#1#2{{\textstyle{#1\choose#2}}}
\def\Cal#1{{\cal#1}}
}{}

\newcommand{\footer}[1]{{\def\thefootnote{}\footnotetext{#1}}}

\def\mat{\array{*{16}{c}}} \def\endmat{\endarray}
\def\pmat{\left(\mat} \def\endpmat{\endmat\right)}
\def\bmat{\left[\mat} \def\endbmat{\endmat\right]}
\def\vmat{\left|\mat} \def\endvmat{\endmat\right|}
\def\cas{\left\{\array{l@{\quad}l}} \def\endcas{\endarray\right.}

\def\proclaim#1{\bgroup\trivlist\item[\hskip\labelsep{\bf#1}]\sl}
\def\endproclaim{\endtrivlist\egroup}

\def\EquationsBySection{\def\theequation{\thesection.\arabic{equation}}%
\@addtoreset{equation}{section}}
\def\EquationsBySubsection{\def\theequation{\thesubsection.\arabic{equation}}%
\@addtoreset{equation}{subsection}}

\def\proofheaderfont{\bf}
\def\proofbodyfont{}
\def\proofindent{}
\def\proofpunctuation{:}
\def\proofname{Proof}

\def\proof{\@proof{\proofname\proofpunctuation}}
\def\@proof#1{\par\addvspace{\medskipamount}\proofbodyfont
  \noindent\proofindent{\proofheaderfont#1}\enspace\ignorespaces}
\@namedef{proof*}#1{\@proof{#1}}
\@namedef{endproof*}{\endproof}
\def\endproof{\@endproof}
\def\@endproof{\par\addvspace{\smallskipamount}}
\def\QED{\def\endproof{\qed\@endproof}}
%\def\qedbox{\rule{1.ex}{1.em}}
%\def\qedbox{\raisebox{\fboxsep}{\fbox{}}}
\def\qedbox{\vbox{\hrule\hbox{\vrule height1.3ex\hskip0.8ex\vrule}\hrule}}
\def\qed{%
   {%
      \unskip
      \nobreak \hfil
      \penalty 50               % TeX should break here if necessary
      \hskip 1em                % mimium amount of distance
      \null \nobreak \hfil
      \qedbox
      \parfillskip=\z@skip
      \finalhyphendemerits=\z@  % no line break at last line of paragraph
      \endgraf                  % don't know what \par is in this moment...
   }}

% Plain macros for LaTeX
\def\eqalignno#1{\let\\=\cr\displ@y \tabskip\@centering
  \halign to\displaywidth{\hfil$\@lign\displaystyle{##}$\tabskip\z@skip
    &$\@lign\displaystyle{{}##}$\hfil\tabskip\@centering
    &\llap{$\@lign##$}\tabskip\z@skip\crcr
    #1\crcr}}
\def\leqalignno#1{\let\\=\cr\displ@y \tabskip\@centering
  \halign to\displaywidth{\hfil$\@lign\displaystyle{##}$\tabskip\z@skip
    &$\@lign\displaystyle{{}##}$\hfil\tabskip\@centering
    &\kern-\displaywidth\rlap{$\@lign##$}\tabskip\displaywidth\crcr
    #1\crcr}}
\def\eqalign#1{\null\,\vcenter{\openup\jot\m@th
  \ialign{\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil
      \crcr#1\crcr}}\,}
\def\rank{{\rm rank \,}}
\def\tr{{\rm tr \,}}
\def\re{{\rm Re\,}}
\def\conv{\buildrel \wedge \over}
\def\Sim{\buildrel \sim \over}
\def\diag{{\rm diag\,}}
\def\det{{\rm det\, }}
\def\Ad{{\rm Ad\,}}
\def\ad{{\rm ad\,}}
\def\dim{{\rm dim\,}}
\def\Aut{{\rm Aut\,}}
\def\End{{\rm End\,}}

\endinput
% \proclaim can be defined so that:
%  * The spacing matches theorems from \newtheorem
%  * The commands 
%		\begin{theorem} ... \end{theorem}
%		\proclaim{\theorem} ... \endproclaim
%    produce the same output.
% \def\proclaim#1{\trivlist\item[\hskip\labelsep{%
% \def\@xthm##1##2{\ignorespaces##2 \@currentlabel}\bf#1}]\bgroup\it}
% \def\endproclaim{\egroup\endtrivlist}