% siam.sty 11 Feb 88, based on article.sty 5 Feb 88
% Changed to hardwire the right headings for publications
% Christian Bischof, 22 January 1990
% last modified by P. Duggan 12/11/92
% Modified by TCI Software 12 July 94 . Commented \sev... stuff
\typeout{Document Style "siamltex". v2.1 Released 1 January 1993}
\def\myoddhead{ }
\def\myevenhead{ }

\def\@ptsize{0} \@namedef{ds@11pt}{\def\@ptsize{1}}
\@namedef{ds@12pt}{\def\@ptsize{2}} 
\def\ds@twoside{\@twosidetrue \@mparswitchtrue} \def\ds@draft{\overfullrule
5pt} 
\@options
\input siam1\@ptsize.sty\relax


\def\labelenumi{\arabic{enumi}.} 
\def\theenumi{\arabic{enumi}} 
\def\labelenumii{(\alph{enumii})}
\def\theenumii{(\alph{enumii})}
\def\p@enumii{\theenumi}
\def\labelenumiii{\roman{enumiii}.}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi\theenumii}
\def\labelenumiv{\Alph{enumiv}.}
\def\theenumiv{\Alph{enumiv}} 
\def\p@enumiv{\p@enumiii\theenumiii}

\def\labelitemi{$\bullet$}
\def\labelitemii{\bf --}
\def\labelitemiii{$\ast$}
\def\labelitemiv{$\cdot$}

\def\verse{\let\\=\@centercr 
 \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent 
 \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\listparindent 1.5em
 \itemindent\listparindent
 \rightmargin\leftmargin \parsep 0pt plus 1pt}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

%\def\descriptionlabel#1{\hspace\labelsep \bf #1}
%\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
% \let\makelabel\descriptionlabel}}
%\let\enddescription\endlist

\def\descriptionlabel#1{\bf #1}
\def\description{\list{}{\labelwidth10pt
 \let\makelabel\descriptionlabel}}
\let\enddescription\endlist

\newcounter{rmnum}

\newenvironment{romannum}{\begin{list}{{\rm (\roman{rmnum})}}{\usecounter{rmnum}
\setlength{\leftmargin}{0pt}\setlength{\itemindent}{42pt}}}{\end{list}}

\newcounter{muni}

\newenvironment{remunerate}{\begin{list}{{\rm \arabic{muni}.}}{\usecounter{muni}
\setlength{\leftmargin}{0pt}\setlength{\itemindent}{38pt}}}{\end{list}}


\newcounter{part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]

\def\@begintheorem#1#2{\par\bgroup{\sc #1\ #2. }\it\ignorespaces}
\def\@opargbegintheorem#1#2#3{\par\bgroup{\sc #1\ #2\ (#3). }\it\ignorespaces}
\def\@endtheorem{\egroup\par}
\def\proof{\par{\it Proof}. \ignorespaces}
\def\endproof{{\ \vbox{\hrule\hbox{%
   \vrule height1.3ex\hskip0.8ex\vrule}\hrule
  }}\par}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{proposition}[theorem]{Proposition}

\def\theequation{\arabic{equation}}
\def\@eqnnum{\hbox to .01pt{}\rlap{\rm \hskip -\displaywidth(\theequation)}}


\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
 \else \newpage \fi \thispagestyle{empty}\c@page\z@}
\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}

\arraycolsep 5pt \tabcolsep 6pt \arrayrulewidth .4pt \doublerulesep 2pt 
\tabbingsep \labelsep 

\skip\@mpfootins = \skip\footins
\fboxsep = 3pt \fboxrule = .4pt 

\def\thepart{\Roman{part}} \def\thesection {\arabic{section}}
\def\thesubsection {\thesection.\arabic{subsection}}
\def\thesubsubsection {\thesubsection .\arabic{subsubsection}}
\def\theparagraph {\thesubsubsection.\arabic{paragraph}}
\def\thesubparagraph {\theparagraph.\arabic{subparagraph}}
\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
     \def\@svsec{}\else 
     \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname.\hskip .5em }\fi
     \@tempskipa #5\relax
      \ifdim \@tempskipa>\z@ 
        \begingroup #6\relax
          \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}
        \endgroup
       \csname #1mark\endcsname{#7}\addcontentsline
         {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                      \protect\numberline{\csname the#1\endcsname}\fi
                    #7}\else
        \def\@svsechd{#6\hskip #3\@svsec #8.\csname #1mark\endcsname
                      {#7}\addcontentsline
                           {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                             \protect\numberline{\csname the#1\endcsname}\fi
                       #7}}\fi
     \@xsect{#5}}
\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax
   \ifdim \@tempskipa>\z@
     \begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M
#5.\par}\endgroup
   \else \def\@svsechd{#4\hskip #1\relax #5.}\fi
    \@xsect{#3}}


\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}

\def\tableofcontents{\section*{Contents\@mkboth{CONTENTS}{CONTENTS}}
 \@starttoc{toc}}
\def\l@part#1#2{\addpenalty{\@secpenalty}
 \addvspace{2.25em plus 1pt} \begingroup
 \@tempdima 3em \parindent \z@ \rightskip \@pnumwidth \parfillskip
-\@pnumwidth 
 {\bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
 \nobreak \endgroup}
\def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{1.0em plus 1pt}
\@tempdima 1.5em \begingroup
 \parindent \z@ \rightskip \@pnumwidth 
 \parfillskip -\@pnumwidth 
 \bf \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip #1\nobreak\hfil
\nobreak\hbox to\@pnumwidth{\hss #2}\par
 \endgroup}
\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\def\listoffigures{\section*{List of Figures\@mkboth
 {LIST OF FIGURES}{LIST OF FIGURES}}\@starttoc{lof}}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\def\listoftables{\section*{List of Tables\@mkboth
 {LIST OF TABLES}{LIST OF TABLES}}\@starttoc{lot}}
\let\l@table\l@figure


\def\thebibliography#1{\par\addvspace{.25in}%
\begin{center}\footnotesize REFERENCES\end{center}\@mkboth
 {REFERENCES}{REFERENCES}\addvspace{.15in}\nopagebreak\list
 {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}\leftmargin\labelwidth
 \advance\leftmargin\labelsep \advance\leftmargin 16pt \itemindent -16pt
 \usecounter{enumi}}
 \def\newblock{\hskip .11em plus .33em minus .07em}
 \sloppy\clubpenalty4000\widowpenalty4000
 \sfcode`\.=1000\relax\footnotesize}
\let\endthebibliography=\endlist
 

\newif\if@restonecol
\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
\columnseprule \z@
\columnsep 35pt\twocolumn[\section*{Index}]
 \@mkboth{INDEX}{INDEX}\thispagestyle{plain}\parindent\z@
 \parskip\z@ plus .3pt\relax\let\item\@idxitem}
\def\@idxitem{\par\hangindent 40pt}
\def\subitem{\par\hangindent 40pt \hspace*{20pt}}
\def\subsubitem{\par\hangindent 40pt \hspace*{30pt}}
\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}

\def\footnoterule{\kern-3\p@ 
 \hrule width .5in 
 \kern 2.6\p@} 

\long\def\@makefntext#1{\parindent .25in\noindent 
 \hbox to .25in{\hss$^{\@thefnmark}$\kern 3pt}#1}


\setcounter{topnumber}{2}
\def\topfraction{.9}
\setcounter{bottomnumber}{1}
\def\bottomfraction{.1}
\setcounter{totalnumber}{3}
\def\textfraction{.1}
\def\floatpagefraction{.91}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.7}
\def\dblfloatpagefraction{.5}


\def\@tabtxt{table}
\long\def\@makecaption#1#2{\footnotesize
        \setlength{\parindent}{1.5pc}
 \ifx\@captype\@tabtxt
\hbox to\hsize{\hfil{\sc #1}\hfil}%
 \setbox\@tempboxa\hbox{{\it #2}}%
 \ifdim \wd\@tempboxa >\hsize {\it #2}\par \else
 \hbox to \hsize{\hfil\box\@tempboxa\hfil}\fi
 \vskip 10pt
\else \vskip 10pt 
 \setbox\@tempboxa\hbox{{\sc #1}. {\it #2}}
 \ifdim \wd\@tempboxa >\hsize {\sc #1}. {\it #2}\par \else \hbox
to\hsize{\hfil\box\@tempboxa\hfil}%
 \fi
 \fi}


\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\fps@figure{tp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{Fig.\ \thefigure}
\def\figure{\@float{figure}}
\let\endfigure\end@float
\@namedef{figure*}{\@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}
\newcounter{table}
\def\thetable{\@arabic\c@table}
\def\fps@table{tp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{Table \thetable}
\def\table{\@float{table}}
\let\endtable\end@float
\@namedef{table*}{\@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}


\def\maketitle{\par
 \begingroup
 \def\thefootnote{\fnsymbol{footnote}}
 \def\@makefnmark{\hbox 
 to 0pt{$^{\@thefnmark}$\hss}} 
 \if@twocolumn 
 \twocolumn[\@maketitle] 
 \else %%%% commented out for \newpage
 \global\@topnum\z@ \@maketitle \fi\thispagestyle{plain}\@thanks
 \endgroup
 \setcounter{footnote}{0}
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax}
\def\@maketitle{%%% commented out\newpage
 \null
 \begin{center}
  {\bf\@ucnothanks\@title\par}\vskip .075in
  {\footnotesize\spaceskip=1.5\fontdimen2\the\font
  \def\and{\ \scriptsize AND }\@tempswafalse\expandafter\@doauth\@author\and\relax}
 \end{center}
 \par \vskip .11in}
\def\@ucnothanks#1{\expandafter\@ucnt#1\thanks\relax}
\def\@ucnt#1\thanks{\uppercase{#1}\futurelet\@tempa\@ucnta}
\def\@ucnta{\ifx\@tempa\relax\else\@ucntb\fi}
\def\@ucntb#1\thanks\relax{\thanks{#1}}
\def\@doauth#1\and{\let\@nextdoa=\@doauth
 \def\@tempc{\@ucnothanks{#1}}
 \futurelet\@tempa\@doautha}
\def\@doautha{\ifx\@tempa\relax
  \if@tempswa {\and}\fi
  \let\@nextdoa=\relax
 \else
  \if@tempswa \gdef\and{,\ \scriptsize AND }, \fi
 \fi
 \@tempc\unskip\@tempswatrue\@nextdoa}
\let\and=\relax
\def\@abssec#1{\vspace{.05in}\footnotesize \parindent .2in
{\bf #1. }\ignorespaces}
\def\abstract{\@abssec{Abstract}}
\def\keywords{\@abssec{Key words}}
\def\AMS{\@abssec{AMS subject classifications}}
\def\AM{\@abssec{AMS subject classification}}

\def\endabstract{\par\vspace{.1in}}
\let\endkeywords\endabstract
\let\endAMS\endabstract
\let\endAM\endabstract

\mark{{}{}} 

\def\ps@plain{\let\@mkboth\@gobbletwo
     \def\@oddhead{}\def\@oddfoot{\footnotesize\rm\hfil\thepage
     \hfil}\def\@evenhead{}\let\@evenfoot\@oddfoot}
\if@twoside \def\ps@headings{\let\@mkboth\markboth
\def\@oddfoot{}\def\@evenfoot{}\def\@evenhead{
\rm\rlap{\thepage}\footnotesize\rm
\hfil \leftmark\hfil}\def\@oddhead{\hbox{}\hfil
{\footnotesize\rm\rightmark \hfil}\llap{\rm\thepage}}
\def\sectionmark##1{\markboth {\uppercase{\ifnum \c@secnumdepth
>\z@
 \thesection.\hskip 1em\relax \fi ##1}}{}}\def\subsectionmark##1{\markright
{\ifnum \c@secnumdepth >\@ne
 \thesubsection.\hskip 1em\relax \fi ##1}}}
\else \def\ps@headings{\let\@mkboth\markboth\def\@oddfoot{}\def\@evenfoot{}%
\def\@oddhead{\hbox{}\hfil{\footnotesize\rm \rightmark}\hfil
\llap{\rm\thepage}}\def\sectionmark##1{\markright
{\uppercase{\ifnum \c@secnumdepth >\z@
 \thesection.\hskip 1em\relax \fi ##1}}}}
\fi
\def\ps@myheadings{\let\@mkboth\@gobbletwo
\def\@oddhead{\hbox{}\hfil{\footnotesize\rm {\scriptsize \myoddhead}
\rightmark}\hfil
\llap{\rm\thepage}}\def\@oddfoot{}%
\def\@evenhead{\rm\rlap{\thepage}\footnotesize\rm
\hfil \leftmark {\scriptsize \myevenhead}
\hfil\hbox{}}\def\@evenfoot{}\def\sectionmark##1{}%
\def\subsectionmark##1{}}

\def\sameauthor{\leavevmode\vrule height 2pt depth -1.6pt width 23pt}

\def\endproof{\vbox{\hrule\hbox{%
   \vrule height1.3ex\hskip0.8ex\vrule}\hrule
  }}

\def\today{\ifcase\month\or
 January\or February\or March\or April\or May\or June\or
 July\or August\or September\or October\or November\or December\fi
 \space\number\day, \number\year}


\ps@plain \pagenumbering{arabic} \onecolumn \if@twoside\else\raggedbottom\fi

% JCS - removed several lines here so that the style will run through 
% LaTeX2e

%\font\sevbf=cmbx7
%\@addfontinfo\@xpt{\def\pbf{\fam\bffam\tenbf}\scriptfont\bffam\sevbf}

%\font\eightbf=cmbx8
%\@addfontinfo\@viiipt{\def\pbf{\fam\bffam\tenbf}\textfont\bffam\eightbf}

%\font\sevsyb=cmbsy7
%\@addfontinfo\@xpt{\def\pbf{\fam\bffam\tensyb}\scriptfont\bffam\sevsyb}

%\font\sevsf=cmss8
%\@addfontinfo\@xpt{\def\psf{\fam\sffam\tensf}\scriptfont\sffam\sevsf}

%\@getfont\psc\scfam\@viiipt{cmcsc8} % this font is installation dependant

%\font\sevmib=cmmib7
%\@addfontinfo\@xpt{\def\boldmath{\@prtct\@nomathbold
%\scriptfont\@ne\sevmib \@prtct\@boldtrue}}

% FIXUP DOCUMENT STYLE OPTION
%    for LaTeX Version 2.09 <25 Jan 1988>
%        by John Hobby
%
% If the fleqn style option is also used, it should precede this one.
 
 
\hyphenation{bi-dif-fer-en-tial buzz-word data-path equi-vari-ant gauss-ian
    hexa-dec-i-mal le-gendre mass-a-chu-setts non-smooth
    qua-si-smooth stand-alone time-stamp wave-guide white-space}
 
 
 
 
% Fix Plain's \bigl, \Bigl, etc. macros so that they try to scale with
% LaTeX size changes.  This uses the fact that \@setsize sets \ht\strutbox
% to be 70% of the normal unstretched baselineskip.
 
\def\big#1{{\hbox{$\left#1\vcenter to1.428\ht\strutbox{}\right.\n@space$}}}
\def\Big#1{{\hbox{$\left#1\vcenter to2.142\ht\strutbox{}\right.\n@space$}}}
\def\bigg#1{{\hbox{$\left#1\vcenter to2.857\ht\strutbox{}\right.\n@space$}}}
\def\Bigg#1{{\hbox{$\left#1\vcenter to3.571\ht\strutbox{}\right.\n@space$}}}
\def\biggg#1{{\hbox{$\left#1\vcenter to4.286\ht\strutbox{}\right.\n@space$}}}
\def\Biggg#1{{\hbox{$\left#1\vcenter to5.000\ht\strutbox{}\right.\n@space$}}}
 
 
 
 
 
% Fix \sbox and \mbox so that they do not take the box contents as a
%parameter.
% This makes environments that  depend on catcode changes work inside
 
\def\sbox#1{\setbox#1\hbox}
\def\mbox{\leavevmode\hbox}
 
 
 
 
 
 
% Apply \addpenalty's trick for not confusing \addvspace so that the \write
% from \addtocontents or \addcontentsline will not mess up vertical spacing
 
\def\addvstuff#1{%
    \ifvmode\ifdim\lastskip=\z@ #1%
        \else \@tempskipb\lastskip
          \vskip -\lastskip #1\vskip\@tempskipb
        \fi
    \else #1\fi}
 
\def\addpenalty#1{\ifvmode
   \if@minipage\else\if@nobreak\else
      \addvstuff{\penalty#1}%
      \fi\fi
   \else\@noitemerr\fi}
 
\long\def\addtocontents#1#2{%
    \if@filesw \begingroup
    \let\label\@gobble \let\index\@gobble
    \def\protect##1{\string\string\string##1\string\space\space}%
    \edef\@tempa{\write \@auxout {\string\@writefile{#1}{#2}}}%
    \addvstuff{\@tempa \if@nobreak \ifvmode\nobreak\fi\fi}%
    \endgroup\fi}
 
\def\addcontentsline#1#2#3{%
    \if@filesw \begingroup
    \let\label\@gobble \let\index\@gobble
    \def\protect##1{\string\string\string##1\string\space\space}%
    \@temptokena{\thepage}%
    \edef\@tempa{\write \@auxout{\string\@writefile{#1}%
            {\protect\contentsline{#2}{#3}{\the\@temptokena}}}}%
    \addvstuff{\@tempa \if@nobreak \ifvmode\nobreak\fi\fi}%
    \endgroup\fi}
 
 
 
 
% Make floats use the trick from the minipage environment to avoid extraneous
% space at the top.  e.g., "\begin{figure} \begin{center}..."
 
\def\@xfloat#1[#2]{\ifhmode \@bsphack\@floatpenalty -\@Mii\else
   \@floatpenalty-\@Miii\fi\def\@captype{#1}\ifinner
      \@parmoderr\@floatpenalty\z@
    \else\@next\@currbox\@freelist{\@tempcnta\csname ftype@#1\endcsname
       \multiply\@tempcnta\@xxxii\advance\@tempcnta\sixt@@n
       \@tfor \@tempa :=#2\do
                        {\if\@tempa h\advance\@tempcnta \@ne\fi
                         \if\@tempa t\advance\@tempcnta \tw@\fi
                         \if\@tempa b\advance\@tempcnta 4\relax\fi
                         \if\@tempa p\advance\@tempcnta 8\relax\fi
         }\global\count\@currbox\@tempcnta}\@fltovf\fi
    \global\setbox\@currbox\vbox\bgroup
    \hsize\columnwidth \@parboxrestore
    \@minipagetrue
    \everypar{\global\@minipagefalse\everypar{}}}
 
 
 
 
% We now redefine the eqnarray environment to correct the space around
% the operator.  Since the fleqn document style option also redefines
% this environment, we carefully check the previous definition before
% making any changes.  Any changes to the definition in LaTeX itself
% or in the fleqn document style option will cause the `Warning: unable...'
% message to appear.  If this happens it will be necessary to update the
% definitions of \@tempa and \@tempb below and incorperate the changes into
% the new definitions of \eqnarray.
 
 
% This is the current definition of \eqnarray for the fleqn document style
% option:
 
\def\@tempa{\stepcounter{equation}\let\@currentlabel=\theequation
\global\@eqnswtrue
\global\@eqcnt\z@\tabskip\mathindent\let\\=\@eqncr
\abovedisplayskip\topsep\ifvmode\advance\abovedisplayskip\partopsep\fi
\belowdisplayskip\abovedisplayskip
\belowdisplayshortskip\abovedisplayskip
\abovedisplayshortskip\abovedisplayskip
$$\halign to
\linewidth\bgroup\@eqnsel\hskip\@centering$\displaystyle\tabskip\z@
{##}$&\global\@eqcnt\@ne \hskip 2\arraycolsep \hfil${##}$\hfil
&\global\@eqcnt\tw@ \hskip 2\arraycolsep $\displaystyle{##}$\hfil
\tabskip\@centering&\llap{##}\tabskip\z@\cr}
 
 
% Here is the corresponding defintion from latex.tex:
 
\def\@tempb{\stepcounter{equation}\let\@currentlabel=\theequation
\global\@eqnswtrue
\global\@eqcnt\z@\tabskip\@centering\let\\=\@eqncr
$$\halign to \displaywidth\bgroup\@eqnsel\hskip\@centering
 $\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@ne
  \hskip 2\arraycolsep \hfil${##}$\hfil
  &\global\@eqcnt\tw@ \hskip 2\arraycolsep $\displaystyle\tabskip\z@{##}$\hfil
   \tabskip\@centering&\llap{##}\tabskip\z@\cr}
 
 
\ifx\eqnarray\@tempa        % If the fleqn document style option is in effect
 
    \def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
    \global\@eqnswtrue
    \global\@eqcnt\z@\tabskip\mathindent\let\\=\@eqncr
    \abovedisplayskip\topsep\ifvmode\advance\abovedisplayskip\partopsep\fi
    \belowdisplayskip\abovedisplayskip
    \belowdisplayshortskip\abovedisplayskip
    \abovedisplayshortskip\abovedisplayskip
    $$\halign to \linewidth\bgroup\hfil
      $\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@ne
      \hfil$\displaystyle{{}##{}}$\hfil
      &\global\@eqcnt\tw@ $\displaystyle{##}$\hfil
       \tabskip\@centering&\llap{##}\tabskip\z@\cr}
 
\else\ifx\eqnarray\@tempb    % Else try the default eqnarray environment
 
    \def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
    \global\@eqnswtrue
    \global\@eqcnt\z@\tabskip\@centering\let\\=\@eqncr
    $$\halign to \displaywidth\bgroup\hfil
      $\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@ne
      \hfil$\displaystyle{{}##{}}$\hfil
      &\global\@eqcnt\tw@ $\displaystyle{##}$\hfil
       \tabskip\@centering&\llap{##}\tabskip\z@\cr}
 
\else    \typeout{Warning: Unable to fix unknown version of \string\enarray.}
\fi\fi
 
\def\@tempa{}            % Free up TeX's memory
\def\@tempb{}