\typeout{TCILATEX Macros for Scientific Word and Scientific WorkPlace 5.5 <06 Oct 2005>.}
\typeout{NOTICE:  This macro file is NOT proprietary and may be
freely copied and distributed.}

\makeatletter


\ifx\pdfoutput\relax\let\pdfoutput=\undefined\fi
\newcount\msipdfoutput
\ifx\pdfoutput\undefined
\else
 \ifcase\pdfoutput
 \else
    \msipdfoutput=1
    \ifx\paperwidth\undefined
    \else
      \ifdim\paperheight=0pt\relax
      \else
        \pdfpageheight\paperheight
      \fi
      \ifdim\paperwidth=0pt\relax
      \else
        \pdfpagewidth\paperwidth
      \fi
    \fi
  \fi
\fi


\def\FMTeXButton#1{#1}


\newcount\@hour\newcount\@minute\chardef\@x10\chardef\@xv60
\def\tcitime{
\def\@time{
  \@minute\time\@hour\@minute\divide\@hour\@xv
  \ifnum\@hour<\@x 0\fi\the\@hour:
  \multiply\@hour\@xv\advance\@minute-\@hour
  \ifnum\@minute<\@x 0\fi\the\@minute
  }}


\def\x@hyperref#1#2#3{
   
   \catcode`\~ = 12
   \catcode`\$ = 12
   \catcode`\_ = 12
   \catcode`\# = 12
   \catcode`\& = 12
   \catcode`\% = 12
   \y@hyperref{#1}{#2}{#3}
}

\def\y@hyperref#1#2#3#4{
   #2\ref{#4}#3
   \catcode`\~ = 13
   \catcode`\$ = 3
   \catcode`\_ = 8
   \catcode`\# = 6
   \catcode`\& = 4
   \catcode`\% = 14
}

\@ifundefined{hyperref}{\let\hyperref\x@hyperref}{}
\@ifundefined{msihyperref}{\let\msihyperref\x@hyperref}{}


\@ifundefined{qExtProgCall}{\def\qExtProgCall#1#2#3#4#5#6{\relax}}{}


\def\FILENAME#1{#1}

\def\QCTOpt[#1]#2{
  \def\QCTOptB{#1}
  \def\QCTOptA{#2}
}
\def\QCTNOpt#1{
  \def\QCTOptA{#1}
  \let\QCTOptB\empty
}
\def\Qct{
  \@ifnextchar[{
    \QCTOpt}{\QCTNOpt}
}
\def\QCBOpt[#1]#2{
  \def\QCBOptB{#1}
  \def\QCBOptA{#2}
}
\def\QCBNOpt#1{
  \def\QCBOptA{#1}
  \let\QCBOptB\empty
}
\def\Qcb{
  \@ifnextchar[{
    \QCBOpt}{\QCBNOpt}
}
\def\PrepCapArgs{
  \ifx\QCBOptA\empty
    \ifx\QCTOptA\empty
      {}
    \else
      \ifx\QCTOptB\empty
        {\QCTOptA}
      \else
        [\QCTOptB]{\QCTOptA}
      \fi
    \fi
  \else
    \ifx\QCBOptA\empty
      {}
    \else
      \ifx\QCBOptB\empty
        {\QCBOptA}
      \else
        [\QCBOptB]{\QCBOptA}
      \fi
    \fi
  \fi
}
\newcount\GRAPHICSTYPE


\GRAPHICSTYPE=\z@
\def\GRAPHICSPS#1{
 \ifcase\GRAPHICSTYPE
   \special{ps: #1}
 \or
   \special{language "PS", include "#1"}


 \fi
}

\def\GRAPHICSHP#1{\special{include #1}}


\def\graffile#1#2#3#4{


  
  
    \bgroup
       \@inlabelfalse
       \leavevmode
       \@ifundefined{bbl@deactivate}{\def~{\string~}}{\activesoff}
        \raise -#4 \BOXTHEFRAME{
           \hbox to #2{\raise #3\hbox to #2{\null #1\hfil}}}
    \egroup
}


\def\draftbox#1#2#3#4{
 \leavevmode\raise -#4 \hbox{
  \frame{\rlap{\protect\tiny #1}\hbox to #2
   {\vrule height#3 width\z@ depth\z@\hfil}
  }
 }
}

\newcount\@msidraft
\@msidraft=\z@
\let\nographics=\@msidraft
\newif\ifwasdraft
\wasdraftfalse


\def\GRAPHIC#1#2#3#4#5{
   \ifnum\@msidraft=\@ne\draftbox{#2}{#3}{#4}{#5}
   \else\graffile{#1}{#3}{#4}{#5}
   \fi
}

\def\addtoLaTeXparams#1{
    \edef\LaTeXparams{\LaTeXparams #1}}


\newif\ifBoxFrame \BoxFramefalse
\newif\ifOverFrame \OverFramefalse
\newif\ifUnderFrame \UnderFramefalse

\def\BOXTHEFRAME#1{
   \hbox{
      \ifBoxFrame
         \frame{#1}
      \else
         {#1}
      \fi
   }
}


\def\doFRAMEparams#1{\BoxFramefalse\OverFramefalse\UnderFramefalse\readFRAMEparams#1\end}
\def\readFRAMEparams#1{
 \ifx#1\end
  \let\next=\relax
  \else
  \ifx#1i\dispkind=\z@\fi
  \ifx#1d\dispkind=\@ne\fi
  \ifx#1f\dispkind=\tw@\fi
  \ifx#1t\addtoLaTeXparams{t}\fi
  \ifx#1b\addtoLaTeXparams{b}\fi
  \ifx#1p\addtoLaTeXparams{p}\fi
  \ifx#1h\addtoLaTeXparams{h}\fi
  \ifx#1X\BoxFrametrue\fi
  \ifx#1O\OverFrametrue\fi
  \ifx#1U\UnderFrametrue\fi
  \ifx#1w
    \ifnum\@msidraft=1\wasdrafttrue\else\wasdraftfalse\fi
    \@msidraft=\@ne
  \fi
  \let\next=\readFRAMEparams
  \fi
 \next
 }


\def\IFRAME#1#2#3#4#5#6{
      \bgroup
      \let\QCTOptA\empty
      \let\QCTOptB\empty
      \let\QCBOptA\empty
      \let\QCBOptB\empty
      #6
      \parindent=0pt
      \leftskip=0pt
      \rightskip=0pt
      \setbox0=\hbox{\QCBOptA}
      \@tempdima=#1\relax
      \ifOverFrame
          
          \typeout{This is not implemented yet}
          \show\HELP
      \else
         \ifdim\wd0>\@tempdima
            \advance\@tempdima by \@tempdima
            \ifdim\wd0 >\@tempdima
               \setbox1 =\vbox{
                  \unskip\hbox to \@tempdima{\hfill\GRAPHIC{#5}{#4}{#1}{#2}{#3}\hfill}
                  \unskip\hbox to \@tempdima{\parbox[b]{\@tempdima}{\QCBOptA}}
               }
               \wd1=\@tempdima
            \else
               \textwidth=\wd0
               \setbox1 =\vbox{
                 \noindent\hbox to \wd0{\hfill\GRAPHIC{#5}{#4}{#1}{#2}{#3}\hfill}\\%
                 \noindent\hbox{\QCBOptA}
               }
               \wd1=\wd0
            \fi
         \else
            \ifdim\wd0>0pt
              \hsize=\@tempdima
              \setbox1=\vbox{
                \unskip\GRAPHIC{#5}{#4}{#1}{#2}{0pt}
                \break
                \unskip\hbox to \@tempdima{\hfill \QCBOptA\hfill}
              }
              \wd1=\@tempdima
           \else
              \hsize=\@tempdima
              \setbox1=\vbox{
                \unskip\GRAPHIC{#5}{#4}{#1}{#2}{0pt}
              }
              \wd1=\@tempdima
           \fi
         \fi
         \@tempdimb=\ht1
         
         \advance\@tempdimb by -#2
         \advance\@tempdimb by #3
         \leavevmode
         \raise -\@tempdimb \hbox{\box1}
      \fi
      \egroup
}


\def\DFRAME#1#2#3#4#5{
  \vspace\topsep
  \hfil\break
  \bgroup
     \leftskip\@flushglue
     \rightskip\@flushglue
     \parindent\z@
     \parfillskip\z@skip
     \let\QCTOptA\empty
     \let\QCTOptB\empty
     \let\QCBOptA\empty
     \let\QCBOptB\empty
     \vbox\bgroup
        \ifOverFrame
           #5\QCTOptA\par
        \fi
        \GRAPHIC{#4}{#3}{#1}{#2}{\z@}
        \ifUnderFrame
           \break#5\QCBOptA
        \fi
     \egroup
  \egroup
  \vspace\topsep
  \break
}


\def\FFRAME#1#2#3#4#5#6#7{
 
  \@ifundefined{floatstyle}
    {
     \begin{figure}[#1]
    }
    {
     \ifx#1h
      \begin{figure}[H]
     \else
      \begin{figure}[#1]
     \fi
    }
  \let\QCTOptA\empty
  \let\QCTOptB\empty
  \let\QCBOptA\empty
  \let\QCBOptB\empty
  \ifOverFrame
    #4
    \ifx\QCTOptA\empty
    \else
      \ifx\QCTOptB\empty
        \caption{\QCTOptA}
      \else
        \caption[\QCTOptB]{\QCTOptA}
      \fi
    \fi
    \ifUnderFrame\else
      \label{#5}
    \fi
  \else
    \UnderFrametrue
  \fi
  \begin{center}\GRAPHIC{#7}{#6}{#2}{#3}{\z@}\end{center}
  \ifUnderFrame
    #4
    \ifx\QCBOptA\empty
      \caption{}
    \else
      \ifx\QCBOptB\empty
        \caption{\QCBOptA}
      \else
        \caption[\QCBOptB]{\QCBOptA}
      \fi
    \fi
    \label{#5}
  \fi
  \end{figure}
 }


\newcount\dispkind

\def\makeactives{
  \catcode`\"=\active
  \catcode`\;=\active
  \catcode`\:=\active
  \catcode`\'=\active
  \catcode`\~=\active
}
\bgroup
   \makeactives
   \gdef\activesoff{
      \def"{\string"}
      \def;{\string;}
      \def:{\string:}
      \def'{\string'}
      \def~{\string~}
      
      
      
      
    }
\egroup

\def\FRAME#1#2#3#4#5#6#7#8{
 \bgroup
 \ifnum\@msidraft=\@ne
   \wasdrafttrue
 \else
   \wasdraftfalse
 \fi
 \def\LaTeXparams{}
 \dispkind=\z@
 \def\LaTeXparams{}
 \doFRAMEparams{#1}
 \ifnum\dispkind=\z@\IFRAME{#2}{#3}{#4}{#7}{#8}{#5}\else
  \ifnum\dispkind=\@ne\DFRAME{#2}{#3}{#7}{#8}{#5}\else
   \ifnum\dispkind=\tw@
    \edef\@tempa{\noexpand\FFRAME{\LaTeXparams}}
    \@tempa{#2}{#3}{#5}{#6}{#7}{#8}
    \fi
   \fi
  \fi
  \ifwasdraft\@msidraft=1\else\@msidraft=0\fi{}
  \egroup
 }


\def\TEXUX#1{"texux"}


\def\BF#1{{\bf {#1}}}
\def\NEG#1{\leavevmode\hbox{\rlap{\thinspace/}{$#1$}}}


\def\limfunc#1{\mathop{\rm #1}}
\def\func#1{\mathop{\rm #1}\nolimits}

\def\unit#1{\mathord{\thinspace\rm #1}}


\long\def\QQQ#1#2{
     \long\expandafter\def\csname#1\endcsname{#2}}
\@ifundefined{QTP}{\def\QTP#1{}}{}
\@ifundefined{QEXCLUDE}{\def\QEXCLUDE#1{}}{}
\@ifundefined{Qlb}{\def\Qlb#1{#1}}{}
\@ifundefined{Qlt}{\def\Qlt#1{#1}}{}
\def\QWE{}
\long\def\QQA#1#2{}
\def\QTR#1#2{{\csname#1\endcsname {#2}}}
  
  \let\QQQuline\uline
  \let\QQQsout\sout
  \let\QQQuuline\uuline
  \let\QQQuwave\uwave
  \let\QQQxout\xout
\long\def\TeXButton#1#2{#2}
\long\def\QSubDoc#1#2{#2}
\def\EXPAND#1[#2]#3{}
\def\NOEXPAND#1[#2]#3{}
\def\PROTECTED{}
\def\LaTeXparent#1{}
\def\ChildStyles#1{}
\def\ChildDefaults#1{}
\def\QTagDef#1#2#3{}


\@ifundefined{correctchoice}{\def\correctchoice{\relax}}{}
\@ifundefined{HTML}{\def\HTML#1{\relax}}{}
\@ifundefined{TCIIcon}{\def\TCIIcon#1#2#3#4{\relax}}{}
\if@compatibility
  \typeout{Not defining UNICODE  U or CustomNote commands for LaTeX 2.09.}
\else
  \providecommand{\UNICODE}[2][]{\protect\rule{.1in}{.1in}}
  \providecommand{\U}[1]{\protect\rule{.1in}{.1in}}
  \providecommand{\CustomNote}[3][]{\marginpar{#3}}
\fi

\@ifundefined{lambdabar}{
      \def\lambdabar{\errmessage{You have used the lambdabar symbol.
                      This is available for typesetting only in RevTeX styles.}}
   }{}


\@ifundefined{StyleEditBeginDoc}{\def\StyleEditBeginDoc{\relax}}{}


\def\QQfnmark#1{\footnotemark}
\def\QQfntext#1#2{\addtocounter{footnote}{#1}\footnotetext{#2}}


\@ifundefined{TCIMAKEINDEX}{}{\makeindex}


\@ifundefined{abstract}{
 \def\abstract{
  \if@twocolumn
   \section*{Abstract (Not appropriate in this style!)}
   \else \small
   \begin{center}{\bf Abstract\vspace{-.5em}\vspace{\z@}}\end{center}
   \quotation
   \fi
  }
 }{
 }
\@ifundefined{endabstract}{\def\endabstract
  {\if@twocolumn\else\endquotation\fi}}{}
\@ifundefined{maketitle}{\def\maketitle#1{}}{}
\@ifundefined{affiliation}{\def\affiliation#1{}}{}
\@ifundefined{proof}{\def\proof{\noindent{\bfseries Proof. }}}{}
\@ifundefined{endproof}{\def\endproof{\mbox{\ \rule{.1in}{.1in}}}}{}
\@ifundefined{newfield}{\def\newfield#1#2{}}{}
\@ifundefined{chapter}{\def\chapter#1{\par(Chapter head:)#1\par }
 \newcount\c@chapter}{}
\@ifundefined{part}{\def\part#1{\par(Part head:)#1\par }}{}
\@ifundefined{section}{\def\section#1{\par(Section head:)#1\par }}{}
\@ifundefined{subsection}{\def\subsection#1
 {\par(Subsection head:)#1\par }}{}
\@ifundefined{subsubsection}{\def\subsubsection#1
 {\par(Subsubsection head:)#1\par }}{}
\@ifundefined{paragraph}{\def\paragraph#1
 {\par(Subsubsubsection head:)#1\par }}{}
\@ifundefined{subparagraph}{\def\subparagraph#1
 {\par(Subsubsubsubsection head:)#1\par }}{}


\@ifundefined{therefore}{\def\therefore{}}{}
\@ifundefined{backepsilon}{\def\backepsilon{}}{}
\@ifundefined{yen}{\def\yen{\hbox{\rm\rlap=Y}}}{}
\@ifundefined{registered}{
   \def\registered{\relax\ifmmode{}\r@gistered
                    \else$\m@th\r@gistered$\fi}
 \def\r@gistered{^{\ooalign
  {\hfil\raise.07ex\hbox{$\scriptstyle\rm\text{R}$}\hfil\crcr
  \mathhexbox20D}}}}{}
\@ifundefined{Eth}{\def\Eth{}}{}
\@ifundefined{eth}{\def\eth{}}{}
\@ifundefined{Thorn}{\def\Thorn{}}{}
\@ifundefined{thorn}{\def\thorn{}}{}

\def\TEXTsymbol#1{\mbox{$#1$}}
\@ifundefined{degree}{\def\degree{{}^{\circ}}}{}


\newdimen\theight
\@ifundefined{Column}{\def\Column{
 \vadjust{\setbox\z@=\hbox{\scriptsize\quad\quad tcol}
  \theight=\ht\z@\advance\theight by \dp\z@\advance\theight by \lineskip
  \kern -\theight \vbox to \theight{
   \rightline{\rlap{\box\z@}}
   \vss
   }
  }
 }}{}

\@ifundefined{qed}{\def\qed{
 \ifhmode\unskip\nobreak\fi\ifmmode\ifinner\else\hskip5\p@\fi\fi
 \hbox{\hskip5\p@\vrule width4\p@ height6\p@ depth1.5\p@\hskip\p@}
 }}{}

\@ifundefined{cents}{\def\cents{\hbox{\rm\rlap c/}}}{}
\@ifundefined{tciLaplace}{\def\tciLaplace{\ensuremath{\mathcal{L}}}}{}
\@ifundefined{tciFourier}{\def\tciFourier{\ensuremath{\mathcal{F}}}}{}
\@ifundefined{textcurrency}{\def\textcurrency{\hbox{\rm\rlap xo}}}{}
\@ifundefined{texteuro}{\def\texteuro{\hbox{\rm\rlap C=}}}{}
\@ifundefined{euro}{\def\euro{\hbox{\rm\rlap C=}}}{}
\@ifundefined{textfranc}{\def\textfranc{\hbox{\rm\rlap-F}}}{}
\@ifundefined{textlira}{\def\textlira{\hbox{\rm\rlap L=}}}{}
\@ifundefined{textpeseta}{\def\textpeseta{\hbox{\rm P\negthinspace s}}}{}

\@ifundefined{miss}{\def\miss{\hbox{\vrule height2\p@ width 2\p@ depth\z@}}}{}

\@ifundefined{vvert}{\def\vvert{\Vert}}{}

\@ifundefined{tcol}{\def\tcol#1{{\baselineskip=6\p@ \vcenter{#1}} \Column}}{}

\@ifundefined{dB}{\def\dB{\hbox{{}}}}{}
\@ifundefined{mB}{\def\mB#1{\hbox{$#1$}}}{}
\@ifundefined{nB}{\def\nB#1{\hbox{#1}}}{}

\@ifundefined{note}{\def\note{$^{\dag}}}{}

\def\newfmtname{LaTeX2e}


\ifx\fmtname\newfmtname
  \DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
  \DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
  \DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
  \DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
  \DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
  \DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
  \DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
\fi


\def\alpha{{\Greekmath 010B}}
\def\beta{{\Greekmath 010C}}
\def\gamma{{\Greekmath 010D}}
\def\delta{{\Greekmath 010E}}
\def\epsilon{{\Greekmath 010F}}
\def\zeta{{\Greekmath 0110}}
\def\eta{{\Greekmath 0111}}
\def\theta{{\Greekmath 0112}}
\def\iota{{\Greekmath 0113}}
\def\kappa{{\Greekmath 0114}}
\def\lambda{{\Greekmath 0115}}
\def\mu{{\Greekmath 0116}}
\def\nu{{\Greekmath 0117}}
\def\xi{{\Greekmath 0118}}
\def\pi{{\Greekmath 0119}}
\def\rho{{\Greekmath 011A}}
\def\sigma{{\Greekmath 011B}}
\def\tau{{\Greekmath 011C}}
\def\upsilon{{\Greekmath 011D}}
\def\phi{{\Greekmath 011E}}
\def\chi{{\Greekmath 011F}}
\def\psi{{\Greekmath 0120}}
\def\omega{{\Greekmath 0121}}
\def\varepsilon{{\Greekmath 0122}}
\def\vartheta{{\Greekmath 0123}}
\def\varpi{{\Greekmath 0124}}
\def\varrho{{\Greekmath 0125}}
\def\varsigma{{\Greekmath 0126}}
\def\varphi{{\Greekmath 0127}}

\def\nabla{{\Greekmath 0272}}
\def\FindBoldGroup{
   {\setbox0=\hbox{$\mathbf{x\global\edef\theboldgroup{\the\mathgroup}}$}}
}

\def\Greekmath#1#2#3#4{
    \if@compatibility
        \ifnum\mathgroup=\symbold
           \mathchoice{\mbox{\boldmath$\displaystyle\mathchar"#1#2#3#4$}}
                      {\mbox{\boldmath$\textstyle\mathchar"#1#2#3#4$}}
                      {\mbox{\boldmath$\scriptstyle\mathchar"#1#2#3#4$}}
                      {\mbox{\boldmath$\scriptscriptstyle\mathchar"#1#2#3#4$}}
        \else
           \mathchar"#1#2#3#4
        \fi
    \else
        \FindBoldGroup
        \ifnum\mathgroup=\theboldgroup 
           \mathchoice{\mbox{\boldmath$\displaystyle\mathchar"#1#2#3#4$}}
                      {\mbox{\boldmath$\textstyle\mathchar"#1#2#3#4$}}
                      {\mbox{\boldmath$\scriptstyle\mathchar"#1#2#3#4$}}
                      {\mbox{\boldmath$\scriptscriptstyle\mathchar"#1#2#3#4$}}
        \else
           \mathchar"#1#2#3#4
        \fi
      \fi}

\newif\ifGreekBold  \GreekBoldfalse
\let\SAVEPBF=\pbf
\def\pbf{\GreekBoldtrue\SAVEPBF}


\@ifundefined{theorem}{\newtheorem{theorem}{Theorem}}{}
\@ifundefined{lemma}{\newtheorem{lemma}{Lemma}}{}
\@ifundefined{corollary}{\newtheorem{corollary}{Corollary}}{}
\@ifundefined{conjecture}{\newtheorem{conjecture}{Conjecture}}{}
\@ifundefined{proposition}{\newtheorem{proposition}{Proposition}}{}
\@ifundefined{axiom}{\newtheorem{axiom}{Axiom}}{}
\@ifundefined{remark}{\newtheorem{remark}{Remark}}{}
\@ifundefined{example}{\newtheorem{example}{Example}}{}
\@ifundefined{exercise}{\newtheorem{exercise}{Exercise}}{}
\@ifundefined{definition}{\newtheorem{definition}{Definition}}{}


\@ifundefined{mathletters}{
  
  \newcounter{equationnumber}
  \def\mathletters{
     \addtocounter{equation}{1}
     \edef\@currentlabel{\theequation}
     \setcounter{equationnumber}{\c@equation}
     \setcounter{equation}{0}
     \edef\theequation{\@currentlabel\noexpand\alph{equation}}
  }
  \def\endmathletters{
     \setcounter{equation}{\value{equationnumber}}
  }
}{}


\@ifundefined{BibTeX}{
    \def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em
                 T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}}{}
\@ifundefined{AmS}
    {\def\AmS{{\protect\usefont{OMS}{cmsy}{m}{n}
                A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}}{}
\@ifundefined{AmSTeX}{\def\AmSTeX{\protect\AmS-\protect\TeX\@}}{}


\def\@@eqncr{\let\@tempa\relax
    \ifcase\@eqcnt \def\@tempa{& & &}\or \def\@tempa{& &}
      \else \def\@tempa{&}\fi
     \@tempa
     \if@eqnsw
        \iftag@
           \@taggnum
        \else
           \@eqnnum\stepcounter{equation}
        \fi
     \fi
     \global\tag@false
     \global\@eqnswtrue
     \global\@eqcnt\z@\cr}


\def\TCItag{\@ifnextchar*{\@TCItagstar}{\@TCItag}}
\def\@TCItag#1{
    \global\tag@true
    \global\def\@taggnum{(#1)}
    \global\def\@currentlabel{#1}}
\def\@TCItagstar*#1{
    \global\tag@true
    \global\def\@taggnum{#1}
    \global\def\@currentlabel{#1}}


\def\QATOP#1#2{{#1 \atop #2}}
\def\QTATOP#1#2{{\textstyle {#1 \atop #2}}}
\def\QDATOP#1#2{{\displaystyle {#1 \atop #2}}}
\def\QABOVE#1#2#3{{#2 \above#1 #3}}
\def\QTABOVE#1#2#3{{\textstyle {#2 \above#1 #3}}}
\def\QDABOVE#1#2#3{{\displaystyle {#2 \above#1 #3}}}
\def\QOVERD#1#2#3#4{{#3 \overwithdelims#1#2 #4}}
\def\QTOVERD#1#2#3#4{{\textstyle {#3 \overwithdelims#1#2 #4}}}
\def\QDOVERD#1#2#3#4{{\displaystyle {#3 \overwithdelims#1#2 #4}}}
\def\QATOPD#1#2#3#4{{#3 \atopwithdelims#1#2 #4}}
\def\QTATOPD#1#2#3#4{{\textstyle {#3 \atopwithdelims#1#2 #4}}}
\def\QDATOPD#1#2#3#4{{\displaystyle {#3 \atopwithdelims#1#2 #4}}}
\def\QABOVED#1#2#3#4#5{{#4 \abovewithdelims#1#2#3 #5}}
\def\QTABOVED#1#2#3#4#5{{\textstyle
   {#4 \abovewithdelims#1#2#3 #5}}}
\def\QDABOVED#1#2#3#4#5{{\displaystyle
   {#4 \abovewithdelims#1#2#3 #5}}}


\def\tint{\msi@int\textstyle\int}
\def\tiint{\msi@int\textstyle\iint}
\def\tiiint{\msi@int\textstyle\iiint}
\def\tiiiint{\msi@int\textstyle\iiiint}
\def\tidotsint{\msi@int\textstyle\idotsint}
\def\toint{\msi@int\textstyle\oint}


\def\tsum{\mathop{\textstyle \sum }}
\def\tprod{\mathop{\textstyle \prod }}
\def\tbigcap{\mathop{\textstyle \bigcap }}
\def\tbigwedge{\mathop{\textstyle \bigwedge }}
\def\tbigoplus{\mathop{\textstyle \bigoplus }}
\def\tbigodot{\mathop{\textstyle \bigodot }}
\def\tbigsqcup{\mathop{\textstyle \bigsqcup }}
\def\tcoprod{\mathop{\textstyle \coprod }}
\def\tbigcup{\mathop{\textstyle \bigcup }}
\def\tbigvee{\mathop{\textstyle \bigvee }}
\def\tbigotimes{\mathop{\textstyle \bigotimes }}
\def\tbiguplus{\mathop{\textstyle \biguplus }}


\newtoks\temptoksa
\newtoks\temptoksb
\newtoks\temptoksc


\def\msi@int#1#2{
 \def\@temp{{#1#2\the\temptoksc_{\the\temptoksa}^{\the\temptoksb}}}
 \futurelet\@nextcs
 \@int
}

\def\@int{
   \ifx\@nextcs\limits
      \typeout{Found limits}
      \temptoksc={\limits}
      \let\@next\@intgobble
   \else\ifx\@nextcs\nolimits
      \typeout{Found nolimits}
      \temptoksc={\nolimits}
      \let\@next\@intgobble
   \else
      \typeout{Did not find limits or no limits}
      \temptoksc={}
      \let\@next\msi@limits
   \fi\fi
   \@next
}

\def\@intgobble#1{
   \typeout{arg is #1}
   \msi@limits
}


\def\msi@limits{
   \temptoksa={}
   \temptoksb={}
   \@ifnextchar_{\@limitsa}{\@limitsb}
}

\def\@limitsa_#1{
   \temptoksa={#1}
   \@ifnextchar^{\@limitsc}{\@temp}
}

\def\@limitsb{
   \@ifnextchar^{\@limitsc}{\@temp}
}

\def\@limitsc^#1{
   \temptoksb={#1}
   \@ifnextchar_{\@limitsd}{\@temp}
}

\def\@limitsd_#1{
   \temptoksa={#1}
   \@temp
}


\def\dint{\msi@int\displaystyle\int}
\def\diint{\msi@int\displaystyle\iint}
\def\diiint{\msi@int\displaystyle\iiint}
\def\diiiint{\msi@int\displaystyle\iiiint}
\def\didotsint{\msi@int\displaystyle\idotsint}
\def\doint{\msi@int\displaystyle\oint}

\def\dsum{\mathop{\displaystyle \sum }}
\def\dprod{\mathop{\displaystyle \prod }}
\def\dbigcap{\mathop{\displaystyle \bigcap }}
\def\dbigwedge{\mathop{\displaystyle \bigwedge }}
\def\dbigoplus{\mathop{\displaystyle \bigoplus }}
\def\dbigodot{\mathop{\displaystyle \bigodot }}
\def\dbigsqcup{\mathop{\displaystyle \bigsqcup }}
\def\dcoprod{\mathop{\displaystyle \coprod }}
\def\dbigcup{\mathop{\displaystyle \bigcup }}
\def\dbigvee{\mathop{\displaystyle \bigvee }}
\def\dbigotimes{\mathop{\displaystyle \bigotimes }}
\def\dbiguplus{\mathop{\displaystyle \biguplus }}

\if@compatibility\else
  
  \RequirePackage{amsmath}
\fi

\def\ExitTCILatex{\makeatother\endinput}

\bgroup
\ifx\ds@amstex\relax
   \message{amstex already loaded}\aftergroup\ExitTCILatex
\else
   \@ifpackageloaded{amsmath}
      {\if@compatibility\message{amsmath already loaded}\fi\aftergroup\ExitTCILatex}
      {}
   \@ifpackageloaded{amstex}
      {\if@compatibility\message{amstex already loaded}\fi\aftergroup\ExitTCILatex}
      {}
   \@ifpackageloaded{amsgen}
      {\if@compatibility\message{amsgen already loaded}\fi\aftergroup\ExitTCILatex}
      {}
\fi
\egroup


\typeout{TCILATEX defining AMS-like constructs in LaTeX 2.09 COMPATIBILITY MODE}


\let\DOTSI\relax
\def\RIfM@{\relax\ifmmode}
\def\FN@{\futurelet\next}
\newcount\intno@
\def\iint{\DOTSI\intno@\tw@\FN@\ints@}
\def\iiint{\DOTSI\intno@\thr@@\FN@\ints@}
\def\iiiint{\DOTSI\intno@4 \FN@\ints@}
\def\idotsint{\DOTSI\intno@\z@\FN@\ints@}
\def\ints@{\findlimits@\ints@@}
\newif\iflimtoken@
\newif\iflimits@
\def\findlimits@{\limtoken@true\ifx\next\limits\limits@true
 \else\ifx\next\nolimits\limits@false\else
 \limtoken@false\ifx\ilimits@\nolimits\limits@false\else
 \ifinner\limits@false\else\limits@true\fi\fi\fi\fi}
\def\multint@{\int\ifnum\intno@=\z@\intdots@                          
 \else\intkern@\fi                                                    
 \ifnum\intno@>\tw@\int\intkern@\fi                                   
 \ifnum\intno@>\thr@@\int\intkern@\fi                                 
 \int}
\def\multintlimits@{\intop\ifnum\intno@=\z@\intdots@\else\intkern@\fi
 \ifnum\intno@>\tw@\intop\intkern@\fi
 \ifnum\intno@>\thr@@\intop\intkern@\fi\intop}
\def\intic@{
    \mathchoice{\hskip.5em}{\hskip.4em}{\hskip.4em}{\hskip.4em}}
\def\negintic@{\mathchoice
 {\hskip-.5em}{\hskip-.4em}{\hskip-.4em}{\hskip-.4em}}
\def\ints@@{\iflimtoken@                                              
 \def\ints@@@{\iflimits@\negintic@
   \mathop{\intic@\multintlimits@}\limits                             
  \else\multint@\nolimits\fi                                          
  \eat@}
 \else                                                                
 \def\ints@@@{\iflimits@\negintic@
  \mathop{\intic@\multintlimits@}\limits\else
  \multint@\nolimits\fi}\fi\ints@@@}
\def\intkern@{\mathchoice{\!\!\!}{\!\!}{\!\!}{\!\!}}
\def\plaincdots@{\mathinner{\cdotp\cdotp\cdotp}}
\def\intdots@{\mathchoice{\plaincdots@}
 {{\cdotp}\mkern1.5mu{\cdotp}\mkern1.5mu{\cdotp}}
 {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}
 {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}}


\def\RIfM@{\relax\protect\ifmmode}
\def\text{\RIfM@\expandafter\text@\else\expandafter\mbox\fi}
\let\nfss@text\text
\def\text@#1{\mathchoice
   {\textdef@\displaystyle\f@size{#1}}
   {\textdef@\textstyle\tf@size{\firstchoice@false #1}}
   {\textdef@\textstyle\sf@size{\firstchoice@false #1}}
   {\textdef@\textstyle \ssf@size{\firstchoice@false #1}}
   \glb@settings}

\def\textdef@#1#2#3{\hbox{{
                    \everymath{#1}
                    \let\f@size#2\selectfont
                    #3}}}
\newif\iffirstchoice@
\firstchoice@true


\def\Let@{\relax\iffalse{\fi\let\\=\cr\iffalse}\fi}
\def\vspace@{\def\vspace##1{\crcr\noalign{\vskip##1\relax}}}
\def\multilimits@{\bgroup\vspace@\Let@
 \baselineskip\fontdimen10 \scriptfont\tw@
 \advance\baselineskip\fontdimen12 \scriptfont\tw@
 \lineskip\thr@@\fontdimen8 \scriptfont\thr@@
 \lineskiplimit\lineskip
 \vbox\bgroup\ialign\bgroup\hfil$\m@th\scriptstyle{##}$\hfil\crcr}
\def\Sb{_\multilimits@}
\def\endSb{\crcr\egroup\egroup\egroup}
\def\Sp{^\multilimits@}
\let\endSp\endSb


\newdimen\ex@
\ex@.2326ex
\def\rightarrowfill@#1{$#1\m@th\mathord-\mkern-6mu\cleaders
 \hbox{$#1\mkern-2mu\mathord-\mkern-2mu$}\hfill
 \mkern-6mu\mathord\rightarrow$}
\def\leftarrowfill@#1{$#1\m@th\mathord\leftarrow\mkern-6mu\cleaders
 \hbox{$#1\mkern-2mu\mathord-\mkern-2mu$}\hfill\mkern-6mu\mathord-$}
\def\leftrightarrowfill@#1{$#1\m@th\mathord\leftarrow
\mkern-6mu\cleaders
 \hbox{$#1\mkern-2mu\mathord-\mkern-2mu$}\hfill
 \mkern-6mu\mathord\rightarrow$}
\def\overrightarrow{\mathpalette\overrightarrow@}
\def\overrightarrow@#1#2{\vbox{\ialign{##\crcr\rightarrowfill@#1\crcr
 \noalign{\kern-\ex@\nointerlineskip}$\m@th\hfil#1#2\hfil$\crcr}}}
\let\overarrow\overrightarrow
\def\overleftarrow{\mathpalette\overleftarrow@}
\def\overleftarrow@#1#2{\vbox{\ialign{##\crcr\leftarrowfill@#1\crcr
 \noalign{\kern-\ex@\nointerlineskip}$\m@th\hfil#1#2\hfil$\crcr}}}
\def\overleftrightarrow{\mathpalette\overleftrightarrow@}
\def\overleftrightarrow@#1#2{\vbox{\ialign{##\crcr
   \leftrightarrowfill@#1\crcr
 \noalign{\kern-\ex@\nointerlineskip}$\m@th\hfil#1#2\hfil$\crcr}}}
\def\underrightarrow{\mathpalette\underrightarrow@}
\def\underrightarrow@#1#2{\vtop{\ialign{##\crcr$\m@th\hfil#1#2\hfil
  $\crcr\noalign{\nointerlineskip}\rightarrowfill@#1\crcr}}}
\let\underarrow\underrightarrow
\def\underleftarrow{\mathpalette\underleftarrow@}
\def\underleftarrow@#1#2{\vtop{\ialign{##\crcr$\m@th\hfil#1#2\hfil
  $\crcr\noalign{\nointerlineskip}\leftarrowfill@#1\crcr}}}
\def\underleftrightarrow{\mathpalette\underleftrightarrow@}
\def\underleftrightarrow@#1#2{\vtop{\ialign{##\crcr$\m@th
  \hfil#1#2\hfil$\crcr
 \noalign{\nointerlineskip}\leftrightarrowfill@#1\crcr}}}


\def\qopnamewl@#1{\mathop{\operator@font#1}\nlimits@}
\let\nlimits@\displaylimits
\def\setboxz@h{\setbox\z@\hbox}


\def\varlim@#1#2{\mathop{\vtop{\ialign{##\crcr
 \hfil$#1\m@th\operator@font lim$\hfil\crcr
 \noalign{\nointerlineskip}#2#1\crcr
 \noalign{\nointerlineskip\kern-\ex@}\crcr}}}}

 \def\rightarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@
  $#1\copy\z@\mkern-6mu\cleaders
  \hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
  \mkern-6mu\mathord\rightarrow$}
\def\leftarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@
  $#1\mathord\leftarrow\mkern-6mu\cleaders
  \hbox{$#1\mkern-2mu\copy\z@\mkern-2mu$}\hfill
  \mkern-6mu\box\z@$}


\def\projlim{\qopnamewl@{proj\,lim}}
\def\injlim{\qopnamewl@{inj\,lim}}
\def\varinjlim{\mathpalette\varlim@\rightarrowfill@}
\def\varprojlim{\mathpalette\varlim@\leftarrowfill@}
\def\varliminf{\mathpalette\varliminf@{}}
\def\varliminf@#1{\mathop{\underline{\vrule\@depth.2\ex@\@width\z@
   \hbox{$#1\m@th\operator@font lim$}}}}
\def\varlimsup{\mathpalette\varlimsup@{}}
\def\varlimsup@#1{\mathop{\overline
  {\hbox{$#1\m@th\operator@font lim$}}}}


\def\stackunder#1#2{\mathrel{\mathop{#2}\limits_{#1}}}


\begingroup \catcode `|=0 \catcode `[= 1
\catcode`]=2 \catcode `\{=12 \catcode `\}=12
\catcode`\\=12
|gdef|@alignverbatim#1\end{align}[#1|end[align]]
|gdef|@salignverbatim#1\end{align*}[#1|end[align*]]

|gdef|@alignatverbatim#1\end{alignat}[#1|end[alignat]]
|gdef|@salignatverbatim#1\end{alignat*}[#1|end[alignat*]]

|gdef|@xalignatverbatim#1\end{xalignat}[#1|end[xalignat]]
|gdef|@sxalignatverbatim#1\end{xalignat*}[#1|end[xalignat*]]

|gdef|@gatherverbatim#1\end{gather}[#1|end[gather]]
|gdef|@sgatherverbatim#1\end{gather*}[#1|end[gather*]]

|gdef|@gatherverbatim#1\end{gather}[#1|end[gather]]
|gdef|@sgatherverbatim#1\end{gather*}[#1|end[gather*]]


|gdef|@multilineverbatim#1\end{multiline}[#1|end[multiline]]
|gdef|@smultilineverbatim#1\end{multiline*}[#1|end[multiline*]]

|gdef|@arraxverbatim#1\end{arrax}[#1|end[arrax]]
|gdef|@sarraxverbatim#1\end{arrax*}[#1|end[arrax*]]

|gdef|@tabulaxverbatim#1\end{tabulax}[#1|end[tabulax]]
|gdef|@stabulaxverbatim#1\end{tabulax*}[#1|end[tabulax*]]


|endgroup


\def\align{\@verbatim \frenchspacing\@vobeyspaces \@alignverbatim
You are using the "align" environment in a style in which it is not defined.}
\let\endalign=\endtrivlist

\@namedef{align*}{\@verbatim\@salignverbatim
You are using the "align*" environment in a style in which it is not defined.}
\expandafter\let\csname endalign*\endcsname =\endtrivlist


\def\alignat{\@verbatim \frenchspacing\@vobeyspaces \@alignatverbatim
You are using the "alignat" environment in a style in which it is not defined.}
\let\endalignat=\endtrivlist

\@namedef{alignat*}{\@verbatim\@salignatverbatim
You are using the "alignat*" environment in a style in which it is not defined.}
\expandafter\let\csname endalignat*\endcsname =\endtrivlist


\def\xalignat{\@verbatim \frenchspacing\@vobeyspaces \@xalignatverbatim
You are using the "xalignat" environment in a style in which it is not defined.}
\let\endxalignat=\endtrivlist

\@namedef{xalignat*}{\@verbatim\@sxalignatverbatim
You are using the "xalignat*" environment in a style in which it is not defined.}
\expandafter\let\csname endxalignat*\endcsname =\endtrivlist


\def\gather{\@verbatim \frenchspacing\@vobeyspaces \@gatherverbatim
You are using the "gather" environment in a style in which it is not defined.}
\let\endgather=\endtrivlist

\@namedef{gather*}{\@verbatim\@sgatherverbatim
You are using the "gather*" environment in a style in which it is not defined.}
\expandafter\let\csname endgather*\endcsname =\endtrivlist


\def\multiline{\@verbatim \frenchspacing\@vobeyspaces \@multilineverbatim
You are using the "multiline" environment in a style in which it is not defined.}
\let\endmultiline=\endtrivlist

\@namedef{multiline*}{\@verbatim\@smultilineverbatim
You are using the "multiline*" environment in a style in which it is not defined.}
\expandafter\let\csname endmultiline*\endcsname =\endtrivlist


\def\arrax{\@verbatim \frenchspacing\@vobeyspaces \@arraxverbatim
You are using a type of "array" construct that is only allowed in AmS-LaTeX.}
\let\endarrax=\endtrivlist

\def\tabulax{\@verbatim \frenchspacing\@vobeyspaces \@tabulaxverbatim
You are using a type of "tabular" construct that is only allowed in AmS-LaTeX.}
\let\endtabulax=\endtrivlist


\@namedef{arrax*}{\@verbatim\@sarraxverbatim
You are using a type of "array*" construct that is only allowed in AmS-LaTeX.}
\expandafter\let\csname endarrax*\endcsname =\endtrivlist

\@namedef{tabulax*}{\@verbatim\@stabulaxverbatim
You are using a type of "tabular*" construct that is only allowed in AmS-LaTeX.}
\expandafter\let\csname endtabulax*\endcsname =\endtrivlist


 \def\endequation{
     \ifmmode\ifinner 
      \iftag@
        \addtocounter{equation}{-1} 
        $\hfil
           \displaywidth\linewidth\@taggnum\egroup \endtrivlist
        \global\tag@false
        \global\@ignoretrue
      \else
        $\hfil
           \displaywidth\linewidth\@eqnnum\egroup \endtrivlist
        \global\tag@false
        \global\@ignoretrue
      \fi
     \else
      \iftag@
        \addtocounter{equation}{-1} 
        \eqno \hbox{\@taggnum}
        \global\tag@false
        $$\global\@ignoretrue
      \else
        \eqno \hbox{\@eqnnum}
        $$\global\@ignoretrue
      \fi
     \fi\fi
 }

 \newif\iftag@ \tag@false

 \def\TCItag{\@ifnextchar*{\@TCItagstar}{\@TCItag}}
 \def\@TCItag#1{
     \global\tag@true
     \global\def\@taggnum{(#1)}
     \global\def\@currentlabel{#1}}
 \def\@TCItagstar*#1{
     \global\tag@true
     \global\def\@taggnum{#1}
     \global\def\@currentlabel{#1}}

  \@ifundefined{tag}{
     \def\tag{\@ifnextchar*{\@tagstar}{\@tag}}
     \def\@tag#1{
         \global\tag@true
         \global\def\@taggnum{(#1)}}
     \def\@tagstar*#1{
         \global\tag@true
         \global\def\@taggnum{#1}}
  }{}

\def\tfrac#1#2{{\textstyle {#1 \over #2}}}
\def\dfrac#1#2{{\displaystyle {#1 \over #2}}}
\def\binom#1#2{{#1 \choose #2}}
\def\tbinom#1#2{{\textstyle {#1 \choose #2}}}
\def\dbinom#1#2{{\displaystyle {#1 \choose #2}}}


\makeatother
\endinput
{"config": "arxiv", "file": "1806.05524/tcilatex.tex"}