% CUP Journal JSC document style -- V1.00  Released 23 January 1992
% for LaTeX version 2.09
% Copyright (C) 1992 Cambridge University Press
%
% based on the original LaTeX ARTICLE DOCUMENT STYLE
% Copyright (C) 1988, 1989 by Leslie Lamport
%
\typeout{Document Style `JSC journal style'.  V1.00 Released 23 January 1992}
%
%  Journals use two-sided printing.
%
\@twosidetrue     %  Defines twoside option.
\@mparswitchtrue  %  Marginpars go on outside of page.
%  draft option
%
\def\ds@draft{\overfullrule 5pt}  % Causes overfull hboxes to be marked.
%
\@options
 

%  ****************************************
%  *               FONTS                  *
%  ****************************************
%
\lineskip 1pt
\normallineskip 1pt
\def\baselinestretch{1}
\def\quarter@line{3pt}
\def\half@line{6pt}
\def\full@line{12pt}

\def\@normalsize{\@setsize\normalsize{\full@line}\xpt\@xpt
 \abovedisplayskip \half@line plus 1pt minus 1pt
 \belowdisplayskip \abovedisplayskip
 \abovedisplayshortskip \quarter@line plus 1pt
 \belowdisplayshortskip  \abovedisplayskip
 \let\@listi\@listI}
\def\small{\@setsize\small{10pt}\ixpt\@ixpt
 \abovedisplayskip 5pt plus 1pt minus 1pt
 \belowdisplayskip \abovedisplayskip
 \abovedisplayshortskip 2.5pt plus 1pt
 \belowdisplayshortskip \abovedisplayskip
 \def\@listi{\leftmargin\leftmargini
  \topsep 10pt plus 1pt minus 1pt
  \parsep \z@
  \itemsep \parsep}}
\def\medium{\@setsize\medium{10pt}\viiipt\@viiipt
 \abovedisplayskip 5pt plus 1pt minus 1pt
 \belowdisplayskip \abovedisplayskip
 \abovedisplayshortskip 2.5pt plus 1pt
 \belowdisplayshortskip \abovedisplayskip
 \def\@listi{\leftmargin\leftmargini
  \topsep 10pt plus 1pt minus 1pt
  \parsep \z@
  \itemsep \parsep}}
\def\footnotesize{\@setsize\footnotesize{9pt}\viiipt\@viiipt
 \abovedisplayskip 4.5pt plus 1pt minus 1pt
 \belowdisplayskip \abovedisplayskip
 \abovedisplayshortskip \z@ plus 1pt
 \belowdisplayshortskip  \abovedisplayskip
 \def\@listi{\leftmargin\leftmargini
  \topsep 9pt plus 1pt minus 1pt
  \parsep \z@
  \itemsep \parsep}}
\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt}
\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt}
\def\large{\@setsize\large{14pt}\xiipt\@xiipt}
\def\Large{\@setsize\Large{16pt}\xivpt\@xivpt}
\def\LARGE{\@setsize\LARGE{21pt}\xviipt\@xviipt}
\def\huge{\@setsize\huge{25pt}\xxpt\@xxpt}
\def\Huge{\@setsize\Huge{30pt}\xxvpt\@xxvpt}
\normalsize  % Choose the normalsize font.
 

%  ****************************************
%  *            PAGE LAYOUT               *
%  ****************************************
%
% All margin dimensions measured from a point one inch from top and side
% of page.
%
% SIDE MARGINS:
\oddsidemargin  2pc      % Left margin on odd-numbered pages.
\evensidemargin 2pc      % Left margin on even-numbered pages.

\marginparwidth 2.0cm    % Width of marginal notes.
\marginparsep 10pt       % Horizontal space between outer margin and
                         % marginal note
% VERTICAL SPACING:
% Top of page:
\topmargin 3pc           %    Nominal distance from top of page to top of
                         %    box containing running head.
\headheight 18pt         %    Height of box containing running head.
\headsep     6pt         %    Space between running head and text.
\topskip =  12pt         %    '\baselineskip' for first line of page.
                         % Bottom of page:

\footheight \full@line   %    Height of box containing running foot.
\footskip 18pt           %    Distance from baseline of box containing foot
                         %    to baseline of last line of text.
% DIMENSION OF TEXT:
%
\textheight = 47\baselineskip \advance\textheight by \topskip
                         % Height of text (including footnotes and figures,
                         % excluding running head and foot).
\textwidth 32pc          % Width of text line.
                         % For two-column mode:
\columnsep 10pt          %    Space between columns
\columnseprule 0pt       %    Width of rule between columns.
%
% FOOTNOTES:
%
\footnotesep \half@line   % Height of strut placed at the beginning of every
                     % footnote = height of normal \footnotesize strut,
                     % so no extra space between footnotes.
\skip\footins \full@line plus \full@line minus 1pt % Space between last line of text and
                                         % top of first footnote.
%  FOR FLOATS ON A TEXT PAGE:
%
\floatsep 12pt plus \half@line minus 1pt % Space between adjacent floats moved
                                         % to top or bottom of text page.
\textfloatsep 18pt plus \half@line minus 3pt
                                         % Space between main text and floats
                                         % at top or bottom of page.
\intextsep 18pt plus \quarter@line minus 2pt
                                        % Space between in-text figures and text
\@maxsep 18pt                            % The maximum of \floatsep,
                                         % \textfloatsep and \intextsep (minus
                                         % the stretch and shrink).
%    TWO-COLUMN FLOATS IN TWO-COLUMN MODE:
\dblfloatsep 12pt plus \half@line minus 2pt
                                           % Same as \floatsep for double-column
\dbltextfloatsep 18pt plus 4.5pt minus 3pt % \textfloatsep for double-column
\@dblmaxsep 18pt                         % The maximum of \dblfloatsep and
                                         % \dbltexfloatsep.
%  FOR FLOATS ON A SEPARATE FLOAT PAGE OR COLUMN:
\@fptop 0pt plus 0fil    % Stretch at top of float page/column. (Must be
                         % 0pt plus ...)
\@fpsep \full@line plus 0fil   % Space between floats on float page/column.
\@fpbot 0pt plus 3fil    % Stretch at bottom of float page/column. (Must be
                         % 0pt plus ... )
%  DOUBLE-COLUMN FLOATS IN TWO-COLUMN MODE.
\@dblfptop 0pt plus 0fil % Stretch at top of float page. (Must be 0pt plus ...)
\@dblfpsep \full@line plus 0fil % Space between floats on float page.
\@dblfpbot 0pt plus 3fil % Stretch at bottom of float page. (Must be
                         % 0pt plus ... )
% MARGINAL NOTES:
\marginparpush 6pt       % Minimum vertical separation between two marginal
                         % notes.
 

%  ****************************************
%  *           PARAGRAPHING               *
%  ****************************************
%
\parskip \z@ plus .1pt             % Extra vertical space between paragraphs.
\parindent 1em                     % Width of paragraph indentation.
\partopsep 0pt plus 1pt            % Extra vertical space, in addition to
%
% The following page-breaking penalties are defined
%
\@lowpenalty   51      % Produced by \nopagebreak[1] or \nolinebreak[1]
\@medpenalty  151      % Produced by \nopagebreak[2] or \nolinebreak[2]
\@highpenalty 301      % Produced by \nopagebreak[3] or \nolinebreak[3]
%
\@beginparpenalty -\@lowpenalty    % Before a list or paragraph environment.
\@endparpenalty   -\@lowpenalty    % After a list or paragraph environment.
\@itempenalty     -\@lowpenalty    % Between list items.
%
\clubpenalty=0        % 'Club line'  at bottom of page is OK.
\widowpenalty=10000   % 'Widow line' at top of page is not good.

 

%  ****************************************
%  *                 PARTS                *
%  ****************************************
%
\def\part{\par
 \addvspace{4ex}
 \@afterindentfalse
 \secdef\@part\@spart}
\def\@part[#1]#2{\ifnum \c@secnumdepth >\m@ne
  \refstepcounter{part}
  \addcontentsline{toc}{part}{Part \thepart: #1}
 \else
  \addcontentsline{toc}{part}{#1}
 \fi
 {\parindent 0pt \raggedright
  \ifnum \c@secnumdepth >\m@ne
   \large\rm PART
   \ifcase\thepart \or ONE \or TWO \or THREE \or FOUR \or FIVE
     \or SIX \or SEVEN \or EIGHT \or NINE \or TEN \else \fi
   \par \nobreak
  \fi
  \LARGE \rm #2
  \markboth{}{}\par }
 \nobreak \vskip 3ex
 \@afterheading
}
% Heading for \part* command
\def\@spart#1{%
 {\parindent 0pt \raggedright
  \LARGE \rm #1\par}
 \nobreak
 \vskip 3ex
 \@afterheading
}
 
%  ****************************************
%  *               SECTIONS               *
%  ****************************************
%
\def\section{\@startsection{section}{1}{\z@}
 {18pt plus 6pt minus 3pt}
 {6pt plus 0pt minus 1pt}
 {\centering\normalsize\bf}}
\def\subsection{\@startsection{subsection}{2}{\z@}
 {\full@line plus 6pt minus 3pt}
 {\full@line plus 3pt minus 1pt}
 {\centering\normalsize\sc}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}
 {\full@line plus 6pt minus 3pt}
 {\full@line plus 3pt minus 1pt}
 {\noindent\normalsize\sc}}
\def\paragraph{\@startsection{paragraph}{4}{\z@}
 {\full@line plus 6pt minus 3pt}
 {\half@line plus 3pt minus 1pt}
 {\noindent\normalsize\rm}}
\def\subparagraph{\@startsection{subparagraph}{4}{\parindent}
 {\half@line plus 3.25pt minus 1pt}
 {-0.5em}
 {\normalsize\sc}}
% The value of the counter secnumdepth gives the depth of the
% highest-level sectioning command that is to produce section numbers.
%
\setcounter{secnumdepth}{3}
%
% Changes to \@sect to achieve full points after numbers in section headings
%
\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 0.5em}\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}}
%
% APPENDIX
%
\def\appendix{\par
 \setcounter{section}{0}
 \setcounter{subsection}{0}
 \def\thesection{\Alph{section}}}
 
%  ****************************************
%  *               SKIPS                  *
%  ****************************************
%
\newskip\@indentskip    % General CUP indent
\newskip\smallindent    % para. indent
\newskip\@footindent    % footnote indent
\newskip\@leftskip      % for CUP float stuff

\@indentskip=2pc
\smallindent=1em
\@footindent=\smallindent
\@leftskip=1pc
 
%  ****************************************
%  *                LISTS                 *
%  ****************************************
%
\leftmargini   \@indentskip
\leftmarginii  1.5pc
\leftmarginiii 1.5pc
\leftmarginiv  1.5pc
\leftmarginv   1pc
\leftmarginvi  1pc
\leftmargin\leftmargini
\labelsep 0.5em
\labelwidth\leftmargini\advance\labelwidth-\labelsep
%
% label macros for Range-Left and Range-Right labels
\def\makeRLlabel#1{\rlap{#1}\hss}
\def\makeRRlabel#1{\hss\llap{#1}}
%
\def\@listI{\leftmargin\leftmargini
 \parsep \z@ plus 1pt minus 1pt
 \topsep \full@line plus 1pt minus 1pt
 \itemsep \z@ plus 1pt minus 1pt
 \let\makelabel\makeRRlabel}
\let\@listi\@listI
\@listi
\def\@listii{\leftmargin\leftmarginii
 \labelwidth\leftmarginii\advance\labelwidth-\labelsep
 \topsep \half@line plus 1pt minus 1pt
 \parsep \z@
 \itemsep \parsep
 \let\makelabel\makeRRlabel}
\def\@listiii{\leftmargin\leftmarginiii
 \labelwidth\leftmarginiii\advance\labelwidth-\labelsep
 \topsep \half@line plus 1pt minus 1pt
 \parsep \z@
 \partopsep \z@
 \itemsep \parsep
 \let\makelabel\makeRRlabel}
\def\@listiv{\leftmargin\leftmarginiv
 \labelwidth\leftmarginiv\advance\labelwidth-\labelsep
 \let\makelabel\makeRRlabel}
\def\@listv{\leftmargin\leftmarginv
 \labelwidth\leftmarginv\advance\labelwidth-\labelsep
 \let\makelabel\makeRRlabel}
\def\@listvi{\leftmargin\leftmarginvi
 \labelwidth\leftmarginvi\advance\labelwidth-\labelsep
 \let\makelabel\makeRRlabel}
%
% ENUMERATE
\def\enumerate{\ifnum \@enumdepth >3 \@toodeep
 \else
  \advance\@enumdepth \@ne
  \edef\@enumctr{enum\romannumeral\the\@enumdepth}%
  \list{\csname label\@enumctr\endcsname}%
       {\usecounter{\@enumctr}\let\makelabel\makeRRlabel}%
 \fi}

\def\labelenumi{\theenumi}
\def\theenumi{\arabic{enumi}}

\def\labelenumii{(\theenumii)}
\def\theenumii{\alph{enumii}}
\def\p@enumii{\theenumi}

\def\labelenumiii{\theenumiii}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi(\theenumii)}

\def\labelenumiv{\theenumiv}
\def\theenumiv{\Alph{enumiv}}
\def\p@enumiv{\p@enumiii\theenumiii}
%
% ITEMIZE
%
\def\itemize{\ifnum \@itemdepth >3 \@toodeep
  \else
   \advance\@itemdepth \@ne
   \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
   \list{\csname\@itemitem\endcsname}{\let\makelabel\makeRRlabel}%
  \fi}

\def\labelitemi{\quad}
\def\labelitemii{\bf --}
\def\labelitemiii{$\ast$}
\def\labelitemiv{$\cdot$}
%
% DESCRIPTION
%
\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
       \let\makelabel\descriptionlabel}}
\let\enddescription\endlist
%
% Unlabelled run-in list
%\def\unnumlabel#1{\rm #1}
\def\unnum{\list{}{\labelwidth\z@
%       \let\makelabel\unnumlabel
       \leftmargin \parindent
       \itemindent-\parindent
}}
\let\endunnum\endlist
%
% VERSE
%
\def\verse{\let\\=\@centercr
  \list{}{\itemsep\z@
          \itemindent -\@indentskip
          \listparindent \itemindent
          \rightmargin\leftmargin
          \advance\leftmargin \@indentskip}\item[]}
\let\endverse\endlist
%
% QUOTATION
%
\def\quotation{\list{}{\listparindent \smallindent
    \itemindent\listparindent
    \leftmargin2.5pc\rightmargin\leftmargin
    \parsep 0pt plus 1pt}\item[]\small}
\let\endquotation=\endlist
%
% QUOTE -- same as quotation except no paragraph indentation,
%
\def\quote{\list{}{\leftmargin2.5pc\rightmargin\leftmargin}\item[]\small}
\let\endquote=\endlist
%
 
%  ****************************************
%  *         TITLE AND ABSTRACT           *
%  ****************************************
%
\def\maketitle{\par
 \begingroup
   \def\thefootnote{\fnsymbol{footnote}}
   \def\@makefnmark{\hbox to 0pt{$^{\@thefnmark}$\hss}}
   \newpage
   \global\@topnum\z@
   \@maketitle
   \thispagestyle{titlepage}
   \@thanks
 \endgroup
 \setcounter{footnote}{0}
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}
% \gdef\@author{}\gdef\@title{}
 \let\thanks\relax}
\def\and{\end{author@tabular}\vskip .25em\par
   \begin{author@tabular}[t]{@{}c@{}}}

\def\@maketitle{\newpage
 \vspace*{26pt}
 {\parindent 0pt \centering\sloppy
  {\Large \bf \@title \par}
   \vskip 14pt
  {\normalsize
   \begin{author@tabular}[t]{@{}c@{}}\@author
   \end{author@tabular}\par}
  \vskip 9pt
  {\small\it (Received \@date)}
  \par\noindent}
  \vspace{-10pt}
}
\def\abstract{\list{}{\leftmargin 2.5pc\rightmargin \leftmargin
    \parsep 0pt plus 1pt\listparindent 1em\labelsep \z@}%
    \item[]\medium\top@eightrule\ignorespaces} % SFB to remove space
\def\endabstract{\bottom@eightrule\endlist\vspace{14pt}}
 
%  ****************************************
%  *            PAGE STYLES               *
%  ****************************************
%
\mark{{}{}}   % Initializes TeX's marks

\gdef\@author{\mbox{}} % SFB 0.02
\def\author{\@ifnextchar [{\@authortwo}{\@authorone}}
\def\@authortwo[#1]#2{\gdef\@author{#2}\gdef\@shortauthor{#1}}
\def\@authorone#1{\gdef\@author{#1}\gdef\@shortauthor{#1}}
\def\shortauthor#1{\gdef\@shortauthor{#1}}
\gdef\@shortauthor{\@author}
\gdef\@title{\mbox{}} % SFB 0.02
\def\title{\@ifnextchar [{\@titletwo}{\@titleone}}
\def\@titletwo[#1]#2{\gdef\@title{#2}\gdef\@shorttitle{#1}}
\def\@titleone#1{\gdef\@title{#1}\gdef\@shorttitle{#1}}
\def\shorttitle#1{\gdef\@shorttitle{#1}}
\gdef\@shorttitle{\@title}
\def\volume#1{\gdef\@volume{#1}}
\gdef\@volume{11}
\def\pagerange#1{\gdef\@pagerange{#1}}
\gdef\@pagerange{1--000}
\def\journal#1{\gdef\@journal{#1}}
\gdef\@journal{{\it J. Symbolic Computation\/}
  (\number\year) {\bf \@volume}, \@pagerange}

% \ps@empty and \ps@plain defined in LATEX.TEX

\def\ps@headings{\let\@mkboth\markboth
 \def\@oddhead{\hss\vbox{\hsize=\textwidth \hbox to \textwidth
               {\strut\hfill\footnotesize\rm \@shorttitle \hspace{3em}\thepage}
               \vskip 2.5pt
               \hrule height \arrayrulewidth}}
 \def\@oddfoot{}
 \def\@evenhead{\hss\vbox{\hsize=\textwidth \hbox to \textwidth
               {\strut\footnotesize\rm\thepage\hspace{3em}\@shortauthor\hfill}
               \vskip 2.5pt
               \hrule height \arrayrulewidth}}
 \def\@evenfoot{}
 \def\sectionmark##1{\markboth{##1}{}}
 \def\subsectionmark##1{\markright{##1}}
}
% Definition of 'myheadings' page style.
%
\def\ps@myheadings{\let\@mkboth\@gobbletwo
 \def\@oddhead{\hss\vbox{\hsize=\textwidth \hbox to \textwidth
               {\strut\hfill\footnotesize\rm\rightmark\hspace{3em}\thepage}
               \vskip 2.5pt
               \hrule height \arrayrulewidth}}
 \def\@oddfoot{}
 \def\@evenhead{\hss\vbox{\hsize=\textwidth \hbox to \textwidth
               {\strut\footnotesize\rm\thepage\hspace{3em}\leftmark\hfill}
               \vskip 2.5pt
               \hrule height \arrayrulewidth}}
 \def\@evenfoot{}
 \def\sectionmark##1{}
 \def\subsectionmark##1{}
}
\def\ps@titlepage{\let\@mkboth\@gobbletwo
 \def\@oddhead{\hss\vbox{\hsize=\textwidth \hbox to \textwidth
               {\strut\small\rm\@journal\hfill}
               \vskip 2.5pt \vskip \arrayrulewidth}}
 \def\@oddfoot{\footnotesize 0747--7171/90/000000 + 00\hspace{0.5em}\$03.00/0
                      \hfill \copyright\ \number\year\ Academic Press Limited}
 \def\@evenhead{\hss\vbox{\hsize=\textwidth \hbox to \textwidth
               {\strut\small\rm\@journal\hfill}
               \vskip 2.5pt \vskip \arrayrulewidth}}
 \def\@evenfoot{\footnotesize 0747--7171/90/000000 + 00\hspace{0.5em}\$03.00/0
                      \hfill \copyright\ \number\year\ Academic Press Limited}
 \def\sectionmark##1{}
 \def\subsectionmark##1{}
}
 
%  ****************************************
%  *         OTHER ENVIRONMENTS           *
%  ****************************************
%
% THEOREM
%
%\def\@thmcounter#1{\noexpand\thesection.\noexpand\arabic{#1}}
%\@addtoreset{#1}{section}
\def\@nthm#1#2{\@ifnextchar[{\@xnthm{#1}{#2}}{\@xnthm{#1}{#2}[section]}}

\def\@begintheorem#1#2{\it \trivlist
 \item[\hskip \labelsep{\sc #1\ #2.}]}
\def\@opargbegintheorem#1#2#3{\it \trivlist
  \item[\hskip \labelsep{\sc #1\ #2.\hspace{0.5em}(#3)}]}
\def\@endtheorem{\endtrivlist}

\def\proof{\rm \trivlist
% \item[\hskip \labelsep{\sc Proof.\hspace{0.5em}}]}
 \item[\hskip \labelsep{\sc Proof.}]}
\def\endproof{{\large$\Box$}\endtrivlist}
\@namedef{proof*}{\rm \trivlist
 \item[\hskip \labelsep{\sc Proof.}]}
\@namedef{endproof*}{\endtrivlist}

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

% ARRAY AND TABULAR
%
\arraycolsep 5pt     % Half the space between columns in an array environment.
\tabcolsep 6pt       % Half the space between columns in a tabular environment.
\arrayrulewidth .4pt % Width of rules in array and tabular environment.
\doublerulesep 1.5pt % Space between adjacent rules in array or tabular env.

%\renewcommand{\arraystretch}{1}

\def\tabular{\def\@halignto{}
 \doublerulesep \z@
 \def\hline{\noalign{\ifnum0=`}\fi
  \vskip 4.5pt
  \hrule \@height \arrayrulewidth
  \vskip 4.5pt
  \futurelet \@tempa\@xhline}
 \def\@xhline{\ifx\@tempa\hline
   \vskip -9pt
   \vskip \doublerulesep
  \fi
  \ifnum0=`{\fi}}
  \def\@arrayrule{\@addtopreamble{\hskip -.5\arrayrulewidth
%                                  \vrule \@width \arrayrulewidth
                                  \hskip .5\arrayrulewidth}}
\@tabular
}
% TABBING
%
\tabbingsep \labelsep   % Space used by the \'75ommand.  (See LaTeX manual.)

% MINIPAGE
%
\skip\@mpfootins = \skip\footins

% FRAMEBOX
%
\fboxsep = 3pt    % Space left between box and text by \fbox and \framebox.
\fboxrule = \arrayrulewidth % Width of rules in box made by \fbox and \framebox.
 
%  ****************************************
%  *              SECTIONS                *
%  ****************************************
%
\newcounter{part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]

\def\thepart          {\arabic{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}}
 
%  ****************************************
%  *         TABLE OF CONTENTS, ETC.      *
%  ****************************************
%
\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{1}

\def\@undottedtocline#1#2#3#4#5{\ifnum #1>\c@tocdepth
  \else
   \vskip \z@ plus .2pt
   {\hangindent #2\relax
    \rightskip \@tocrmarg
    \parfillskip -\rightskip
    \parindent #2\relax
    \@afterindenttrue
    \interlinepenalty\@M
    \leavevmode
    \@tempdima #3\relax
    #4\nobreak
    \hfill \nobreak
    \hbox to\@pnumwidth{\hfil\rm \ }\par}\fi}

% TABLEOFCONTENTS
%
\def\tableofcontents{\@restonecolfalse
  \if@twocolumn\@restonecoltrue\onecolumn\fi
  \section*{Contents}
  \@starttoc{toc}
  \if@restonecol\twocolumn\fi
  \par\vspace{\full@line}}

\def\l@part#1#2{\addpenalty{-\@highpenalty}
 \addvspace{2.25em plus 1pt}
 \begingroup
  \parindent \z@ \rightskip \@pnumwidth
  \parfillskip -\@pnumwidth
  {\normalsize\rm
   \leavevmode
   \hspace*{3pc}
   #1\hfil \hbox to\@pnumwidth{\hss \ }}\par
  \nobreak
  \global\@nobreaktrue
  \everypar{\global\@nobreakfalse\everypar{}}%
 \endgroup
}
\def\l@section#1#2{\addpenalty{\@secpenalty}
 \@tempdima 1.5em
 \begingroup
  \parindent \z@ \rightskip \@pnumwidth
  \parfillskip -\@pnumwidth
  \rm \leavevmode
  \advance\leftskip\@tempdima
  \hskip -\leftskip
  #1\nobreak\hfil \nobreak\hbox to\@pnumwidth{\hss \ }\par
 \endgroup
}
\def\l@subsection{\@undottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@undottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@undottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@undottedtocline{5}{10em}{5em}}

% LIST OF FIGURES
%
\def\listoffigures{\@restonecolfalse
 \if@twocolumn\@restonecoltrue\onecolumn\fi
 \section*{List of Figures\@mkboth{List of Figures}{List of Figures}}
 \@starttoc{lof}
 \if@restonecol\twocolumn\fi
}
\def\l@figure{\@undottedtocline{1}{1.5em}{2.3em}}

% LIST OF TABLES
%
\def\listoftables{\@restonecolfalse
 \if@twocolumn\@restonecoltrue\onecolumn\fi
 \section*{List of Tables\@mkboth{List of Tables}{List of Tables}}
 \@starttoc{lot}
 \if@restonecol\twocolumn\fi
}
\let\l@table\l@figure
 
%  ****************************************
%  *             BIBLIOGRAPHY             *
%  ****************************************
%
\def\@biblabel#1{#1}
\def\thebibliography#1{\section*{References}
  \addcontentsline{toc}{section}{References}
  \list{}{\labelwidth\z@
%    \leftmargin \@indentskip
    \leftmargin 1.5pc
    \itemindent-\leftmargin}
    \footnotesize
    \parindent\z@
    \parskip\z@ plus .1pt\relax
    \def\newblock{\hskip .11em plus .33em minus .07em}
    \sloppy\clubpenalty4000\widowpenalty4000
    \sfcode`\.=1000\relax}
\let\endthebibliography=\endlist
 
%  ****************************************
%  *              THE INDEX               *
%  ****************************************
%
\newif\if@restonecol
\def\theindex{\section*{Index}
    \addcontentsline{toc}{section}{Index}
    \footnotesize
    \parindent\z@
    \parskip\z@ plus .1pt\relax
    \let\item\@idxitem}
\def\@idxitem{\par\hangindent 1pc}
\def\subitem {\par\hangindent 1pc \hspace*{1pc}}
\def\subsubitem{\par\hangindent 1pc\hspace*{1pc}}
\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
\def\indexspace{\par\vskip\baselineskip \relax}
 
%  ****************************************
%  *             FOOTNOTES                *
%  ****************************************
%
\def\footnoterule{\kern-3\p@ \hrule width .4\columnwidth height \z@ \kern 3\p@}

\long\def\@makefntext#1{\parindent 1em\noindent
            \hbox to 1.5em{\hss$^{\@thefnmark}$}\hspace{0.5em}#1}

%\long\def\@makefntext#1{\@setpar{\@@par\@tempdima \hsize
%  \advance\@tempdima-\@footindent
%  \parshape \@ne \@footindent \@tempdima}\par
%  \noindent \hbox to \z@{\hss$^{\@thefnmark}$\ }#1}
%
\renewcommand{\thefootnote}{\mbox{$\fnsymbol{footnote}$}}
\@addtoreset{footnote}{page}

\def\@fnsymbol#1{\ifcase#1\or \dagger\or \ddagger\or
   \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
   \or \ddagger\ddagger \else\@ctrerr\fi\relax}
 
%  ****************************************
%  *         FIGURES AND TABLES           *
%  ****************************************
%
\setcounter{topnumber}{2}
\def\topfraction{.9}
\setcounter{bottomnumber}{1}
\def\bottomfraction{.9}
\setcounter{totalnumber}{3}
\def\textfraction{.1}
\def\floatpagefraction{.75}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.9}
\def\dblfloatpagefraction{.75}
%
\long\def\@makecaption#1#2{\vskip \half@line
 \ifwide@float
  \raggedright\sloppy #1. #2\par
 \else
  \raggedright\sloppy #1. #2\par
 \fi}

% TABLE
%
\newcounter{table}
\def\thetable{\@arabic\c@table}
\def\fps@table{tbp}
\def\ftype@table{1}
\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\fstyle@table{\footnotesize\rm}
\def\fjust@table{\centering}

\def\fcapjust@table{\centering\sloppy}
\def\fcapsize@table{\normalsize\bf}
\def\fcapstyle@table{\normalsize\rm}
%
% FIGURE
%
\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\fps@figure{tbp}
\def\ftype@figure{2}
\def\ext@figure{lof}
\def\fnum@figure{Figure\ \thefigure}
\def\figure{\@float{figure}}
\let\endfigure\end@float
\@namedef{figure*}{\@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}
\def\fstyle@figure{\footnotesize\rm}
\def\fjust@figure{\centering}

\def\fcapjust@figure{\centering\sloppy}
\def\fcapsize@figure{\footnotesize\bf}
\def\fcapstyle@figure{\footnotesize\rm}
%
% stuff for different style float captions
%
\newif\ifwide@float
\wide@floatfalse

\long\def\@caption#1[#2]#3{\addcontentsline{\csname ext@#1\endcsname}{#1}%
 {\protect\numberline{\csname the#1\endcsname}%
 {\ignorespaces #2}}\par
 \begingroup
  \ifwide@float\@parboxrestore\else\@myparboxrestore\fi
  \@makecaption{\csname fcapjust@#1\endcsname
                \csname fcapsize@#1\endcsname
                \csname fnum@#1\endcsname}%
               {\csname fcapstyle@#1\endcsname \ignorespaces #3}\par
 \endgroup
}
\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
 \boxmaxdepth\z@
 \csname fstyle@#1\endcsname
 \ifwide@float \hsize\textwidth \linewidth\textwidth
  \@parboxrestore
 \else \hsize\textwidth \linewidth\textwidth
  \@parboxrestore
%\hsize\columnwidth \addtolength{\hsize}{-2pc} \@rightskip 2pc
%                \@myparboxrestore
 \fi
 \csname fjust@#1\endcsname
}
\def\@myarrayparboxrestore{\let\par\@@par
 \let\-\@dischyph
 \let\'\@acci \let\`\@accii \let\=\@acciii
 \parindent\z@
 \everypar{}\linewidth\hsize
 \@totalleftmargin\z@ \leftskip\@leftskip
 \rightskip\@rightskip
 \parfillskip\@flushglue \lineskip\normallineskip
 \baselineskip\normalbaselineskip\sloppy
}
\def\@myparboxrestore{\@myarrayparboxrestore\let\\=\@normalcr}
%
% stuff for wide floats
%
\def\@dblfloat{\wide@floattrue\@float}
\def\end@dblfloat{\if@twocolumn\egroup
 \ifnum\@floatpenalty <\z@ \@cons\@dbldeferlist\@currbox\fi
 \ifnum \@floatpenalty =-\@Mii \@esphack\fi\else\end@float\fi
 \wide@floatfalse
}
 
%  ****************************************
%  *           CUP specials               *
%  ****************************************
%
\def\author@tabular{\def\@halignto{}\@authortable}
\let\endauthor@tabular=\endtabular
\def\author@tabularcr{{\ifnum0=`}\fi
 \@xtabularcr[4pt]\small\it\ignorespaces}
\def\author@tabularcrnospace{{\ifnum0=`}\fi
 \@xtabularcr[-2pt]\small\it\ignorespaces}
\def\@authortable{\leavevmode \hbox \bgroup $\let\@acol\@tabacol
 \let\@classz\@tabclassz
 \let\@classiv\@tabclassiv
 \let\\\author@tabularcr
 \let\nextaddress\author@tabularcrnospace 
 \@tabarray}

\def\long@rule{\par\noindent\rule{\textwidth}{\arrayrulewidth}\par\noindent}
\def\short@rule{\par\noindent\rule{27pc}{\arrayrulewidth}\par\noindent}
\def\top@eightrule{\par%
  \rule{27pc}{\arrayrulewidth}\vspace{4pt}\par\noindent}
\def\bottom@eightrule{\par\noindent%
  \vspace{-1pt}\rule{27pc}{\arrayrulewidth}\par\noindent}

\@addtoreset{equation}{section}
\def\theequation{\thesection.\arabic{equation}}
 
%  ****************************************
%  *            MISCELLANEOUS             *
%  ****************************************
%
% DATE
%
\def\today{\number\day\
 \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 \ \number\year}
 
%  ****************************************
%  *           INITIALIZATION             *
%  ****************************************
%
% Default initializations

\ps@headings                % `headings' page style
\pagenumbering{arabic}      % Arabic page numbers
\onecolumn                  % Switch to \onecolumn and disable \twocolumn.
\let\onecolumn=\relax
\def\twocolumn{\typeout{Two column mode not available with CUP styles.}}
%
\flushbottom
\frenchspacing
 
