path: root/Master/texmf-dist/tex/latex/nath/nath.sty

% NATH.STY --- a LaTeX document style implementing NAtural maTH notation
%
% Copyright (c) 1996-2003 by Michal Marvan
%

\ifx\nathstyle\undefined
\else \typeout{NATH.STY will not be loaded twice.}
 \expandafter\endinput
\fi

\newlinechar`\^^J

\typeout{^^JNath as of 21 March 2003 
 ^^JImplementing NAtural maTH notation}
%
%   U s a g e 
%
%     \documentstyle[nath]{article}
%
% or
%
%     \documentclass{article}
%     \usepackage{nath}
%

%
%   L i c e n s e
%

% Nath is a free software distributed under the terms of the GNU General 
% Public License <http://www.gnu.org/copyleft/gpl.html> as published by 
% the Free Software Foundation; either version 2 of the License, or 
% (at your option) any later version.
%
% In particular, Nath comes with ABSOLUTELY NO WARRANTY.

%
%   O p t i o n s
%

% Options may be also set in the body by \nathstyle.

\def\nathstyle#1{\@for\@tempa:={#1}\do{\expandafter\nathstyle@\@tempa==\relax}%
 \ignorespaces}

\def\on@@@{on}
\def\off@@@{off}

\def\nathstyle@#1=#2=#3{\def\@tempa{#1}%
 \expandafter\ifx\csname if#1\endcsname\relax
  \n@err{Unknown nath style}{I am ignoring the option `#1' in \nathstyle}
 \else \def\@tempb{#2}%  #3 is `\relax' or `='
  \ifx\@tempb\empty \csname #1true\endcsname \else 
   \ifx\@tempb\on@@@ \csname #1true\endcsname \else 
    \ifx\@tempb\off@@@ \csname #1false\endcsname \else 
     \n@err{Invalid argument in \string\nathstyle}%
      {Nath style argument must be either name or name=on or name=off}%
  \fi\fi\fi
 \fi}

\newif\ifgeometry
\newif\iftensors
\newif\ifleqno
\newif\ifdebug
\newif\ifsilent

%
%   E r r o r    m e s s a g e s   a n d   w a r n i n g s
%
 
% Nath errors are marked by a black box, sometimes wrongly placed. 

\def\natherrormark{\hbox{\vrule \@height\prorated@ em \@width\prorated@ ex}}

\def\n@err#1#2{\errhelp\expandafter{#2}\errmessage{#1}\natherrormark}

\def\n@warning#1{\ifsilent\else\typeout{Nath Warning: #1\on@line.}\fi}

\ifx\Nath\undefined\else 
 \n@warning{NATH.STY will not be loaded again}
\expandafter\endinput\fi

%
%   F o n t s
%

% This style does not introduce any new fonts. It is recommended (but not 
% required) to have a standard set of AMS fonts introduced independently.

%
%   D i m e n s i o n s
%

% A new dimension called \mex (math ex) is equal to 1 ex prorated 
% according to the level of \mathcount@ (see currstyle)

\newdimen\mex
\mex=1ex

% Approximately, 1 mex = 8 mu, but can be used where mu cannot, e.g,
% with \ifdim, height, depth, width, etc.

\def\prorated@{\ifcase\mathcount@ 1 \or.7 \else.5 \fi}

%
%   P r o t e c t e d   d e f s
%

% I want that all math commands are robust:

\newtoks\protect@toks

\def\pdef#1{\protect@toks=\expandafter{\the\protect@toks
 \pdef@#1}%
 \def#1}

\def\pdef@#1{\def#1{\protect#1}}

% ... even begin and end

\let\o@begin\begin
\pdef\begin{\o@begin}

\let\o@end\end
\pdef\end{\o@end}

% Macro to make an existing command robust

\def\makerobust#1{%
 \expandafter\let\csname @o@\expandafter\@gobble\string #1\endcsname=#1
 \edef#1{\noexpand\protect
 \expandafter\noexpand\csname @o@\expandafter\@gobble\string #1\endcsname}}

% Making composed math symbols robust:

\makerobust\cong
\makerobust\notin

%
%   C o n t r o l   m a c r o s  
%

% Here is a global version of TeX's loop macro:

\def\g@loop#1\repeat{\gdef\g@body{#1}\g@iterate}

\def\g@iterate{\g@body\global\let\gnext=\g@iterate
  \else \global\let\gnext=\relax \fi
 \gnext}

% Some tests put their result into \ifresult@

\newif\ifresult@

\def\old#1{\csname o@#1\endcsname}

%
%   S t a c k s
%

\def\put@#1#2{\edef#2{#1\relax#2}}

\def\get@#1#2{\expandafter\get@@#2\endget@@#1#2}

\def\get@@#1\relax#2\endget@@#3#4{\edef#3{#1}\edef#4{#2}}

%
%   M a t h c o d e s
%

% Many characters are live (\mathcode = "8000) in math mode. 

% After saving their original mathcodes:

\edef\mc@lparenthesis{\mathchar\the\mathcode`(\relax}
\edef\mc@rparenthesis{\mathchar\the\mathcode`)\relax} 
\edef\mc@lbrack{\mathchar\the\mathcode`[\relax} 
\edef\mc@rbrack{\mathchar\the\mathcode`]\relax} 
\edef\mc@comma{\mathchar\the\mathcode`,\relax}
\edef\mc@semicolon{\mathchar\the\mathcode`;\relax}
\edef\lt{\mathchar\the\mathcode`<\relax}
\edef\gt{\mathchar\the\mathcode`>\relax}
\edef\mc@factorial{\mathchar\the\mathcode`!\relax}
\edef\mc@slash{\mathchar\the\mathcode`/\relax}
\edef\vert{\mathchar\the\mathcode`|\relax} 

% we assign new ones:

\mathcode`\(="8000 \mathcode`\[="8000 \mathcode`\<="8000 
\mathcode`\)="8000 \mathcode`\]="8000 \mathcode`\>="8000 
\mathcode`\,="8000 \mathcode`\;="8000 \mathcode`\^="8000
\mathcode`\!="8000 \mathcode`\`="8000 \mathcode`\_="8000

% Before defining live characters, one must call \livechars@ to
% set catcodes to 13 (active).

\def\livechars@{
 \catcode`\(=13 \catcode`\[=13 \catcode`\<=13 
 \catcode`\)=13 \catcode`\]=13 \catcode`\>=13 
 \catcode`\,=13 \catcode`\;=13
 \catcode`\!=13 \catcode`\`=13} 

\def\killchars@{
 \catcode`\(=12 \catcode`\[=12 \catcode`\<=12 
 \catcode`\)=12 \catcode`\]=12 \catcode`\>=12 
 \catcode`\,=12 \catcode`\;=12
 \catcode`\!=12 \catcode`\`=12} 

% Here are the definitions:

\livechars@

\def({\delim@l 1\ch@lparenthesis}
\def){\delim@r 1\ch@rparenthesis}
\def[{\delim@l 1\o@lbrack}
\def]{\delim@r 1\o@rbrack}
\def!{\factorial}
\def,{\@comma}
\def;{\@semicolon}
\def`{\abbreviation}

% Every math calls \mathoptions@on to set live definition of <, >
% depending on the current value of ifgeometry; and to set 
% fontdimens according to the current value of iftensors

% The following control sequences contain

\def\mathoptions@on{%
 \ifgeometry % if geometry=on
  \def<{\delim@l 1\o@langle}%
  \def>{\delim@r 1\o@rangle}%
 \else % if geometry=off
  \def<{\lt}%
  \def>{\gt}%
 \fi
 \iftensors % if tensors=on
  \edef\fdviii@textfontiii{\the\fontdimen8\textfont3}% 
  \edef\fdxiii@textfontii{\the\fontdimen13\textfont2}% 
  \edef\fdxiv@textfontii{\the\fontdimen14\textfont2}% 
  \edef\fdxv@textfontii{\the\fontdimen15\textfont2}% 
  \edef\fdxvi@textfontii{\the\fontdimen16\textfont2}% 
  \fontdimen 8\textfont3=.075ex% 1/4 of min superscript/subscript clearance
  \fontdimen13\textfont2=1.3ex% min superscript shift in displaystyle
  \fontdimen14\textfont2=1.3ex% min superscript shift otherwise
  \fontdimen15\textfont2=1.3ex% min superscript shift in restricted style
  \fontdimen16\textfont2=.65ex% min subscript shift if no superscript
  \fontdimen17\textfont2=0ex% min subscript shift if no superscript
  \relax
 \fi
}

\def\mathoptions@off{%
 \iftensors
  \fontdimen 8\textfont3=\fdviii@textfontiii
  \fontdimen13\textfont2=\fdxiii@textfontii
  \fontdimen14\textfont2=\fdxiv@textfontii
  \fontdimen15\textfont2=\fdxv@textfontii
  \fontdimen16\textfont2=\fdxvi@textfontii
  \relax
 \fi}


\killchars@

%
%   D o l l a r s
%

% Math mode is inline or displayed.
% Top level macros to start either mode are:

%      To start         use 
%   ----------------  ------------------------ 
%    inline math       $ ... $
%    displayed math    $$ ... $$ or \[ ... \]
%                      or math environments such
%                      as equation, eqns, eqns*

% The $ is active (catcode = 13).
%
% The original $ (catcode = 3) is stored in \o@dollar.
% \o@math is the original $ followed by \relax.
% \o@display is the original double $$.

\let\o@dollar=$
\def\o@math{\o@dollar\relax}       % calls \everymath 
\def\o@display{\o@dollar\o@dollar}  % calls \everydisplay  

% \everymath and \everydisplay

\everymath{} % keep empty
\everydisplay{} % keep empty


\catcode`\$=13

\def$#1${\@@dollar{#1}}

\pdef\@@dollar#1{%
 \ifmmode\else\begingroup\fi % no begingroup if closing $
 \def\next{#1}% 
 \ifx\next\empty % if $$
  \ifmmode % if closing $$
   \] \def\next{\endgroup\ignorespaces}%
  \else \[ \def\next{\relax}%
  \fi 
 \else                     % if $; #1 = the whole content between $'s
  \imath@{#1}%
  \let\next\endgroup
 \fi
 \next}

\catcode`\$=3


% $'s eventually call internal commands to start math mode, which are
%    \imath@{ ... } 
%     ... \dmathoff@

\def\dmathon@{\o@math
 \setbox\sizebox\delimstrut@ % initialize sizebox
 \begingroup
 \mathoptions@on
 \displayon@ % start displayed
}

% \dmathoff@ == end displayed style
%   end group

\def\dmathoff@{\enddisplaydelims@
 \mathoptions@off
 \endgroup
 \o@math}

\def\imath@#1{\mathoptions@on\o@math\inline{#1}\o@math\mathoptions@off}

\def\(#1\){\imath@{#1}}

% The math environment is disabled

\def\math{\n@err{Disabled environment. Use $ to begin math}
 {I am inserting $ to start inline math mode.}\o@math}
\def\endmath{\n@err{Obsolete command. Use $ to end math.}
 {I am inserting $ to end inline math mode.}\o@math}

%
%   G e n e r i c   d i s p l a y   m a t h   m a c r o
%

% $$, \[, \], and all displayed math environments use low-level macros 
% make@eq/endmake@eq to format a displayed formula.
% Usage:
%
%    \o@display \make@eq
%    ...
%    \endmake@eq \o@display

% There is a dimension register called \mathindent to control the 
% positioning. If \mathindent > 0, formulas are left-indented that
% amount, otherwise they are centered.

\newdimen\mathindent     
\mathindent=4pc

\newdimen\disp@box@width 
\newdimen\disp@width     

\let\o@label=\label % store the original \label

\newif\ifmultiline@

\let\o@eqno=\eqno % store the TeX's \eqno
\let\o@leqno=\leqno % store the TeX's \leqno

\def\make@eq{%
 \global\let\do@eqno=\curr@eqno 
 \def\the@eqlabel{}%
 \def\label##1{\gdef\the@eqlabel{##1}}%
 \display@true
 \nodisplay@false
 \protectinline@false
 \ifdim\mathindent<0pc  % if centered then nothing
 \else  % if flushleft
  \disp@box@width=\linewidth \advance\disp@box@width -\mathindent
  \disp@width=\disp@box@width \advance\disp@width -\mathindent
  \hbox to \disp@width\bgroup 
  \vbox\bgroup % \ifdebug\hrule\fi
  \hsize\disp@box@width
  \parindent=0pt
  \parfillskip=0pt
  \leavevmode\o@math
 \fi
 \global\multiline@false
 \setbox0 \vbox\bgroup} % starting (multiline) vbox

\def\endmake@eq{\egroup % ending (multiline) vbox
 \ifeqnumbering@ 
  \ifmultiline@
   \vcenter{\box0} % make the equation number vertically centered
  \else \box0
  \fi
  \ifdim\mathindent<0pc  % if centered
   \ifleqno\else \o@eqno{\do@eqno}\fi
  \else % if flushleft
   \o@math
   \hfil\null
   \ifleqno\else \hfil\null\hfil \hbox{\do@eqno} \fi
   \egroup
   \hss\egroup
  \fi
  \ifleqno \o@leqno{\do@eqno} \fi
 \else % if no numbering
  \ifdim\mathindent<0pc  % if centered
   \box0 
  \else \box0\o@math \hfil \null\egroup \hss \egroup
  \fi
 \fi
}

% The purpose of the vbox with parfillskip = 0 and triple filling
% is that the equation number will go on the line following the
% formula if the formula is too long.

% Catch the global option `leqno':

\def\ds@leqno{\leqnotrue}

%
%   D i s p l a y   l i n e s   a n d   b l o c k s 
%

% A single natural-width hbox with displayed material inside 
% is produced by \displayline@.

% Here is the skip between adjacent displaylines

\newskip\interdisplayskip
\interdisplayskip=1.67 ex

% An empty displayline must not produce any vertical space. 
% Empty is if of length < or = to zero

\def\displayline@{\setbox0\hbox\bgroup
 \o@math\dcurrstyle@}

\def\enddisplayline{\o@math\egroup 
 \ifdim\wd0>0pt \box0
 \else \box0
  \vskip-\interdisplayskip
 \fi}

% The formula inside may actually be a wall-return block, i.e.,
% may be multiline.

% A multiline block is a top-aligned vbox, followed by new line.
% The command to start a block is \wall, the command to end it 
% is \return. Adjacent returns must not generate an empty line.
%
%      \wall
%        formula; lines separated with \\
%      \return
%

\newif\ifinnerwall@ % if inside another wall-return block
\innerwall@false

% We define generic \d@wall and \d@return here. Actual wall and return 
% are defined in displaydelims, after some escape machinery.

\def\d@wall#1{\hbox\bgroup 
%\ifdebug\vrule\@width 1pt\fi
 \vtop\bgroup\offinterlineskip 
 \if0#1 % if wall 
  \edef\pad@{\relax}
 \else % if shifted
  \edef\pad@{\pad@\@cdr#1\@nil}
 \fi
 \innerwall@true
 \displayline@
}

\def\d@return{\enddisplayline 
 \egroup % end vtop
%\ifdebug\vrule \@width 1pt\fi
 \egroup % end hbox
 \ifinnerwall@ \curr@cr \fi
}

%Inside any wall-return block, \\ should be \d@cr:

\def\d@cr#1{\enddisplayline\vskip\interdisplayskip
 \global\multiline@true
 \displayline@
 #1 % may be \pad@ or \relax
 }

%If \wall is misplaced

\newif\ifwallallowed@
\wallallowed@true

%
%   D i s p l a y m a t h   e n v i r o n m e n t s 
%

% A single equation; unnumbered:
%
%      $$ complete formula $$
% or
%      \[ complete formula \]

% numbered:
%
%      \begin{equation} complete formula \end{equation}

% A pile of equations; unnumbered:
%
%      \begin{eqns*}
%        complete formulas separated with \\
%      \end{eqns*}

% numbered:
%
%      \begin{eqns}
%        complete formulas separated with \\
%      \end{eqns}

% holding the same number; followed by a letter:
%
%      \begin{eqnabc}
%        complete formulas separated with \\
%      \end{eqnabc}

% The environments set ifeqnumbering@
% and call make@eq.
% $$, \[ and \begin{equation} start a wall-return block.
% This means that 

\def\[{\begingroup 
 \global\eqnumbering@false
 \curr@cr@is@wall@cr
 \o@display\make@eq\hbox\bgroup\dmathon@\wall\mathopen{}}

\def\]{\return\dmathoff@\egroup\endmake@eq\o@display
 \endgroup\ignorespaces}
 
\newif\ifeqnumbering@     % global

\def\equation{\begingroup
 \global\eqnumbering@true
 \curr@cr@is@wall@cr
 \o@display\make@eq\hbox\bgroup\dmathon@\wall\mathopen{}}

\def\endequation{\return\dmathoff@\egroup\endmake@eq\o@display
 \endgroup \global\@ignoretrue}

% Unnumbered equation for backward compatibility

\expandafter\def\csname equation*\endcsname{\[}
\expandafter\def\csname endequation*\endcsname{\]\global\@ignoretrue}

% Important! The \mathopen{} after \wall protects active characters from
% being scanned prematurely. 

\def\eqns{\begingroup
 \belowdisplayskip@=\belowdisplayskip
 \belowdisplayskip=0pt
 \belowdisplayshortskip=0pt
 \global\eqnumbering@true
 \def\curr@cr{\eqns@cr \global\eqnumbering@true}
 \let\\\curr@cr
 \postdisplaypenalty=9999
 \belowdisplayshortskip=\belowdisplayskip
 \o@display\make@eq\hbox\bgroup\dmathon@}

\def\endeqns{\dmathoff@\egroup
 \endmake@eq\o@display
 \vskip\belowdisplayskip@
 \endgroup
 \global\@ignoretrue
 \noindent}

\expandafter
\def\csname eqns*\endcsname{\begingroup
 \belowdisplayskip@=\belowdisplayskip
 \belowdisplayskip=0pt
 \belowdisplayshortskip=0pt
 \global\eqnumbering@false
 \def\curr@cr{\eqns@cr \global\eqnumbering@false}
 \let\\\curr@cr
 \postdisplaypenalty=10000
 \belowdisplayshortskip=\belowdisplayskip
 \o@display\make@eq\hbox\bgroup\dmathon@}

\expandafter
\def\csname endeqns*\endcsname{\endeqns}

\def\eqns@cr{\dmathoff@\egroup\endmake@eq\o@display
 \hrule\@height 0pt
 \abovedisplayshortskip=0pt plus 0pt minus 0pt
 \vglue\intereqnsskip
 \hrule\@height 0pt
 \o@display \make@eq\hbox\bgroup\dmathon@}

\def\nonumber{\global\eqnumbering@false}

\def\numbered{\global\eqnumbering@true}

\newskip\intereqnsskip
\intereqnsskip=1ex

\newskip\belowdisplayskip@

%
%   E q u a t i o n   n u m b e r i n g 
%

% Displaymath (namely \endmake@eq) calls \do@eqno to create the
% equation number. At the beginning of each display, \do@eqno is
% set to \curr@eqno. Numbering macros should define \curr@eqno,
% while \eqno changes \do@eqno directly.

% \do@eqno calls \make@eqno, a generic command to make its   
% argument into both the equation number and the currentlabel.

\def\make@eqno#1{\def\make@eqno@{#1}  % \rm removed thanks to E.H. Lohse
 \def\@currentlabel{\make@eqno@} 
 \ifx\the@eqlabel\empty \n@warning{No label in equation (#1)}
 \else 
  \ifeqnumbering@ \o@label{\the@eqlabel}
  \else \n@warning{Label occurs in an unnumbered formula}
  \fi
 \fi 
 \hbox{\rm(\make@eqno@)%
 \ifnum\overfullrule>0 % if draft
  \hbox to 0pt{\hglue 1pc``{\tt\the@eqlabel}''\hss}%
 \fi}%
}

% The command \eqno defines \do@eqno to call \make@eqno on the
% \eqno's argument.

\def\eqno#1{\global\eqnumbering@true \gdef\do@eqno{\make@eqno{#1}}}

% Default \curr@eqno creates the default numbering (N), where 
% N is the current value of \theequation, stepped each time
% \curr@eqno is called.

\def\curr@eqno{\refstepcounter{equation} 
 \make@eqno{\theequation}}

% subabc is an environment to change numbering from (1), (2), (3)
% to (1a), (1b), (1c), i.e., to (NL) where N is the value of 
% \theequation (stepped only when the environment starts) and L is
% the letter corresponding to the current value of the counter
% eqnabc (stepped each time \curr@eqno is called, starting
% from 0 in the beginning of subabc).

\newcount\c@eqnabc

\def\subabc{\refstepcounter{equation}
 \c@eqnabc=0
 \def\curr@eqno{\refstepcounter{eqnabc}
  \make@eqno{\theequation\alph{eqnabc}}}
}

\def\endsubabc{\global\@ignoretrue}

%
%   A l i g n m e n t   e n v i r o n m e n t s
%

\newskip\displaylineskip 
\newskip\displaybaselineskip
\newdimen\displaylineskiplimit

\displaylineskip=1.2ex plus 0.2ex
\displaybaselineskip=3.8ex plus 0.2ex
\displaylineskiplimit=.01ex

\def\dmstrut@{\hbox{\vrule\@height 1.7ex\@depth .7ex\@width 0ex}}

\newdimen\eqnnumlowering@

\def\eqnarray{%
 \global\let\do@eqno=\curr@eqno
 \def\the@eqlabel{}%
 \def\label##1{\gdef\the@eqlabel{##1}}%
 \x@eqnarray}

\expandafter\def\csname eqnarray*\endcsname{\def\@eqnarray@cr{\cr}
 \x@eqnarray}

\def\x@eqnarray{%
 \ifdim\mathindent<\z@ \mathindent=-\mathindent
  \n@warning{Negative \mathindent in eqnarray}
 \fi  
 \o@display\make@eq
 \def\curr@cr{\@eqnarray@cr
  \global\multiline@false
  \global\eqnumbering@true
  \global\let\do@eqno=\curr@eqno}
 \let\\\curr@cr 
 \global\eqnumbering@true
 \vbox\bgroup %%%%
 \ddelimalign@errhelp
 \displaydefs@
 \lineskip\displaylineskip \baselineskip\displaybaselineskip
 \lineskiplimit\displaylineskiplimit
 \ialign to\disp@box@width 
 \bgroup 
  \gdef\missing@tabs{&&&}% 
  \hfil\hbox{\wallallowed@false\dmathon@\dmstrut@##\dmathoff@}% 
  \tabskip 0pt      
  \gdef\missing@tabs{&&}%
 &\hfil\hbox{\wallallowed@false\o@dollar\null##\null\o@dollar}\hfil 
  \tabskip 0pt      
  \gdef\missing@tabs{&}%
 &\setbox0\vbox{\hbox{\o@dollar\dmathon@\dmstrut@\mathopen{}##\dmathoff@
   \o@dollar}}%
  \global\eqnnumlowering@=0pt 
  \global\advance\eqnnumlowering@\dp0
  \box0\hfil
  \tabskip 0pt plus 1000pt 
  \gdef\missing@tabs{}%
 &\setbox0\llap{##}%
 \ifmultiline@ \lower.5\eqnnumlowering@\box0
 \else \box0
 \fi \tabskip 0pt\crcr}

\def\endeqnarray{
 \@eqnarray@cr
 \egroup\egroup
 \global\eqnumbering@false
 \endmake@eq\o@display
 \global\@ignoretrue}

\expandafter\def\csname endeqnarray*\endcsname{\endeqnarray}

\def\@eqnarray@cr{\missing@tabs
 \ifeqnumbering@\do@eqno\fi
 \global\@eqnswtrue\crcr
}

\def\eqnsabc{\subabc\eqns}

\def\endeqnsabc{\endeqns\endsubabc}

\def\eqnarrayabc{\subabc\eqnarray}

\def\endeqnarrayabc{\endeqnarray\endsubabc}

\def\ddelimalign@errhelp{\def\ldelim@errhelp{%
 Alignments interfere badly with display mode of delimiters.
 ^^JEvery alignment cell must be balanced.
 ^^JWhen cells are as follows:
 ^^J alignment A & B1 \\ & B2 \\ & ... endalignment
 ^^Jthen alignment may be replaced with
 ^^J ... A \wall B1 \\ B2 \\ ... \return}
 \let\rdelim@errhelp\ldelim@errhelp}

% The purpose of LaTeX alignment math environments eqnarray
% and eqnarray* is, basically, to align binary relation symbols 
% in two typographically relevant situations:
% 
% (1) a long formula broken into n lines; 
% (2) a pile of n distinct formulas, one below another.

% In case (1), a single wall-return block provides a simple solution
% that saves the 2n alignment symbols `&' required by eqnarray:
%
% A \wall = B1 \\
%         = B2 \\
%           ...
%
%         = Bn \return
%
% In case (2), the alignment of relation symbols is somewhat 
% controversial; this style provides limited support for it. 

%
%   P a r a g r a p h   i t e m s 
%

\expandafter\ifx\csname paritemwd\endcsname\relax
 \newdimen\paritemwd\paritemwd=2pc
\fi

\def\paritem#1{%
 \ifmmode 
  \ifdisplay@
   \ifdim\mathindent<0pt % if centered formula
    \ifleqno % equation numbers on the left
     \paritem@leqno{#1}
    \else
     \n@err{Disallowed \string\paritem}
      {Sorry, I am not programmed to handle this case.
      ^^JSet \mathindent to a positive length to
      circumvent the problem.}
    \fi
   \else % if left-aligned formula
    \ifleqno % equation numbers on the left
     \paritem@leqno{#1}
    \else
     \llap{\hbox to \mathindent{\paritem@{#1}\hfil}}
    \fi
   \fi
  \else \n@err{Misplaced \string\paritem}
    {It is disallowed to start \paritem in inline math mode}
  \fi
 \else
  \par\noindent\paritem@{#1}\kern 1ex
 \fi
 \ignorespaces}

\def\paritem@#1{\hbox to\paritemwd{\hss\rm#1}\ignorespaces}

\def\paritem@leqno#1{
 \ifeqnumbering@
  \n@warning{Left numbering superseded by \string\paritem}
 \else \global\eqnumbering@true 
 \fi
 \global\def\do@eqno{\paritem@{#1}}
}

%
%   M a t h   m o d e s
%

% The four math styles of plain TeX (displaystyle, textstyle, scriptstyle, 
% scriptscriptstyle) are abandoned.
% We distinguish two math mode: inline and displayed. 
% They must always apply to a whole subformula and it is not possible to 
% switch between them arbitrarily. 

% While in math mode, 

%      to start          use
%   ----------------   ------------------------
%    inline style       \inline{ ... } 
%    displayed style    \displayed{ ... }

% displayed

\newif\ifnodisplay@

\def\displayon@{%
 \ifnodisplay@ \n@err{Misplaced displayed}%
  {Do not start display mode between inline delimiters.}%
 \else \mspaces@
  \displaydelims@ \dcurrstyle@ 
 \fi}

\def\displayoff@{\enddisplaydelims@}

\pdef\displayed#1{\displayon@#1\displayoff@}

\def\mspaces@{\relax}

% Inline -- I want that user macros expand to reveal Nath behind them

\newif\ifprotectinline@
\protectinline@true

\pdef\inline#1{%
 \begingroup
 \ifprotectinline@
  \begingroup 
  \the\protect@toks 
  \def\protect{\noexpand} 
  \xdef\inline@{\noexpand\wrapfrac@{ #1}}
  \endgroup
  \protectinline@false
 \else
  \def\inline@{\wrapfrac@{#1}}%
 \fi
 \display@false
 \inlinedelims@\icurrstyle@ 
 \inline@ 
 \ldelim@warningcheck{\idelimlevel@}%
 \endgroup}

% We need a script level count

\newcount\mathcount@  % means the level of sub- and super-script (0,1,2,...)

% and an \ifdisplay

\newif\ifdisplay@  % if a displayed formula

% We store the four math style switches for future use.

\let\o@displaystyle=\displaystyle
\let\o@textstyle=\textstyle
\let\o@scriptstyle=\scriptstyle
\let\o@scriptscriptstyle=\scriptscriptstyle

% We redefine \displaystyle and \textstyle; their original effect is disabled.
% \displaystyle is useful in the context of the principle of smallest fences.
% 
% We also redefine \scriptstyle and \scriptscriptstyle to advance \mathcount@
% by 1 and 2, respectively. 
% Observe that \scriptstyle\scriptstyle now has the same effect as
% \scriptscriptstyle

\def\displaystyle{\setbox0
 \hbox{\vrule\@height 3.2\mex \@depth 2\mex \@width 1pt}%
 \resizebox@0}

\let\textstyle\relax

\def\scriptstyle{\advance\mathcount@1 \currstyle@}

\def\scriptscriptstyle{\advance\mathcount@2 \currstyle@}

%
%   M a t h   s i z e s
%

\newdimen\delimaxis@
\newdimen\strutsize@

\delimaxis@=.3ex
\strutsize@=2.1ex

\def\delimstrut@{\hbox{\@tempdima=\delimaxis@ \@tempdimb=\delimaxis@
 \advance\@tempdima .5\strutsize@ \advance\@tempdimb -.5\strutsize@
 \vrule height\prorated@\@tempdima depth\prorated@\@tempdimb width 0pt}}

\def\dcurrstyle@{\display@true
 \ifcase\mathcount@ \o@displaystyle \mex=1ex 
 \or\o@scriptstyle \mex=.7ex 
 \else\o@scriptscriptstyle \mex=.5ex 
 \fi}

\def\icurrstyle@{\display@false
 \ifcase\mathcount@ \o@textstyle \mex=1ex
 \or\o@scriptstyle \mex=.7ex
 \else\o@scriptscriptstyle \mex=.5ex
 \fi}

\def\currstyle@{%
 \ifcase\mathcount@ \mex=1ex
  \ifdisplay@\o@displaystyle
  \else\o@textstyle
  \fi 
 \or\o@scriptstyle \mex=.7ex
 \else\o@scriptscriptstyle \mex=.5ex
 \fi}

% One step smaller than currstyle is \iscriptstyle@:

\def\iscriptstyle@{\display@false\scriptstyle}

\def\currstyle@hbox#1{%
 \ifdisplay@
  \hbox{\dmathon@\dcurrstyle@ #1%
  \global\setbox\sizebox@\box\sizebox 
  \dmathoff@}%
  \resizebox@{\sizebox@}%
 \else
  \hbox{\imath@{\icurrstyle@#1}}%
 \fi}

\def\scriptstylehbox@#1{\hbox{\imath@{\iscriptstyle@#1}}}

% Frame around a subformula

\let\o@fbox\fbox

\pdef\framed#1{\o@fbox{\o@math\currstyle@hbox{#1}\o@math}}

% A repeated sizebox:

\def\samesize@{\mathopen{}\copy\sizebox}

% We redefine \mathpalette and \mathchoice, although they are no 
% more needed

\def\mathpalette#1#2{{#1\currstyle@{#2}}}

\def\mathchoice#1#2#3#4{%
 \ifcase\mathcount@
  \ifdisplay@ #1 \else #2 \fi 
 \or #3
 \else #4
 \fi }

%
%   R e s t r i c t e d   m o d e 
%

\newif\iftoprestricted@
\toprestricted@true

\newif\ifbotrestricted@
\botrestricted@true

%
%   T e x t
%

\newtoks\curr@rm % global needed?

\pdef\text#1{\mathclose{}\text@
 \hbox\expandafter{\protect\the\curr@rm #1}\mathopen{}
 \penalty\punctpenalty\relax}  % Fixed 5.9.2002 thanks to Hedevang Lohse

\def\text@{%
 \ifcase\mathcount@ \global\curr@rm\expandafter{\the\textfont0 }%
 \or \global\curr@rm\expandafter{\the\scriptfont0 }%
 \else \global\curr@rm\expandafter{\the\scriptscriptfont0 }%
 \fi}

%
%  S i z i n g   c o m m a n d s
%
 
% The size of delimiters is determined by the ``heavy'' part of the 
% sub formula enclosed. ``Ignorable'' elements (sub- and superscripts,
% diacritics) do not contribute.

% We use a local box register called \sizebox. Although empty,
% it has its height and depth, equal to the height and depth of the  
% ``main part'' of the current subformula in displayed style.

\newbox\sizebox % local
\newbox\sizebox@ % global

\def\setsize@#1{%
 \ifdisplay@
  \setbox0\hbox{\o@math\dcurrstyle@#1\o@math}%
  \resizebox@{0}%
 \fi}

% Called by \setsize@ and \currstyle@hbox, the command \resizebox@ compares
% vertical dimensions of \sizebox to those of box#1 and sets them to
% whichever is bigger. 

\def\resizebox@#1{%
 \ifdim\ht\sizebox<\ht#1 \ht\sizebox=\ht#1 \fi
 \ifdim\dp\sizebox<\dp#1 \dp\sizebox=\dp#1 \fi}

% A debugging tool - visualize vertical dimensions of certain boxes

\def\showverticaldimensionsofthebox#1{%
 \hbox{\vrule \@height \ht#1 \@depth \dp#1 \@width .667pt}}

% Sizing commands for every large operator from TeXbook p. 435

\let\o@sum=\sum
\let\o@prod=\prod           
\let\o@coprod=\coprod       
\let\o@int=\int             
\let\o@oint=\oint           
\let\o@bigcap=\bigcap       
\let\o@bigcup=\bigcup       
\let\o@bigsqcup=\bigsqcup   
\let\o@bigvee=\bigvee       
\let\o@bigwedge=\bigwedge   
\let\o@bigodot=\bigodot     
\let\o@bigotimes=\bigotimes 
\let\o@bigoplus=\bigoplus   
\let\o@biguplus=\biguplus   

\pdef\big@op#1{\setsize@{#1}\mathop{#1}}

\def\sum{\big@op\o@sum}
\def\prod{\big@op\o@prod}
\def\coprod{\big@op\o@coprod}
\def\oint{\big@op\o@oint\nolimits}
\def\bigcap{\big@op\o@bigcap}
\def\bigcup{\big@op\o@bigcup}
\def\bigsqcup{\big@op\o@bigsqcup}
\def\bigvee{\big@op\o@bigvee}
\def\bigwedge{\big@op\o@bigwedge}
\def\bigodot{\big@op\o@bigodot}
\def\bigotimes{\big@op\o@bigotimes}
\def\bigoplus{\big@op\o@bigoplus}
\def\biguplus{\big@op\o@biguplus}

% \int sticks to any following \int.

\pdef\int{\setsize@\o@int \int@stick}

\def\int@stick{\afterassignment\int@stick@\let\next=}

\def\int@stick@{
 \ifx\next\int
  \def\next@comm{\intop\int@kern\int}
 \else
  \def\next@comm{\intop\nolimits\next}
 \fi
 \next@comm}

\def\int@kern{\ifdisplay@ \kern-1.4\mex \else \kern -.9\mex \fi} 

%
%   L i v e   d e l i m i t e r s 
%

% Every delimiter stands for itself. No additional presentation markup 
% (such as \biggl,\biggr or \left,\right) is needed. 
% Warning: In math mode [,] no more denote optional arguments.

\newcount\idelimlevel@

% Store \TeX's delimiters for character tests

\let\ch@lparenthesis=( 
\let\ch@rparenthesis=)

\let\ch@lbrack=[ 
\let\ch@rbrack=]

\let\ch@langle=< 
\let\ch@rangle=> 

\let\o@lbrack=\lbrack 
\let\o@rbrack=\rbrack 

\let\o@lfloor=\lfloor  \let\o@lceil=\lceil
\let\o@rfloor=\rfloor  \let\o@rceil=\rceil

\def\o@lbrace{\delimiter"4266308 } \let\{=\o@lbrace
\def\o@rbrace{\delimiter"5267309 } \let\}=\o@rbrace

\let\o@langle=\langle
\let\o@rangle=\rangle

\let\o@uparrow=\uparrow 
\let\o@downarrow=\downarrow 
\let\o@updownarrow=\updownarrow
\let\o@Uparrow=\Uparrow 
\let\o@Downarrow=\Downarrow 
\let\o@Updownarrow=\Updownarrow

\let\o@backslash=\backslash 
\let\o@vert=|
\let\o@Vert=\Vert
 
\pdef\{{\delim@l 1\o@lbrace}
\pdef\}{\delim@r 1\o@rbrace}

\pdef\lvert{\delim@l 1|}
\pdef\rvert{\delim@r 1|}
\pdef\lVert{\delim@l 1\Vert}
\pdef\rVert{\delim@r 1\Vert}
\pdef\lbrack{\delim@l 1\o@lbrack}
\pdef\rbrack{\delim@r 1\o@rbrack}
\pdef\langle{\delim@l 1\o@langle}
\pdef\rangle{\delim@r 1\o@rangle}
\pdef\lbrace{\delim@l 1\o@lbrace}
\pdef\rbrace{\delim@r 1\o@rbrace}
\pdef\lfloor{\delim@l 1\o@lfloor}
\pdef\rfloor{\delim@r 1\o@rfloor}
\pdef\lceil{\delim@l 1\o@lceil}
\pdef\rceil{\delim@r 1\o@rceil}

\pdef\lBrack{\delim@l 2\o@lbrack}
\pdef\rBrack{\delim@r 2\o@rbrack}
\pdef\lAngle{\delim@l 2\o@langle}
\pdef\rAngle{\delim@r 2\o@rangle}
\pdef\lFloor{\delim@l 2\o@lfloor}
\pdef\rFloor{\delim@r 2\o@rfloor}
\pdef\lCeil{\delim@l 2\o@lceil}
\pdef\rCeil{\delim@r 2\o@rceil}

% Null delimiters

\pdef\lnull{\delim@l 0.}
\pdef\rnull{\delim@r 0.}

% Obsolete commands:

\let\Big\relax    \let\Bigg\relax
\let\Bigl\left    \let\Biggl\left
\let\Bigr\right   \let\Biggr\right
\let\Bigm\middle  \let\Biggm\middle

%
%   L e f t,   r i g h t   a n d   m i d d l e
%

% Store \TeX's definitions

\let\o@left=\left    
\let\o@right=\right  
\let\@stop=.

% Here is the new definition for \left:

\livechars@

\pdef\left#1{\left@#1}

\def\left@{\afterassignment\left@@\let\next=}

\def\left@@{\ifx\next\@stop \lnull\else
 \ifx\next|\delim@l 1\o@vert \else
 \ifx\next\|\delim@l 1\o@Vert \else
 \ifx\next\vert\delim@l 1\o@vert \else
 \ifx\next\Vert\delim@l 1\o@Vert \else
 \ifx\next\ch@rbrack\delim@l 1\o@rbrack \else
 \next
 \fi\fi\fi\fi\fi\fi}

% Here is the new definition for \right:

\pdef\right#1{\right@#1}

\def\right@{\afterassignment\right@@\let\next=}

\def\right@@{\ifx\next\@stop \rnull\else
 \ifx\next|\delim@r 1\o@vert \else
 \ifx\next\|\delim@r 1\o@Vert \else
 \ifx\next\vert\delim@r 1\o@vert \else
 \ifx\next\Vert\delim@r 1\o@Vert \else
 \ifx\next\ch@lbrack\delim@r 1\o@lbrack \else
  \next
 \fi\fi\fi\fi\fi\fi}

% Here is the new definition for \middle 
% (a bug fixed 21 Sept. 2002 thanks to E.H. Lohse)

\pdef\middle#1{\mathrel{}\middle@#1\mathrel{}} 
                                                
\def\middle@#1{\def\next{#1}
 \ifx\next\@stop \else
 \ifx\next\o@vert\delim@m 1\o@vert \else
 \delim@m 1#1%
 \fi\fi}

\killchars@

% Some other middle delimiters:

\def\mid{\middle|}

%
%   D o u b l e
%

\pdef\double{\afterassignment\double@@\let\next=}

\def\double@@{%
 \ifx\next\ch@lbrack\delim@l 2\o@lbrack \else
 \ifx\next\ch@langle\delim@l 2\o@langle \else
 \ifx\next\ch@rbrack\delim@r 2\o@rbrack \else
 \ifx\next\ch@rangle\delim@r 2\o@rangle \else
 \ifx\next|\delim@m 2\o@vert \else
 \ifx\next\vert\delim@m 2\o@vert \else
 \ifx\next/\delim@m 2/ \else
 \ifx\next\backslash\delim@m 2\backslash \else
 \n@err{Missing delimiter}{\double must be followed by [,],<,> or |}
 \fi\fi\fi\fi\fi\fi\fi\fi}

\pdef\ldouble{\afterassignment\ldouble@@\let\next=}

\def\ldouble@@{\ifx\next\@stop \lnull\else
 \ifx\next|\delim@l 2\o@vert \else
 \ifx\next\vert\delim@l 2\o@vert \else
 \n@err{Missing delimiter}{\ldouble must be followed by |}\lnull
 \fi\fi\fi}

\pdef\rdouble{\afterassignment\rdouble@@\let\next=}

\def\rdouble@@{\ifx\next\@stop \rnull\else
 \ifx\next|\delim@r 2\o@vert \else
 \ifx\next\vert\delim@r 2\o@vert \else
 \n@err{Missing delimiter}{\rdouble must be followed by |}\rnull
 \fi\fi\fi}


\def\Mid{\double|}

%
%   T r i p l e 
%

\pdef\triple#1{\triple@ #1}

\def\triple@{\afterassignment\triple@@\let\next=}

\def\triple@@{%
 \ifx\next\ch@lbrack\delim@l 3\o@lbrack \else
 \ifx\next\ch@langle\delim@l 3\o@langle \else
 \ifx\next\ch@rbrack\delim@r 3\o@rbrack \else
 \ifx\next\ch@rangle\delim@r 3\o@rangle \else
 \ifx\next|\delim@m 3\o@vert \else
 \ifx\next\vert\delim@m 3\o@vert \else
 \ifx\next\vert\delim@m 3\o@vert \else
 \ifx\next/\delim@m 3/ \else
 \ifx\next\backslash\delim@m 3\backslash \else
 \n@err{Missing delimiter}{\triple must be followed by [,],<,> or |}
 \fi\fi\fi\fi\fi\fi\fi\fi\fi}

\pdef\ltriple#1{\ltriple@ #1}

\def\ltriple@{\afterassignment\ltriple@@\let\next=}

\def\ltriple@@{\ifx\next\@stop \lnull\else
 \ifx\next|\delim@l 3\o@vert \else
 \ifx\next\vert\delim@l 3\o@vert \else
 \n@err{Missing delimiter}{\ltriple must be followed by |}\lnull
 \fi\fi\fi}

\pdef\rtriple#1{\rtriple@ #1}

\def\rtriple@{\afterassignment\rtriple@@\let\next=}

\def\rtriple@@{\ifx\next\@stop \rnull\else
 \ifx\next|\delim@r 3\o@vert \else
 \ifx\next\vert\delim@r 3\o@vert \else
 \n@err{Missing delimiter}{\rtriple must be followed by |}\rnull
 \fi\fi\fi}

%
%   N e s t e d   d e l i m i t e r s
%

% Here is a count to count nesting of delimiters

\newcount\ddelimlevel@

% Missing delimiters checking

\def\rdelim@error{\n@err{Unmatched right delimiter}%
  \rdelim@errhelp
  \ddelimlevel@=0}

\def\rdelim@errhelp{Delimiters must be balanced within groups
 and alignment cells.
   ^^JI am ignoring whatever is superfluous.}

\def\ldelim@error#1{\n@err{Unmatched \number#1 left delimiter(s)}%
 \ldelim@errhelp
 \\\ddcount@@=#1
 \loop\ifnum\ddcount@@>0 \rnull \advance\ddcount@@-1 \repeat}

\def\ldelim@errhelp{Delimiters must be balanced within groups
 and alignment cells.
  ^^JI am inserting `)' for every missing left delimiter.
  ^^JLots of error messages may follow; better fix it before going on.}

\def\ldelim@warningcheck#1{\ifnum#1>0
  \n@warning{Unmatched \number#1 left delimiter(s)}%
 \fi}

\def\mdelim@error{\n@err{Misplaced \string\middle}%
  {This command must occur between a left and a right delimiter.
   ^^JDoesn't, so I am ignoring it.}%
  \ddelimlevel@=0}

% Default mode of delimiters

\def\defaultdelims@{%
 \def\delim@l##1##2{\if##10\else\o@left##2\o@right.\fi}%
 \def\delim@r##1##2{\if##10\else\o@left##2\o@right.\fi}%
 \def\delim@m##1##2{\if##10\else\o@left##2\o@right.\fi}% 
}

\defaultdelims@

%
%   D i s p l a y   d e l i m i t e r s 
%

% Displayed material is put into box registers numbered by \ddelim@count
% starting from \firstddelim@no. All they are hboxes.

% Token registers with the same numbers contain material whose typesetting
% is postponed. They may be:
%   (i) extensible tokens (left and middle; e.g., delimiters).
%       Typesetting of extensibles is postponed until their size is
%       known (after the same level right delimiter is found);
%  (ii) escape tokens = interspersed macros (such as \wall, \return, etc.).
%       Typesetting postponed until all box registers are ejected.

\newcount\ddelim@count

% \firstddelim@no is set by \setfirstddelim@no to the first unused
% box and toks register pair.
% Every \displaydelims@ calls \setfirstddelim@no.

\def\setfirstddelim@no{%
 \edef\firstddelim@no{\the\count14 }% unused box register
 \ifnum\firstddelim@no<\the\count15 %
  \edef\firstddelim@no{\the\count15 }% unused toks register
 \fi}

% The commands to fill the hboxes are \startddelimbox@ and \finishddelimbox@.

\def\startddelimbox@{\hbox\bgroup\o@math
 \ifnum\ddelim@count<\insc@unt % if less than the insertion count
 \else \n@err{Formula too large}%
   {No free box to store the next chunk of displayed material.
    ^^JThe rest of the formula will be ignored.
    ^^JDivide big formulas into small parts.}%
  \o@math\egroup
 \fi
 \dcurrstyle@
 \mathopen{}
}

\def\finishddelimbox@{\mathclose{}
 \o@math\egroup}

% To distinguish between extensibles and escape tokens, they start with
% control sequence \ext@tok and \esc@tok, respectively.
% The nth token register may be tested by 
%
%   \if\ext@tok\first@tok{n} yes \else no \fi
%
% etc.

\def\ext@tok{1}
\def\esc@tok{2}

\def\@car#1#2\@nil{#1} % LaTeX's definition
\def\@cdr#1#2\@nil{#2} % LaTeX's definition
\def\@cadr#1#2#3\@nil{#2}

\def\first@tok#1{\expandafter\@car\the\toks#1\relax \noexpand\@nil}
\def\second@tok#1{\expandafter\@cadr\the\toks#1\relax \noexpand\@nil}
\def\tail@toks#1{\expandafter\@cdr\the\toks#1\relax \noexpand\@nil}

\def\first@token#1{\expandafter\@car#1\relax \noexpand\@nil}
\def\second@token#1{\expandafter\@cadr#1\relax \noexpand\@nil}
\def\tail@tokens#1{\expandafter\@cdr#1\relax \noexpand\@nil}

% \displaydelims@ is called by \displayon@ to start display mode of
% delimiters, which includes defining \delim@l, \delim@r and
% \delim@m within displayed formulas and starting the first delimbox.

\def\displaydelims@{\global\setbox\sizebox@\delimstrut@
 \displaydefs@
 \setfirstddelim@no 
 \ddelim@count=\firstddelim@no % the first dbox has this number
 \ddelimlevel@=0 %
 \def\f@stack{\relax}% initiating \f@stack
 \def\ht@stack{\relax}% initiating \ht@stack
 \def\dp@stack{\relax}% initiating \dp@stack
 \toks\number\ddelim@count={\ext@tok 0x}% void extensible token
 \put@{\number\ddelim@count}\f@stack % store the number of the starting box
 \setbox\number\ddelim@count\startddelimbox@ % now inside ddelimbox
}

\def\displaydefs@{%
 \let\delim@l=\ddelim@l
 \let\delim@m=\ddelim@m
 \let\delim@r=\ddelim@r}


\def\ddelim@l#1#2{\mathopen{} 
 \finishddelimbox@ % now outside ddelimbox
 \put@{\the\ht\sizebox}\ht@stack % save height of sizebox
 \put@{\the\dp\sizebox}\dp@stack % save depth of sizebox
 \setbox\sizebox\delimstrut@% set minimal size of delimiters
 \advance\ddelimlevel@ by 1
 \advance\ddelim@count by 1 
 % left delimiter -> extensible token:
 \toks\number\ddelim@count={\ext@tok#1#2}%
 \put@{\number\ddelim@count}\f@stack % store the number of the starting box
 \setbox\number\ddelim@count\startddelimbox@ % now inside ddelimbox
}

\def\ddelim@m#1#2{%
 \ifnum\ddelimlevel@>-1
  \finishddelimbox@ % now outside ddelimbox
  \advance\ddelim@count by 1 
  % middle delimiter -> extensible token:
  \toks\number\ddelim@count={\ext@tok#1#2}%
  \setbox\number\ddelim@count\startddelimbox@ % now inside ddelimbox
 \else
  \mdelim@error#2%
 \fi}

\def\ddelim@r#1#2{\ifnum\ddelimlevel@<1 \rdelim@error \fi
 \finishddelimbox@ % now outside ddelimbox
 \advance\ddelimlevel@ by -1
 \ifnum\ddelimlevel@>-1 % if not error
 \unite@dboxes#1#2% unite box registers on this delimlevel;
  % append #1 times #2
 \fi 
 \setbox0\copy\sizebox % save the sizebox in box0, then let it grow:
 \sizebox@grow
 \advance\ddelim@count by 1
 % empty delimiter -> extensible token:
 \toks\number\ddelim@count={\ext@tok 0.}% emptying toks ddelim@count
 \setbox\number\ddelim@count\startddelimbox@ % now inside ddelimbox
 % eject the sizebox as stored in box0 -- for placement of sub- and
 % superscripts:
 \box0}



\def\checkleftdelims@{\ifnum\ddelimlevel@>0 \ldelim@error{\ddelimlevel@}\fi}

\def\enddisplaydelims@{\checkleftdelims@
 \finishddelimbox@ % now outside ddelimbox
 \unite@dboxes 0.% unite all box registers
 \eject@dboxes
}

% Called by \delim@r, the command \unite@dboxes runs through box registers 
% between \f@ddelim and the current value of \ddelim@count. Collapsed
% into a single hbox is every contiguous interval of hboxes, interspersed
% with extensible elements that were stored in token registers and in #1,
% adjusted to the size of the current \ddelimstrutbox.

% Two global counts are needed:

\newcount\ddcount@  % to count boxes to be collapsed; global
\newcount\ddcount@@ % to count boxes to gather the former; local

\def\unite@dboxes#1#2{% now outside ddelimbox; #1#2 = the right delimiter
 \get@\f@ddelim\f@stack
 \global\ddcount@=\f@ddelim % set ddcount@ to starting position
 \ddcount@@=\f@ddelim % set ddcount@@ to starting position
 \advance\ddelim@count 1
 % starting box number ddcount@@
 \setbox\number\ddcount@@\hbox\bgroup % now inside ddelimbox
 \g@loop\ifnum\ddcount@<\ddelim@count
  \if\ext@tok\first@tok{\number\ddcount@}\relax % if extensible element
   \if0\second@tok{\number\ddcount@}\relax % if `0' then do nothing 
   \else % else eject the resized extensible
    \expandafter\size@\the\toks\number\ddcount@\relax 
   \fi 
   \unhbox\number\ddcount@ % unbox the box
  \else 
   \if\esc@tok\first@tok{\number\ddcount@}\relax % else if escape element
    \egroup % finishing box number ddcount@@; now outside ddelimbox
    \advance\ddcount@@ by 1 
    % moving toks ddcount@ to toks ddcount@@ -- if unequal
    \ifnum\ddcount@=\ddcount@@ \else
     \toks\number\ddcount@@=\expandafter{\the\toks\number\ddcount@}%
     \toks\number\ddcount@={\ext@tok 0.}% emptying toks ddcount@
    \fi
    % starting box ddcount@@:
    \setbox\number\ddcount@@\hbox\bgroup % now inside ddelimbox 
    \unhbox\number\ddcount@ 
   \else
    \n@err{Unexpected contents in toks \number\ddcount@}{Shocked? Me too.}%
   \fi
  \fi 
  \global\advance\ddcount@ by 1 
 \repeat 
 \size@ \ext@tok#1#2 \delimtype@right\relax % resized right delimiter
 \egroup % now outside ddelimbox
 \toks\f@ddelim={\ext@tok 0.}% emptying toks f@ddelim
 \ddelim@count=\ddcount@@}

%
%   D e l i m i t e r   g r o w t h
%

\newdimen\delimincrement@
\newcount\delimgrowth@

\def\delimgrowth{\afterassignment\delimgrowth@@\delimgrowth@}

\def\delimgrowth@@{\ifnum\delimgrowth@<1 \delimgrowth@=1
  \n@warning{\string\delimgrowth\space must be a positive natural number}%
 \fi
 \delimincrement@=.66ex 
 \divide\delimincrement@ by \delimgrowth@}

\def\sizebox@grow{\@tempdima=\ht\sizebox 
 \advance\@tempdima\delimincrement@ %\relax
 \ht\sizebox=\@tempdima
 \@tempdima=\dp\sizebox
 \advance\@tempdima\delimincrement@ %\relax
 \dp\sizebox=\@tempdima
 \get@\@tempa\ht@stack
 \ifdim\the\ht\sizebox<\@tempa \ht\sizebox=\@tempa\fi 
 \get@\@tempa\dp@stack
 \ifdim\the\dp\sizebox<\@tempa \dp\sizebox=\@tempa\fi
} 

% Called by the last \delim@r, the command \eject@dboxes ejects all the
% box and token registers filled. Uses the global count \ddcount@

\newcount\ddcount@ % global

\def\eject@dboxes{\global\ddcount@=\firstddelim@no{}%
 \box\number\ddcount@
 \g@loop\ifnum\ddcount@<\ddelim@count
  \global\advance\ddcount@ by 1
  \if\ext@tok\first@tok{\number\ddcount@}\relax
   \n@err{Forgotten extensible \number\ddcount@\space}%
    {An internal error, induced by the previous errors. 
     ^^JSomething will be lost.}
  \else
   \if\esc@tok\first@tok{\number\ddcount@}\relax
    \tail@toks{\number\ddcount@}\relax
   \else\n@err{Unable to eject \number\ddcount@}%
    {Sorry, the box or toks have never been filled.
     ^^JIs an internal error and should never happen.}%
   \fi
  \fi
  \box\number\ddcount@ 
  \repeat}

%
%   S i z i n g   d e l i m i t e r s
%

% The following commands are called by \unite@dboxes.
% Parameters:
%
% #1 = always \ext@tok, hence ignored
% if #2 = ":" then sizable fraction
%   #3 = numerator and #4 = denominator
% otherwise
%   #2 = number of repetitions (from 0 to 9),
%   #3 = a delimiter 
%   #4 = a type (\delimtype@right or \relax)

\def\size@#1#2#3#4{%
 \if:#2\relax % if a numeric fraction 
  \o@math\size@frac{#3}{#4}\relax\o@math 
 \else % else a delimiter
  \if0#2\relax % zero repetitions -- do nothing
  \else 
   \ifx#4\delimtype@right % if right delimiter, set sizebox
    \setbox0\hbox{\o@math \extend@delim#2#3\sizebox\o@math}%
%%% \ht\sizebox=\ht0 \dp\sizebox=\dp0 % 
    \box0 % 
   \else
    \o@math \extend@delim#2#3\sizebox \o@math
   \fi
  \fi
 \fi}

%
%   E x t e n d i n g   d e l i m i t e r s
%

% Not all expressions have their height equal to depth. So we put
% the expression in a vcenter, create delimiters that match the vcenter,
% and then shift the delimiter vertically the appropriate amount.

% A surprise was that [ sometimes acquired bigger size than (.
% So I had to modify the procedure: first extend [, then (.

% The three arguments to \extend@delim are: 
% #1 = the number of repetitions
% #2 = a delimiter
% #3 = a box register of zero width, or -1 to indicate base size

% Setting values of \delimiterfactor and \delimitershortfall such that
% \delimfactor works well:

\delimiterfactor=920
\delimitershortfall=3pt

% Not all expressions have their height equal to depth. So we put
% the expression in a vcenter, create delimiters that match the vcenter,
% and then shift the delimiter vertically the appropriate amount.

% A surprise was that [ sometimes acquired bigger size than (.
% So I had to modify the procedure: first extend [, then (.

% The three arguments to \extend@delim are: 
% #1 = the number of repetitions
% #2 = a delimiter
% #3 = a box register of zero width, or -1 to indicate base size

\def\extend@delim#1#2#3{%
 \ifnum#1<1 
  % do absolutely nothing
 \else\begingroup % do box0 = extended delimiter
  \nulldelimiterspace=0pt
  \ifnum#3<0 % if #3 not a box register
   \setbox0\hbox{\o@math\icurrstyle@\o@left#2\o@right.\o@math}%
   \@tempdima=0pt 
  \else % if #3 = box register
   \setbox\@tempboxa\hbox{\o@math\vcenter{\copy#3}\o@math}%
   \@tempdima=\ht\@tempboxa %\hbox{\the\@tempdima/\the\dp\@tempboxa}%
   \ifdim\@tempdima>3\mex \checkangle@{#2}%
    \ifresult@\n@warning{angle brackets do not grow that size}\fi
   \fi
   \advance\@tempdima -\ht#3
   \setbigstrutbox@
   \setbox0\hbox{\o@math\icurrstyle@\o@left#2 
   \ifdim\ht\@tempboxa>.86\ht\bigstrut@box
    \vrule height \ht\bigstrut@box width 0pt
   \fi 
   \ifdim\dp\@tempboxa>.86\dp\bigstrut@box
    \vrule depth \dp\bigstrut@box width 0pt
   \fi
   \box\@tempboxa\o@right.\o@math}%
  \fi % now copy box0 #1 times
  \count@=1 
  \loop\ifnum\count@<#1 
   \lower\@tempdima\copy0
   \hskip -.75\wd0 \hskip .25\mex
   \advance\count@ 1
  \repeat
  \lower\@tempdima\box0
  \endgroup
 \fi}

% Check for an angle bracket

\def\checkangle@#1{\def\@tempa{#1}
 \def\@tempb{\o@langle}
 \ifx\@tempa\@tempb\result@true
 \else
  \def\@tempb{\o@rangle}
  \ifx\@tempa\@tempb\result@true
  \else
   \result@false
 \fi\fi}

%
%   E s c a p e   c o m m a n d s 
%

% Escape commands are ones that, if not stored, would interfere with the
% display mode. 

\def\wall@cr{\checkpunct@ 
 \ifpunct@ \global\punct@false 
  \ifnum\ddelimlevel@>0  % elements of a list
   \store@ec{\d@cr{\pad@}}{}% padded
   \mathopen{} % new expression
  \else % separate equations
   \store@ec{\d@cr{\relax}}{}% unpadded
   \mathopen{} % new expression
  \fi
 \else % broken formula
  \store@ec{\d@cr{\pad@}}{}% padded
  \mkern-\thickmuskip \mathinner{} % continuing expression
 \fi}

\def\curr@cr@is@wall@cr{\def\curr@cr{\wall@cr}\let\\\curr@cr}

\def\wall{\mathrel{}
 \ifwallallowed@
  \ifdisplay@
   \store@ec{\d@wall{0}}{\let\\\wall@cr}%
  \else
   \n@warning{Non-display. I am ignoring the misplaced \string\wall}%
  \fi 
 \else \n@err{Misplaced \string\wall}{\wall is disallowed here}%
 \fi
 \mathopen{}
}
 

\def\return{\checkpunct@
 \ifdisplay@ 
  \store@ec{\d@return}{\let\\\curr@cr}
 \else
  \n@warning{Non-display. I am ignoring the misplaced \string\return}%
 \fi 
 \ifpunct@ \global\punct@false
  \mathopen{}
 \else
  \mkern-\thickmuskip \mathinner{}
 \fi
}


% \padded is another form of \wall.
% \padded{A} prefixes each line except the first with A.
% Typically A is a void box or a kern.
% Nested \padded have cummulative effect.

\def\padded#1{%
 \ifwallallowed@
  \ifdisplay@
   \store@ec{\d@wall{1#1}}{\let\\\wall@cr}%
  \else
   \n@warning{Non-display. I am ignoring the misplaced \string\padded}%
  \fi 
 \else \n@err{Misplaced \string\padded}{\padded is disallowed here}%
 \fi 
 \mathopen{}
}

\def\pad@{}


% \store@ec is the generic command to store an escape command #1 in token
% registers. It also performs #2 while outside ddelimbox.

\def\store@ec#1#2{\finishddelimbox@ % now outside ddelimbox
 \advance\ddelim@count 1
 \toks\number\ddelim@count={\esc@tok#1}% #1 -> escape token
 #2% keep % here
 \setbox\number\ddelim@count\startddelimbox@ % now inside ddelimbox
}


%
%   I n l i n e   d e l i m i t e r s 
%

\newcount\big@ \big@=0
\newcount\big@@ \big@@=0
\newbox\bigstrut@box

\mathchardef\biglbracket@="0302  %% \biglbracket@ is of fixed size in LaTeX !!

\def\setbigstrutbox@{\setbox\bigstrut@box
 \hbox{\o@math\vcenter{\hbox{\o@math\icurrstyle@
  \mathchar\biglbracket@\o@math}}\o@math}
 \setbox\bigstrut@box\hbox{\vrule height\prorated@\ht\bigstrut@box
  depth\prorated@\dp\bigstrut@box
  width 0pt}
}

\pdef\big{\advance\big@ 1\relax}
\pdef\bigg{\advance\big@ 2\relax}
\pdef\biggg{\advance\big@ 3\relax}

\def\bigl{\big\left}
\def\biggl{\bigg\left}

\let\bigm=\middle
\let\biggm=\middle

\let\bigr=\right
\let\biggr=\right


% inline mode 

\def\inlinedelims@{%
 \idelimlevel@=0\relax
 \big@=0\relax
 \big@@=0\relax
 \let\delim@l=\idelim@l
 \let\delim@m=\idelim@m
 \let\delim@r=\idelim@r
}

\def\idelim@l#1#2{\mathopen{}
 \nodisplay@true
 \advance\idelimlevel@ by 1 
 \ifnum\big@>0 \advance\big@@\big@ 
  \ifnum\idelimlevel@>\big@@ \n@err{Misplaced \string\big}
    {Too late for \big -- a big must not occur inside a non-big}
  \fi
  \ifnum\idelimlevel@<1 \n@err{Misplaced \string\big}
    {\big must not occur on negative level of fencing.}
  \fi
 \fi
 \big@=0 
 \ifnum\idelimlevel@>\big@@ \extend@delim#1#2{-1} % normal size
 \else
  \ifnum\idelimlevel@<1 \extend@delim#1#2{-1} % normal size
  \else
   \setbigstrutbox@ \extend@delim#1#2\bigstrut@box
  \fi
 \fi
 \mathopen{}}

\def\idelim@m#1#2{\mathclose{}
 \nodisplay@true
 \big@=0 
 \ifnum\idelimlevel@>\big@@ \extend@delim#1#2{-1} % normal size
 \else
  \ifnum\idelimlevel@<1 \extend@delim#1#2{-1} % normal size
  \else
   \setbigstrutbox@ \extend@delim#1#2\bigstrut@box
  \fi
 \fi
 \mathopen{}}
 
\def\idelim@r#1#2{\mathclose{}
 \big@=0 
 \ifnum\idelimlevel@>\big@@ \extend@delim#1#2{-1} % normal size
 \else
  \ifnum\idelimlevel@<1 \extend@delim#1#2{-1} % normal size
  \else
   \setbigstrutbox@ \extend@delim#1#2\bigstrut@box
   \advance\big@@ -1
  \fi
 \fi
 \advance\idelimlevel@ by -1
 \mathclose{}}

%
%   A u x i l i a r y   p r o c e d u r e s
%
\def\replacebindelims@#1#2{\begingroup
 \idelimlevel@=0\relax
 \def\delim@l##1##2{#2\advance\idelimlevel@ by 1 
  \setbox0\hbox\bgroup\o@math}%
 \def\delim@r##1##2{\mathclose{}\advance\idelimlevel@ by -1
  \o@math\egroup}%
 \def\delim@m##1##2{}%
 \def\inlineopen@{#2\advance\idelimlevel@ by 1 
  \setbox0\hbox\bgroup\o@math}%
 \def\inlineclose@{\mathclose{}\advance\idelimlevel@ by -1
  \o@math\egroup}%
 #1
 \endgroup}

%
%  S u b s c r i p t s   a n d   s u p e r s c r i p t s 
%

\let\o@sp^
\let\o@sb_ % (MathTime macros destroy plain TeX's \sp,\sb)

\catcode`\^=13
\catcode`\_=13

\pdef_#1{\o@sb{\display@false\advance\mathcount@ 1 \inline{#1}}}

\pdef^#1{\o@sp{\display@false\advance\mathcount@ 1 \inline{#1}}}

\catcode`\^=12
\catcode`\_=12

%
%  P a r s i n g   o f   s u b -   a n d   s u p e r s c r i p t s
%

% The comand \parse@ detects whether sub- or superscripts follow.
% If yes, then \sb@true or \sp@true is set and the arguments
% are stored in \sb@toks or \sp@toks, respectively.
% Then \afterparse@ is executed.

\newtoks\sp@toks
\newtoks\sb@toks

\newif\ifsb@
\newif\ifsp@

\def\parse@{\sb@false\sp@false
 \def\next@comm{\afterassignment\parse@@\let\next=}
 \next@comm}

\def\parse@@{%
 \ifx\next_
  \ifsb@\n@err{Double subscript}{The notation x_y_z is ambiguous.}
  \else\sb@true
  \fi
  \def\next@comm{\sb@@}
 \else
  \ifx\next^
   \ifsp@\n@err{Double superscript}{The notation x^y^z is ambiguous.}
   \else\sp@true
   \fi
   \def\next@comm{\sp@@}
  \else
   \def\next@comm{\afterparse@}
  \fi
 \fi
 \next@comm}

\def\sp@@#1{\sp@toks={#1} \afterassignment\parse@@\let\next=}

\def\sb@@#1{\sb@toks={#1} \afterassignment\parse@@\let\next=}

\def\parse@next{\parse@\next}

%
%  O p e r a t o r s
%

% \mathop is redefined to stop misinterpretation of following Bins 
% as unary operators (cf. TeXbook, p. 170). 

\let\o@mathop\mathop

% The following definition determines spacing between Op and Bin.
% (According to [TeXBook, p. 170], ``such case never arises, 
% so plain TeX leaves it undefined, making the Bin into unary.'')

\newif\iflimits@
\limits@true

\pdef\mathop#1{%
 \ifnum\mathcount@>0  % in sub- and superscripts 
  \def\next@comm{\o@mathop{#1}}       % just @mathop
 \else \def\mathop@arg{#1}
  \def\afterparse@{\mathop@@}
  \sb@false\sp@false
  \ifdisplay@\limits@true\else\limits@false\fi
  \def\next@comm{\afterassignment\mathop@\let\next=}
 \fi
 \next@comm}

\def\mathop@{\def\next@comm{\parse@next}
 \ifx\next\limits 
  \ifdisplay@ \limits@true 
  \else \iflimits@ \else \n@warning{Ignoring inline \string\limits}\fi
  \fi
  \def\next@comm{\parse@}
 \else
  \ifx\next\nolimits \limits@false \def\next@comm{\parse@}\fi
 \fi
 \next@comm}

\def\mathop@@{\mathoptest@ % sets \ifresult@ true if a left delimiter follows
 \ifresult@
  \iflimits@ 
   \o@mathop{\mathop@arg}\mathop@@@l
  \else 
   \o@mathop{\mathop@arg}\nolimits\mathop@@@
  \fi
 \else
  \iflimits@ 
   \mathinner{\o@mathop{\mathop@arg}\mathop@@@l}
  \else 
   \mathinner{\mathop@arg}\mathop@@@
  \fi
 \fi
 \next}


\catcode`\^=13
\catcode`\_=13

\def\mathop@@@{%
 \ifsp@
  ^{\hbox{\edef\@tempa{\noexpand\imath@{\the\sp@toks}}%
   \def\\{,\ }\@tempa}}
 \fi
 \ifsb@
  _{\hbox{\edef\@tempa{\noexpand\imath@{\the\sb@toks}}%
   \def\\{,\ }\@tempa}}
 \fi}

\def\mathop@@@l{\limits
 \ifsp@ ^{\lmathop@@@l@{\the\sp@toks}} \fi
 \ifsb@ _{\lmathop@@@l@{\the\sb@toks}} \fi}

\def\lmathop@@@l@#1{\vbox{\let\\=\crcr 
 \baselineskip=0pt \lineskip=2pt
 \edef\@tempa{\vbox{\noexpand\ialign{%
  \hfil\noexpand\imath@{####}\hfil\crcr
  #1 \crcr}}}  
 \@tempa}}

\catcode`\^=12
\catcode`\_=12


\catcode`\(=13 \catcode`\[=13 \catcode`\<=13 

\newif\iftesting@
\testing@false

\def\mathoptest@{%
 \iftesting@
  \result@true
 \else 
  \result@false
  \ifx\next\ch@lparenthesis\result@true \else
  \ifx\next\ch@lbrack\result@true \else
  \ifx\next<\result@true \else
  \ifx\next\{\result@true \else
  \ifx\next\left\result@true \else
  \ifx\next\langle\result@true \else
  \ifx\next\lfloor\result@true \else
  \ifx\next\lceil\result@true \else
  \ifx\next\mathopen\result@true 
  \fi\fi\fi\fi\fi\fi\fi\fi\fi 
 \fi}

% \lvert and \lVert are intentionally omitted

\catcode`\(=12 \catcode`\[=12 \catcode`\<=12 

%
%  A b b r e v i a t i o n s
%
\newcount\abbrevlength@

\pdef\abbreviation{\def\abbrev@@{}\abbrevlength@=0
   \def\abbrev@@@{\afterassignment\abbrev@\let\abbrev@next= }%
   \result@false\abbrev@@@}

\long\def\abbrev@{%
 \ifx`\abbrev@next \result@false
 \else 
  \edef\next{\meaning\abbrev@next}
  \expandafter\letter@test\next\endletter@test
 \fi
 \ifresult@
  \edef\abbrev@@{\abbrev@@\theletter@}
  \advance\abbrevlength@ 1\relax
 \else
  \ifnum\abbrevlength@>1 
   \ifnum\mathcount@>0 \o@mathop\bgroup
   \else \mathinner\bgroup
   \fi
  \else\bgroup
  \fi
  {\rm \abbrev@@\kern 0pt}
  \def\abbrev@@@{\egroup\result@false
   \mathclose{}\mathopen{}\mathop{}\nolimits\abbrev@next}
 \fi
 \abbrev@@@}

\def\letter@test #1#2#3#4#5\endletter@test{
 \if l#4\result@true\letter@test@#5 
 \else\result@false\fi}

\def\letter@test@#1#2#3#4#5#6{\def\theletter@{#6}}

%
%   S p e c i a l   s y m b o l s
%

% Inequalities

%\let\leq=\le           \let\geq=\ge
%\let\leqq=\le          \let\geqq=\ge

% factorial

\def\factorial{\mc@factorial\mathopen{}\mathinner{}}

% vingl

\pdef\vin{\mathrel{\hbox{\hglue .1\mex
  \vrule \@height .06\mex \@width 1\mex
  \vrule \@height 1.33\mex \@width .06\mex
  \hglue .4\mex}}}

\pdef\niv{\mathrel{\hbox{\hglue .2\mex
  \vrule \@height 1.33\mex \@width .06\mex
  \vrule \@height .06\mex \@width 1\mex
  \hglue .5\mex}}}

\def\stackrel#1#2{\mathrel{\limits@true\mathop{#2}\limits^{\rm #1}}} %%%%%%%%%%

\makerobust\stackrel

%
%   E x p a n d a b l e   b a r s   a n d   a r r o w s
%

% Save even if not needed

\let\o@overline=\overline
\let\o@underline=\underline

\newdimen\er@wd

\def\er@sep{.06ex}
\def\er@gap{.33\mex}
\def\er@short{.6\mex}
\def\er@rulewd{.05ex}
\def\er@minwd{.6\mex}
\def\er@kerna{.15\mex}
\def\er@kernb{.15\mex}

\def\overline#1{\setmathtype@{#1}%
 {\o@er@{#1}{\leaders\hrule \@height\er@rulewd \hfill}}
}
\def\underline#1{\setmathtype@{#1}%
 {\u@er@{#1}{\leaders\hrule \@height\er@rulewd \hfill}}
}
\def\overrightarrow#1{\setmathtype@{#1}%
 {\o@er@{#1}{\o@math\iscriptstyle@ \longrightarrowfill\o@math}}
}
\def\underrightarrow#1{\setmathtype@{#1}%
 {\u@er@{#1}{\o@math\iscriptstyle@ \longrightarrowfill\o@math}}
}
\def\overleftarrow#1{\setmathtype@{#1}%
 {\o@er@{#1}{\o@math\iscriptstyle@ \longleftarrowfill\o@math}}
}
\def\underleftarrow#1{\setmathtype@{#1}%
 {\u@er@{#1}{\o@math\iscriptstyle@ \longleftarrowfill\o@math}}
}
\def\overleftrightarrow#1{\setmathtype@{#1}%
 {\o@er@{#1}{\o@math\iscriptstyle@ \longleftrightarrowfill\o@math}}
}
\def\underleftrightarrow#1{\setmathtype@{#1}%
 {\u@er@{#1}{\o@math\iscriptstyle@ \longleftrightarrowfill\o@math}}
}

% Inside

\pdef\o@er@#1#2{\inlineopen@
 \begingroup
 \setbox0\currstyle@hbox{\toprestricted@true #1}
 \er@wd=\wd0 \advance\er@wd-\er@short
 \ifdim \er@wd<\er@minwd \er@wd=\er@minwd \fi
 \kern\er@kerna
 \hbox to\wd0{\hss
  \vbox{\offinterlineskip
   \vglue\er@sep
   \hbox to\er@wd{#2}%
   \vskip\er@gap
   \hbox to\er@wd{\hss\box0\hss}}%
  \hss}
 \kern\er@kernb
 \endgroup
 \inlineclose@}

\pdef\u@er@#1#2{\inlineopen@
 \begingroup
 \setbox0\currstyle@hbox{\botrestricted@true #1}
 \er@wd=\wd0 \advance\er@wd -\er@short
 \ifdim \er@wd<\er@minwd \er@wd=\er@minwd \fi
 \kern\er@kerna
 \hbox to\wd0{\hss
  \vtop{\offinterlineskip
   \hbox to\er@wd{\hss\box0\hss}
   \vskip\er@gap
   \hbox to\er@wd{#2}%
   \vglue\er@sep}%
  \hss}
 \kern\er@kernb
 \endgroup
 \inlineclose@}

\def\longrightarrowfill{\axis@@@\hfill\mskip-6mu\rightarrow}
\def\longleftarrowfill{\leftarrow\mskip-6mu\axis@@@\hfill}
\def\longleftrightarrowfill{\leftarrow\mskip-6mu
 \axis@@@\hfill\mskip-6mu\rightarrow}

% Setting math type

\def\setmathtype@#1#2{
 \setbox0\hbox{\o@math \setmathtype@@@000 x#1x\o@math}
 \@tempdima=\wd0
 \setbox0\hbox{\o@math \setmathtype@@@100 x#1x\o@math}
 \ifdim\wd0>\@tempdima \o@mathop{#2}
 \else \setbox0\hbox{\o@math \setmathtype@@@010 x#1x\o@math}
  \ifdim\wd0>\@tempdima \mathrel{#2}
  \else \setbox0\hbox{\o@math \setmathtype@@@001 x#1x\o@math}
   \ifdim\wd0>\@tempdima \mathbin{#2}
   \else \mathord{#2}
   \fi
  \fi
 \fi}

\def\setmathtype@@@#1#2#3{\thinmuskip=#1mu \thickmuskip=#2mu \medmuskip=#3mu
 \relax}

%
%   M u l t i p l e   a n d   e x t e n s i b l e   a c c e n t s
%

% Extensible accents: 

\let\o@hat=\hat
\let\o@widehat=\widehat

\let\o@tilde=\tilde
\let\o@widetilde=\widetilde

\let\o@bar=\bar

\def\widebar#1{\ifdim\wd0<\prorated@ em \mathaccent"07B {#1}
 \else \mathaccent"07C {#1}
 \fi}
 
% Limits of extensibility: 
%
% narrow accent
%   threshold = \widethr@
% wide accent
%   threshold = \wrapthr@
% attached accent

\def\widethr@{1.6ex}
\def\wrapthr@{5.8\mex}

% Non-extensible accents

\let\o@dot=\dot
\let\o@ddot=\ddot
\let\o@breve=\breve
\let\o@check=\check

\def\uo{\mathaccent"017 }

% Multiple accents

\newtoks\acc@toks % toks to store a sequence of accents in reverse order

\newif\ifextacc@

\pdef\hat{\acc@toks={\H@} \extacc@true \acc@@}
\pdef\tilde{\acc@toks={\T@} \extacc@true \acc@@}
\pdef\bar{\acc@toks={\B@} \extacc@true \acc@@}
\pdef\dot{\acc@toks={\D@} \extacc@false \acc@@}
\pdef\ddot{\acc@toks={\DD@} \extacc@false \acc@@}
\pdef\breve{\acc@toks={\BR@} \extacc@false \acc@@}
\pdef\check{\acc@toks={\CH@} \extacc@false \acc@@}

% Defaults are printable (for debugging purposes)

\def\H@{H} \def\T@{T} \def\B@{B}
 \def\D@{D} \def\DD@{DD}
 \def\BR@{BR} \def\CH@{CH}

% See TeXbook p. 374 for the trick with \expandafter:

\def\acc@@#1{\def\next@comm{\acc@@} \def\@tempa{#1} \def\@tempb{\hat}
 \ifx \@tempa\@tempb
  \acc@toks=\expandafter{\expandafter \H@\the\acc@toks}
 \else \def\@tempb{\tilde}
  \ifx \@tempa\@tempb
   \acc@toks=\expandafter{\expandafter \T@\the\acc@toks}
  \else \def\@tempb{\bar}
   \ifx \@tempa\@tempb
    \acc@toks=\expandafter{\expandafter \B@\the\acc@toks}
   \else \def\@tempb{\dot}
    \ifx \@tempa\@tempb
     \acc@toks=\expandafter{\expandafter \D@\the\acc@toks}
     \extacc@false
    \else \def\@tempb{\ddot}
     \ifx \@tempa\@tempb
      \acc@toks=\expandafter{\expandafter \DD@\the\acc@toks}
      \extacc@false
     \else \def\@tempb{\breve}
      \ifx \@tempa\@tempb
       \acc@toks=\expandafter{\expandafter \BR@\the\acc@toks}
       \extacc@false
      \else \def\@tempb{\check}
       \ifx \@tempa\@tempb
        \acc@toks=\expandafter{\expandafter \CH@\the\acc@toks}
        \extacc@false
       \else \def\next@comm{\acc@@@{#1}} 
       \fi
      \fi
     \fi
    \fi
   \fi
  \fi
 \fi
 \next@comm}

\def\acc@@@#1{
 \inlineopen@   
 \setbox0\currstyle@hbox{#1} 
 \ifdim\wd0>\wrapthr@ % long
  \wrap@@@acc{#1}
 \else 
  \checkcompound@{#1}% #1=accented material
  \ifcompound@ % not a single character
   \ifextacc@
    \ifdim\wd0>\widethr@ \wide@@@acc{#1} 
     \else \@@@acc{#1}
    \fi \acc@kern 
   \else \wrap@@@acc{#1}
   \fi 
  \else % single character
   \ifdim\wd0>\widethr@ \wide@@@acc{#1} 
   \else \@@@acc{#1}
   \fi \acc@kern 
  \fi
 \fi 
 \inlineclose@}

\def\acc@kern {\mkern1.2mu }

% Checking if single character

\newif\ifcompound@

\def\checkcompound@#1{\compound@false 
 \edef\fdxxii@textfontii{\the\fontdimen22\textfont2}% 
 \fontdimen22\textfont2=300pc
 \setbox\@tempboxa\hbox{\o@math\defaultdelims@
  \def\frac{xx\@gobbletwo}
  #1\o@math} 
 \@tempdima=\ht\@tempboxa
 \setbox\@tempboxa\hbox{\o@math\defaultdelims@
  \def\frac{xx\@gobbletwo}
  \o@mathop{#1}\o@math} 
 \ifdim\ht\@tempboxa=\@tempdima
  \compound@true  
 \fi
 \fontdimen22\textfont2=\fdxxii@textfontii
}


% Attaching accents to #1, putting parentheses around if necessary.

\def\wrap@@@acc#1{
 \setbox\@tempboxa\currstyle@hbox{\nodisplay@false
  \replacebindelims@{#1}{x}}
 \ifdim\wd\@tempboxa>2\mex 
  \ifdisplay@ \currstyle@hbox{(#1)} \else (\inline{#1}) \fi
  \samesize@^{\wrap@@@acc@}
 \else
  \ifdisplay@ \currstyle@hbox{#1} \else \inline{#1} \fi
  \samesize@^{\wrap@@@acc@}
 \fi
}

\def\wrap@@@acc@{\begingroup 
 \def\H@{\land} \def\T@{\sim} \def\B@{-}
 \def\D@{\raise.5\mex\hbox{\bf.}} \def\DD@{\raise.5\mex\hbox{\bf..}}
 \def\BR@{\smile} \def\CH@{\lor}
 \the\acc@toks \endgroup}

% Stacked accents

\newdimen\xheight@

\def\acc@def#1#2#3#4{\def#1{\fontdimen5 #4=\@tempdima
 \ifcompound@ % if compound
  \rlap{\o@math#2{\currstyle@hbox{#3}}\o@math} 
 \else % if single character
  \rlap{\currstyle@hbox{#2{#3}}}
 \fi
 \advance\@tempdima\@tempdimb}}

\def\xacc@def#1#2#3#4{\def#1{\begingroup
 \advance\@tempdima 1.5\@tempdimb
 \fontdimen5 #4=\@tempdima
 \ifcompound@ % if compound
  \rlap{\o@math#2{\currstyle@hbox{#3}}\o@math}
 \else
  \rlap{\currstyle@hbox{#2{#3}}}
 \fi
 \endgroup
 \fontdimen5 #4=\xxheight@
 \advance\@tempdima\@tempdimb}}

\def\wide@@@acc#1{% uses fontdimens
 \ifcase\mathcount@ \def\acc@font{\textfont3 } \def\xacc@font{\textfont0 }
 \or \def\acc@font{\scriptfont3 } \def\xacc@font{\scriptfont0 }
 \else \def\acc@font{\scriptscriptfont3 } \def\xacc@font{\scriptscriptfont0 }
 \fi 
 \edef\xheight@{\the\fontdimen5\acc@font}%
 \edef\xxheight@{\the\fontdimen5\xacc@font}%
 \@tempdima=\xheight@ \@tempdimb=-.55\@tempdima
 \acc@def{\H@}{\o@widehat}{#1}\acc@font
 \acc@def{\T@}{\o@widetilde}{#1}\acc@font
 \xacc@def{\B@}{\widebar}{#1}\xacc@font
 \acc@def{\D@}{\o@dot}{#1}\xacc@font
 \acc@def{\DD@}{\o@ddot}{#1}\xacc@font
 \acc@def{\BR@}{\o@breve}{#1}\xacc@font
 \acc@def{\CH@}{\o@check}{#1}\xacc@font
 \the\acc@toks 
 \currstyle@hbox{#1} 
 \fontdimen5\acc@font=\xheight@
 \fontdimen5\xacc@font=\xxheight@
}

\def\@@@acc#1{% uses fontdimens!
 \ifcase\mathcount@ \def\acc@font{\textfont0 }
 \or \def\acc@font{\scriptfont0 }
 \else \def\acc@font{\scriptscriptfont0 }
 \fi
 \edef\xheight@{\the\fontdimen5\acc@font}%
 \@tempdima=\xheight@ \@tempdimb=-.55\@tempdima
 \acc@def{\H@}{\o@hat}{#1}\acc@font
 \acc@def{\T@}{\o@tilde}{#1}\acc@font
 \acc@def{\B@}{\o@bar}{#1}\acc@font
 \acc@def{\D@}{\o@dot}{#1}\acc@font
 \acc@def{\DD@}{\o@ddot}{#1}\acc@font
 \acc@def{\BR@}{\o@breve}{#1}\acc@font
 \acc@def{\CH@}{\o@check}{#1}\acc@font
 \the\acc@toks
 \currstyle@hbox{#1}
 \fontdimen5\acc@font=\xheight@
}

\let\inlineopen@\relax
\let\inlineclose@\relax

%
%  E x p a n d a b l e   h o r i z o n t a l  a r r o w s
%

\def\longrightarrow@#1#2{\mathrel{\mathopen-\axis@@
 \axis@{#1}{#2}
 \axis@@\mathclose\rightarrow}}

\def\longleftarrow@#1#2{\mathrel{\mathopen\leftarrow\axis@@
 \axis@{#1}{#2}
 \axis@@\mathclose-}}

\def\longleftrightarrow@#1#2{\mathrel{\mathopen\leftarrow\axis@@
 \axis@{#1}{#2}
 \axis@@\mathclose\rightarrow}}

\pdef\to{\def\afterparse@{
 \longrightarrow@{\ifsp@\sp@toks@\fi}{\ifsb@\sb@toks@\fi}\next}
 \sb@false\sp@false
 \def\next@comm{\afterassignment\parse@next\let\next=}
 \next@comm}

\pdef\ot{\def\afterparse@{
 \longleftarrow@{\ifsp@\sp@toks@\fi}{\ifsb@\sb@toks@\fi}\next}
 \sb@false\sp@false
 \def\next@comm{\afterassignment\parse@next\let\next=} 
 \next@comm}

\pdef\otto{\def\afterparse@{
 \longleftrightarrow@{\ifsp@\sp@toks@\fi}{\ifsb@\sb@toks@\fi}\next}
 \sb@false\sp@false
 \def\next@comm{\afterassignment\parse@next\let\next=} 
 \next@comm}

\pdef\mapsto{\mathrel{\mapstochar}\nobreak\mathclose{}\mathopen{}\to}
 % \nobreak inserted thanks to E.H. Lohse

\def\sp@toks@{\edef\@tempa{\noexpand\noexpand\noexpand\inline{\the\sp@toks}}
 \@tempa}

\def\sb@toks@{\edef\@tempa{\noexpand\noexpand\noexpand\inline{\the\sb@toks}}
 \@tempa}

\def\axis@#1#2{\setbox0\scriptstylehbox@{\protectinline@true #1}
 \er@wd=\wd0
 \setbox\@tempboxa\scriptstylehbox@{\protectinline@true #2}
 \ifdim\wd\@tempboxa>\er@wd \er@wd=\wd\@tempboxa\fi
 \@tempdima=\ht\@tempboxa
 \advance\@tempdima\dp\@tempboxa
 \advance\@tempdima-.42\mex
 \vtop{\offinterlineskip
 \hbox{\vbox{\hbox to\er@wd{\hss\box0\hss}%
 \vskip -.26\mex
 \hbox to\er@wd{\axis@@@\hfill}}}
 \vskip -.26\mex
 \hbox to\er@wd{\hss\box\@tempboxa\hss}}
 }

\def\axis@@{\mkern-4.5mu    %%% mkern setting adjusted 24 Sept. 2002
 \axis@@@\mskip 3mu plus \arrow@expandability mu   %%% thanks to E.H. Lohse
 \mkern-4.5mu}

\def\axis@@@{%
 \cleaders\hbox{\o@math\mkern-3mu \icurrstyle@\mathord- \mkern-3mu\o@math}}

\def\arrow@expandability{1.2}

%
%   R o o t s
%
\def\o@sqrt{\radical"270370 }

\pdef\sqrt#1{\inlineopen@\kern.4\mex\root@{}{#1}\inlineclose@} 
% \def changed to \pdef on 25 Sept. 2002 thanks to Michal Malek

\pdef\root#1#2{\inlineopen@\kern.5\mex\root@{#1}{#2}\inlineclose@}
% \def changed to \pdef on 25 Sept. 2002 thanks to Michal Malek

\def\root@#1#2{%
 \setbox0\currstyle@hbox{\toprestricted@true #2
  \vrule \@height 1.6\mex \@depth0pt \@width 0pt} % mathstrut's top
 \setbox\@tempboxa\hbox{\o@math\currstyle@
  \ifdisplay@ \@tempdima=.6\dp\sizebox@ % bottom is half of that of sizebox 
  \else \@tempdima=.2\mex % bottom is a bit below the baseline
  \fi
  \setbox\@tempboxa\hbox to\wd0{%
   \vrule \@height\ht0 \@depth\@tempdima \@width 0pt\hss}%
  \global\setbox\sizebox@\copy\@tempboxa
  \setbox\@tempboxa\hbox{\o@math\currstyle@\o@sqrt{\box\@tempboxa}\o@math}%
  \@tempdima=\ht\@tempboxa \advance\@tempdima-\dp\@tempboxa
  \advance\@tempdima 1.6\mex
  \raise.4\@tempdima\hbox{\advance\mathcount@2\imath@{#1}}%
  \kern-.3\mex
  \box\@tempboxa
  \o@math} % tempboxa := the radical sign with #1 and without #2
 \resizebox@{\sizebox@} % sizebox matches top of #2 and bottom at @tempdima
 \setbox0\hbox to\wd\@tempboxa{\hss\box0} % box0 = #1 shifted right
 \setbox0\vbox{\offinterlineskip
  \vskip-.1\mex
  \@tempdima=\ht\@tempboxa
  \dimen@=\dp\@tempboxa
  \advance\@tempdima \dimen@
  \advance\@tempdima -.55\mex
  \box\@tempboxa
  \vskip -\@tempdima
  \box0} % box0 = the result
 \box0\kern.3\mex\relax % space following the root
} 

%
%   U n d e r b r a c e   a n d   o v e r b r a c e
%

% Underbrace and overbrace are designed as escape commands, because they
% may extend accross unbalanced delimiters:

\def\@underbrace#1{\o@mathop{\vtop{%
 \ialign{##\crcr 
 \o@math\hfil\dcurrstyle@{#1}\hfil\o@math\crcr
 \noalign{\kern 3pt\nointerlineskip} \upbracefill \crcr 
 \noalign{\kern 3pt}}}}\limits}

\def\underbrace#1#2#3{\null\!
 \def\@tempa{#2}\def\@tempb{_}%
 \ifx\@tempa\@tempb
  \b@ubrace@#1\e@ubrace@{#3}\!
 \else\n@err{Missing _ after \string\underbrace}
  {Wrong syntax. I expected something like \underbrace{...}_{...}}
  #1
 \fi}

\def\b@ubrace@{%
 \ifdisplay@ \store@ec{\b@ubrace@@}{}
 \else \b@ubrace@@
 \fi}

\def\b@ubrace@@{\setbox0\hbox\bgroup}

\def\e@ubrace@#1{%
 \ifdisplay@ \store@ec{\e@ubrace@@{#1}}{}
 \else \e@ubrace@@{#1}
 \fi}

\def\e@ubrace@@#1{\egroup\@underbrace{\box0}_{#1}}

\def\@overbrace#1{\o@mathop{\vbox{%
 \ialign{##\crcr 
 \noalign{\kern 3pt\nointerlineskip}
 \downbracefill \crcr 
 \noalign{\kern 3pt}\crcr
 \o@math\hfil\dcurrstyle@{#1}\hfil\o@math\crcr}}}\limits}

\def\overbrace#1#2#3{\null\!
 \def\@tempa{#2}\def\@tempb{^}%
 \ifx\@tempa\@tempb
  \b@obrace@#1\e@obrace@{#3}\!
 \else\n@err{Missing ^ after \string\overbrace}
  {Wrong syntax. I expected something like \overbrace{...}^{...}}
  #1
 \fi}

\def\b@obrace@{%
 \ifdisplay@ \store@ec{\b@obrace@@}{}
 \else \b@obrace@@
 \fi}

\def\b@obrace@@{\setbox0\hbox\bgroup}

\def\e@obrace@#1{%
 \ifdisplay@ \store@ec{\e@obrace@@{#1}}{}
 \else \e@obrace@@{#1}
 \fi}

\def\e@obrace@@#1{\egroup\@overbrace{\box0}^{#1}}

%
%   F r a c t i o n s
%

% This is tricky.
% See Natural TeX notation in mathematics,
% in: Proc. Conf. EuroTeX 2001, Kerkrade, 23--27 September 2001;
% online at www.ntg.nl/eurotex/proceedings.html

\let\o@over=\over
\let\o@atop=\atop
\let\o@choose=\choose

\def\over{\n@err{Disabled command \string\over }
 {No more a valid command. Replace {A \over B} with \frac A B.}}
\def\atop{\n@err{Disabled command \string\atop }
 {No more a valid command. Use array instead.}}
\def\choose{\n@err{Disabled command \string\choose }
 {No more a valid command. Replace {A \choose B} with \binom A B.}}

% \frac is defined here

\pdef\frac#1#2{%
 \checknumeric@{#1#2} 
 \ifdisplay@
  \ifresult@ % numeric extensible
   \ext@frac{#1}{#2}
  \else \d@Frac{#1}{#2}
  \fi
 \else \inlinefrac@{#1}{#2}
 \fi
}

% displayed fraction with setsize.

\newdimen\htdecrement@ % global
\newdimen\dpdecrement@ % global

\def\d@Frac#1#2{\begingroup 
 \setbox\@tempboxa\hbox{\o@math\dcurrstyle@ 
  {\setbox0\currstyle@hbox{\vrule\@depth .7\mex\@width 0pt
    \botrestricted@false #1}%
   \@tempdima=\ht0 \advance\@tempdima-\ht\sizebox@ 
   \global\htdecrement@=\@tempdima
%  \@tempdima=\dp0 \advance\@tempdima .5ex \dp0=\@tempdima
   \box0
  \above\fracrulethickness@
   \setbox0\currstyle@hbox{\vrule\@height 2\mex\@width 0pt
    \toprestricted@false #2}%
   \@tempdimb=\dp0 \advance\@tempdimb-\dp\sizebox@
   \global\dpdecrement@=\@tempdimb
%  \@tempdimb=\ht0 \advance\@tempdimb .5ex \ht0=\@tempdimb
   \box0
   }%
  \o@math}%
 \setbox0\copy\@tempboxa  
 \iftoprestricted@ \else
   \@tempdimb=\ht0 \advance\@tempdimb .4\mex \ht0=\@tempdimb
 \fi
 \ifbotrestricted@ \else
   \@tempdimb=\dp0 \advance\@tempdimb .5\mex \dp0=\@tempdimb
 \fi 
 \box0  % print
 \@tempdima=\ht\@tempboxa \advance\@tempdima-\htdecrement@
 \ht\@tempboxa=\@tempdima  
 \@tempdima=\dp\@tempboxa \advance\@tempdima-\dpdecrement@
 \dp\@tempboxa=\@tempdima  
 \global\setbox\sizebox@\copy\@tempboxa 
 \endgroup 
 \resizebox@{\sizebox@}}

\newdimen\fracrulethickness@
\fracrulethickness@=.3pt

\def\shillingsign@{/}

\def\inlinefrac@#1#2{%
  \checkcompact@{#1}{\medmuskip=0mu\thickmuskip=0mu\thinmuskip=0mu}%
  \ifresult@ \wrapfrac@{#1} \else (\wrapfrac@{#1}) \fi
 \shillingsign@
  \checkcompact@{\mathord{}#2}{\medmuskip=0mu\thickmuskip=0mu}%
  \ifresult@ \wrapfrac@{#2} \else (\wrapfrac@{#2}) \fi
}

% Extensible fractions are middle delimiters:

\def\ext@frac#1#2{\mathinner{}\ddelim@m:{{#1}{#2}}\mathinner{}}

% Here is the command to size a numeric fraction: small if sizebox fits
% into some bounds. The bounds themselves are bigger than smallest size 
% parentheses.

\def\size@frac#1#2{%
 \ifdim\ht\sizebox>2.3\mex {\dcurrstyle@{#1\o@over#2}}
 \else
  \ifdim\dp\sizebox>1.4\mex {\dcurrstyle@{#1\o@over#2}}
  \else {\icurrstyle@{#1\o@over#2}}
  \fi
 \fi
}

% Here is a macro to recognize a numeric argument. The criterion is that after
% removal of all characters 0--9 the typeset box is of height no greater than 
% 1/2 ex.

\def\checknumeric@#1{\setbox0\hbox{\defaultdelims@
  \o@math\removenums@{#1}\o@math}
 \ifdim\ht0>.5ex\relax  
  \global\result@false
 \else\global\result@true 
 \fi}

\def\removenums@#1{\begingroup \def\frac##1##2{X}
 \uccode``=`|
 \uccode`0=`.\uccode`1=`.\uccode`2=`.\uccode`3=`.\uccode`4=`. 
 \uccode`5=`.\uccode`6=`.\uccode`7=`.\uccode`8=`.\uccode`9=`.\uppercase{#1}
\endgroup}

\def\checkcompact@#1#2{\setbox\@tempboxa\hbox{\o@math
  \def\frac##1##2{\mskip\medmuskip}
  \lowercase{\remove@ss\replacebindelims@{#1}{\mathord{}}}\o@math}
 \@tempdima=\wd\@tempboxa
 \setbox\@tempboxa\hbox{\o@math\def\frac##1##2{\mskip\medmuskip} #2
  \remove@compact{\remove@ss\replacebindelims@{#1}{\mathord{}}}\o@math}
 \advance\@tempdima-\wd\@tempboxa
 \ifdim\@tempdima>0pt \relax\result@false\else\result@true\fi}

\catcode`\^=13
\catcode`\_=13

\def\remove@ss{\def^##1{}\def_##1{}}

\catcode`\^=12  
\catcode`\_=12  


\def\remove@compact#1{\begingroup
 \def\shillingsign@{} \def\backslash{}
 \def\vert{}         \def\Vert{}
 \def\uparrow{}      \def\Uparrow{}
 \def\downarrow{}    \def\Downarrow{}
 \def\updownarrow{}  \def\Updownarrow{}
 \removeslashes@{#1}\endgroup}

\def\removeslashes@#1{\lccode`/=` \lccode`|=` \lowercase{#1}}

\newdimen\wrapfrac@dim
\newbox\wrapfrac@box

\def\wrapfrac@#1{%
 \begingroup
 \@wrapfrac\mathopen{}#1 \relax\mathclose{}\frac\relax\relax\frac
 \endgroup
}
% \relax after #1 added 4.4.2001 
% space after #1 added 7.5.2001

\def\@wrapfrac#1\frac#2#3#4\frac{%
 \def\frac@test{#2}\def\@relax{\relax}
 \ifx\frac@test\@relax #1 
  \def\next@frac{}
 \else 
  \@@wrapfrac{#1}{#2}{#3}{#4} 
  \def\next@frac{\next@frac@#4\frac} 
 \fi
 \next@frac}

\newif\ifwrap@

\def\@@wrapfrac#1#2#3#4{%
 \checknumeric@{#2#3} 
 \ifresult@ #1{#2\o@over#3} \def\next@frac@{\@wrapfrac}
 \else \def\next@frac@{\@wrapfrac\mathord{}}
  \wrap@false % to be true iff #4 starts with Ord, Op, Open, Inner
  \setbox\wrapfrac@box\hbox{\o@math\mathord{}#4\mathinner{}\o@math} 
  \wrapfrac@dim=\wd\wrapfrac@box            
  \setbox\wrapfrac@box\hbox{\o@math\mathrel{}#4\mathinner{}\o@math}  
  \advance\wrapfrac@dim-\wd\wrapfrac@box   
  \ifdim\wrapfrac@dim<0pt \wrap@true\fi
  \ifwrap@ % relax
  \else % now \wrap@false; to be true if #1 ends with Ord, Op, Close, Inner
   \setbox\wrapfrac@box\hbox{\o@math\mathinner{}#1\mathopen{}\o@math}       
   \wrapfrac@dim=\wd\wrapfrac@box             
   \setbox\wrapfrac@box\hbox{\o@math\mathinner{}#1\mathrel{}\o@math} 
   \advance\wrapfrac@dim-\wd\wrapfrac@box  
   \ifdim\wrapfrac@dim<0pt \wrap@true\fi
   \ifwrap@ % now #1 ends with Ord, Op, Close, Inner 
    % now \wrap@true; check whether #1 ends with +,-,\pm,\mp
    \setbox\wrapfrac@box\hbox{\o@math\testing@true \def\pm{=}\def\mp{=}
     \uccode`+=`=\uccode`-=`= \uppercase{#1}\mathclose{}\o@math}       
    \wrapfrac@dim=\wd\wrapfrac@box             
    \setbox\wrapfrac@box\hbox{\o@math\testing@true \def\pm{=}\def\mp{=}
     \uccode`+=`=\uccode`-=`= \uppercase{#1}\mathopen{}\o@math} 
    \advance\wrapfrac@dim-\wd\wrapfrac@box  
    \ifdim\wrapfrac@dim<0pt \wrapexception@{#2}
     \ifresult@\wrap@true \else\wrap@false \fi
    \fi
    \ifwrap@ % now Ord, Op, Close, Inner; test whether Inner
     \setbox\wrapfrac@box\hbox{\o@math\testing@true\mathinner{}#1\mathclose{}
       \o@math}       
     \wrapfrac@dim=\wd\wrapfrac@box             
     \setbox\wrapfrac@box\hbox{\o@math\testing@true\mathinner{}#1\mathpunct{}
       \o@math} 
     \advance\wrapfrac@dim-\wd\wrapfrac@box  
     \ifdim\wrapfrac@dim<0pt \result@true % #1 ends with Inner
     \else % now test whether #1 ends with a digit
      \checkwrapexception@{#1}
     \fi
     \ifresult@ % if wrapexception
      \wrapexception@{\uccode`.=`+ % make numbers into Bins
      \uccode`0=`+ \uccode`1=`+ \uccode`2=`+ \uccode`3=`+ \uccode`4=`+
      \uccode`5=`+ \uccode`6=`+ \uccode`7=`+ \uccode`8=`+ \uccode`9=`+
      \uppercase{#2}}
      \ifresult@\wrap@true \else\wrap@false \fi
     \else \wrap@true 
     \fi
    \fi
   \else % now #1 ends with Bin, Rel, Open, Punct
    \setbox\wrapfrac@box\hbox{\o@math\mathinner{}#1\mathclose{}\o@math}       
    \wrapfrac@dim=\wd\wrapfrac@box             
    \setbox\wrapfrac@box\hbox{\o@math\mathinner{}#1\mathrel{}\o@math} 
    \advance\wrapfrac@dim-\wd\wrapfrac@box  
    \ifdim\wrapfrac@dim<0pt % #1 ends with Bin*
     \wrapexception@{#2}
     \ifresult@\wrap@true \else\wrap@false \fi
    \else \wrap@false
    \fi
   \fi
  \fi
  \ifwrap@ 
   #1(\inlinefrac@{#2}{#3}) 
  \else 
   #1\mathopen{}\inlinefrac@{#2}{#3}\mathclose{} 
  \fi
 \fi}

% Called when #1 ends with Ord, Op, Close, Inner; checks whether
% it ends with a digit. 

\def\checkwrapexception@#1{% checks whether #1 ends with a digit
 \result@false
 \setbox\wrapfrac@box\hbox{\o@math\testing@true
 \uccode`0=`= \uccode`1=`= \uccode`2=`= \uccode`3=`= \uccode`4=`=
 \uccode`5=`= \uccode`6=`= \uccode`7=`= \uccode`8=`= \uccode`9=`=
 \uppercase{#1}\mathclose{}\o@math}       
 \wrapfrac@dim=\wd\wrapfrac@box             
 \setbox\wrapfrac@box\hbox{\o@math\testing@true
 \uccode`0=`= \uccode`1=`= \uccode`2=`= \uccode`3=`= \uccode`4=`=
 \uccode`5=`= \uccode`6=`= \uccode`7=`= \uccode`8=`= \uccode`9=`=
 \uppercase{#1}\mathopen{}\o@math} 
 \advance\wrapfrac@dim-\wd\wrapfrac@box  
 \ifdim\wrapfrac@dim<0pt \result@true \else \fi}
 
\def\wrapexception@#1{% checks whether #1 starts with Bin
 \result@false
 \setbox\wrapfrac@box\hbox{\o@math\mathord{}#1\mathclose{}\o@math}       
 \wrapfrac@dim=\wd\wrapfrac@box             
 \setbox\wrapfrac@box\hbox{\o@math\mathinner{}#1\mathclose{}\o@math} 
 \advance\wrapfrac@dim-\wd\wrapfrac@box  
 \ifdim\wrapfrac@dim=0pt \result@true \fi}

%
%   A r g u m e n t   p l a c e h o l d e r
%

\pdef\adot{\checkpunct@\mathclose{}
 \ifpunct@\else\mkern 1.8mu\fi
 {\cdot}\, \mathopen{}}

%
%   S p a c e s 
%

% Firstly, disable spacefactor -- this makes typesetting easier.
% (US TeXperts may wish to restore.)

\frenchspacing

% Secondly, we redefine `\ ' to produce breakable space in math mode.
% To be used after a punctuation, which itself adds a thinmuskip.

\def\space@{{} } 
\def\mspace@{\mskip 2.4mu plus 3.6mu minus 1.8mu} 

\def\ {\ifmmode\penalty0\mspace@\else\space@\fi}

% Quads are 1pc long:

\def\quad{\null\hskip1pc\relax}
\def\qquad{\null\hskip2pc\relax}
\def\qqquad{\null\hskip3pc\relax}

% Nath also introduces a new environment to set math material tight.

\def\tight{\def\mspaces@{\thinmuskip=2.4mu
 \medmuskip=1.2mu
 \thickmuskip=4.5mu
 \def\mspace@{\mskip 1.5mu}%
 \def\quad{\null\hskip .6pc\relax}%
 \def\qquad{\null\hskip 1.2pc\relax}%
 \def\qqquad{\null\hskip 1.8pc\relax}%
}}
 
\def\endtight{\global\@ignoretrue}

%
%   P u n c t u a t i o n
%

\newif\ifpunct@ % global

\def\punctpenalty{12756} % Earth's diameter in kilometers (> 10000)

\def\@comma{\mc@comma\penalty\punctpenalty\relax}
\def\@semicolon{\mc@semicolon\penalty\punctpenalty\relax}

\def\checkpunct@{\ifnum\lastpenalty=\punctpenalty\relax
 \global\punct@true \else \global\punct@false \fi}

\let\o@dots\dots

\pdef\dots{%
 \ifmmode
  \checkpunct@
  \ifpunct@ \ldots
   \global\punct@false
  \else \cdots
  \fi
 \else \o@dots
 \fi}

%
%   A r r a y
%

\let\o@array=\array
\let\o@endarray=\endarray

\newif\iflasthline@
\global\lasthline@false

\pdef\array{\hskip-\arraycolsep
 \def\@arstrut{}
 \let\hline\arr@hline
 \amp@count=0
 \setbox0\hbox\bgroup
 \ifdisplay@\else\advance\mathcount@ 1
  \n@warning{Array in in-line mode}
 \fi
 \o@math\o@array}

% \@arraycr is \\, but must insert a strut at the end of the line



\def\arraystrut{\vrule height 1.9\mex depth .75\mex width 0pt}

\def\@arraycr{\mathclose{} % no math space 
 \hbox{\arraystrut}%
 \arraycr@@}

\def\arraycr@@{\crcr  % nothing if following another \cr or \halign
 \def\@amp{\hbox{\vrule height\arrayrowsep width 0pt}} 
 \@tempcnta=\amp@count 
 \loop\ifnum\@tempcnta>1
  \edef\@amp{\@amp&} % line sep
  \advance\@tempcnta-1
 \repeat
 \@amp
 \cr}

\pdef\endarray{% may follow after \hline; corrected 18 March 2003
 \iflasthline@ \else \hbox{\arraystrut} \fi
 \o@endarray  % LaTeX's \endarray
 \o@math\egroup
 \@tempdima=\ht0 \advance\@tempdima -.15ex \ht0=\@tempdima
 \@tempdima=\dp0 \advance\@tempdima -.15ex \dp0=\@tempdima
 \resizebox@{0}\box0
 \hskip-\arraycolsep\relax}
\newcount\hline@num

\pdef\arr@hline{\noalign\bgroup   % begin noalign
 \hline@num=1 \result@false 
 \def\hline@@@{\afterassignment\hline@ \global\let\hline@@=}%
 \hline@@@}

\def\hline@{
 \ifx\hline@@\hline \result@false
  \advance\hline@num 1\relax
 \else \result@true 
  \ifx\hline@@\end \global\lasthline@true
  \else \global\lasthline@false
  \fi
 \fi
 \ifresult@ 
  \@tempcnta=\hline@num
  \loop\ifnum \@tempcnta > 0
   \hrule height \arrayrulewidth
   \vskip \doublerulesep
  \vskip -\arrayrulewidth
   \advance \@tempcnta -1
  \repeat
  \vskip -\doublerulesep
  \egroup    % end noalign
  \iflasthline@ % if the bottom line
  \else \arraycr@@
   \mathopen{\hbox{\arraystrut}} 
  \fi
  \def\hline@@@{\hline@@}
 \fi 
 \hline@@@}

\doublerulesep=\arrayrulewidth

% \@arrayclassz now uses display mode, and
% calls \@addamp if \@lastchclass = 4

\def\@arrayclassz{\ifcase\@lastchclass\@acolampacol
 \or\@ampacol \or \or \or\@addamp \or\@acolampacol \or\@firstampfalse\@acol 
 \fi
 \edef\@preamble{\@preamble
  \ifcase \@chnum
   \hfil\protect\dmathon@\@sharp\protect\dmathoff@\hfil
  \or \protect\dmathon@\@sharp\protect\dmathoff@\hfil
  \or \hfil\protect\dmathon@\@sharp\protect\dmathoff@
  \fi}
 }

% New \arraycolsep.

\let\arraycolsepdim=\arraycolsep

\def\arraycolsep{\prorated@\arraycolsepdim}

% New \arrayrowsepdim

\newdimen\arrayrowsepdim

\arrayrowsepdim=.4ex
\def\arrayrowsep{\prorated@\arrayrowsepdim}

% Counting &'s

\newcount\amp@count

\def\@addamp{%
 \if@firstamp \amp@count=1
  \@firstampfalse
 \else \advance\amp@count by 1
  \edef\@preamble{\@preamble &}%
 \fi}



% Cases is arrays

\def\cases{\displayon@\{\hskip.5ex \array{ll}}
\def\endcases{\endarray\right.\displayoff@}

%
%   M a t r i c e s
%

\pdef\matrix{\setbox0\hbox\bgroup\o@math
 \ifdisplay@\else \advance\mathcount@ 1
  \n@warning{Matrix in in-line mode}
 \fi
 \vcenter\bgroup %\vskip-.00005ex
 \let\\=\crcr \baselineskip=2.7\mex \lineskip=1.2\mex
 \ialign\bgroup
 &\hfil\hbox{\dmathon@##\dmathoff@}\hfil\hskip2\mex\crcr}

\pdef\endmatrix{\crcr\egroup %\vskip-.00005ex
 \egroup \o@math\hskip-2\mex\egroup \resizebox@{0}\box0}

%\def\suppressminus@{\afterassignment\suppressminus@@\let\next=}
%\def\@@@minus{-}
%\def\suppressminus@@{\if\next\@@@minus \llap{$-$}\let\next\relax\fi \next}

% Binom is a matrix:

\pdef\binom#1#2{%
 \ifdisplay@ (\matrix\inline{#1}\\\inline{#2}\endmatrix)
 \else \advance\mathcount@ 1
  \vcenter{\hbox{\o@math\biglp@\o@math}}
  \displayed{\matrix\inline{#1}\\\inline{#2}\endmatrix}
  \vcenter{\hbox{\o@math\bigrp@\o@math}}
 \fi}

\mathchardef\biglp@="0300
\mathchardef\bigrp@="0301

%
%   T a b l e   o f   c o n t e n t s
%

\let\o@addcontentsline\addcontentsline

\def\addcontentsline#1#2#3{%
 \begingroup
 \def\acl@{#3}% 
 \the\protect@toks \def\protect{\noexpand}%
 \edef\acl@{\acl@}% 
 \o@addcontentsline{#1}{#2}{\acl@}%
 \endgroup
}

%
%   A M S - L a T e X 
%

% Detecting AmSLaTeX

\ifx\primfrac\undefined
\else \typeout{} \typeout{AmSLaTeX detected.}
 \typeout{Do not expect too much from this combination.}
 \typeout{Consult Nath Guide if things go bad.}
 \gdef\resetMathstrut@{}
 \let\over=\@@over   % restore \over
 \let\above=\@@above % restore \above
\fi

%
%   I n i t i a l i z a t i o n
%

\catcode`\$=13

\geometryfalse
\silentfalse

\frenchspacing

%
%   T h e   l o g o
%

\def\Nath{$`Nath$}

%
%   E n d
%

\endinput