% 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