%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Module: ZzTeX Mathematics Facilities
%
% Synopsis: This file provides the mathematics facilities of
% ZzTeX. All of the Plain TeX math stuff is included.
%
% Author: Paul C. Anagnostopoulos
% Created: 14 November 1990
%
% Copyright 1989--2020 by Paul C. Anagnostopoulos
% under The MIT License (opensource.org/licenses/MIT)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math Version
% ---- -------
\definecount{\zmathver}{0}
\def \mathversion #1{%
\global\zmathver = #1\relax
\input zzmathv#1\relax}
% Alternate Math Fonts
% --------- ---- -----
\outer\def \ComputerModernmathfonts {%
\input zzcmmath\relax}
\outer\def \Lucidamathfonts #1{% {arrows?}
\setflag \zusemar = #1\relax
\input zzlucida\relax}
\outer\def \MathTimefonts {%
\input zzmtime\relax}
% Spacing
% -------
% Note major uses of each kind of space:
% thin: around large operators; after punctuation
% medium: around binary operators
% thick: around relational operators
\def \setmathspaces #1#2#3{% {thin}{medium}{thick}
\global\thinmuskip = #1\relax
\global\medmuskip = #2\relax
\global\thickmuskip = #3\relax}
\def \mthickspace {\mkern 2\thinmuskip}
\def \mthinspace {\mkern \thinmuskip}
\def \mnegthinspace {\mkern -\thinmuskip}
\def \mspace #1{\mkern #1\relax}% {mu}
% Math mode \, \; \! are in ZZHMODE.
\def \setTeXmathspaces {%
\setmathspaces{3mu}{4mu plus 2mu minus 4mu}{5mu plus 5mu}}
% Character Definition
% --------- ----------
% These are the math character classes:
\chardef \classord = 0 % An ordinary symbol (\alpha). %^math_class
\chardef \classlargeop = 1 % A large operator (\sum).. %^math_class
\chardef \classbinop = 2 % A binary operator (+). %^math_class
\chardef \classrel = 3 % A relation (=). %^math_class
\chardef \classopen = 4 % An opening fence ([). %^math_class
\chardef \classclose = 5 % A closing fence (]). %^math_class
\chardef \classpunc = 6 % A punctuation character (,). %^math_class
\chardef \classvarfam = 7 % A character that varies with \fam (\Gamma). %^math_class
\chardef \classactive = 8 % An active character ('). %^math_class
\def \definemathaccent #1#2#3#4{% {name}{class}{family}{hex-code}
{\zcalcmathcode{#2}{#3}{#4}%
\xdef #1{\mathaccent \the\tcounta\relax}}%
\ignorespaces}
\def \definemathchar #1#2#3#4{% {name}{class}{family}{hex-code}
{\zcalcmathcode{#2}{#3}{#4}%
\zdefmathch#1\zmark
\if \znext
\global\mathcode #1= \tcounta
\else
\global\mathchardef #1= \tcounta
\fi}%
\ignorespaces}
\def \definemathdelimiter #1#2#3#4#5#6{% {name}{class}{fam1}{hex1}{fam2}{hex2}
{\zcalcmathcode{#2}{#3}{#4}%
\multiply \tcounta by 16
\advance \tcounta by #5
\multiply \tcounta by 256
\advance \tcounta by "#6\relax
\zdefmathch#1\zmark
\if \znext
\global\delcode #1= \tcounta
\else
\xdef #1{\delimiter\the\tcounta\relax}%
\fi}%
\ignorespaces}
\def \definemathjoinedsymbol #1#2#3#4#5{% {name}{atom}{char1}{char2}{sep}
\gdef #1{#2{{#3}\mspace{#5mu}{#4}}}}
\def \definemathlabeledarrow #1#2#3#4{% {name}{atom}{label}{arrow}
\gdef #1{#2{\mathop{#4}\limits^{#3}}}}
\def \definemathstackedsymbol #1#2#3#4#5{% {name}{atom}{char1}{char2}{sep}
\gdef #1{#2{\mathpalette\zstksym{{#3}{#4}{#5}}}}}
\def \zcalcmathcode #1#2#3{% {class}{family}{hex-code}
\tcounta = #1
\multiply \tcounta by 16
\advance \tcounta by #2
\multiply \tcounta by 256
\advance \tcounta by "#3\relax}
\def \zdefmathch #1#2\zmark{%
\setflag\znext = {\if `\noexpand#1\true \else \false \fi}}
\definedimen{\muwidth}{0pt}
\def \zstksym #1#2{% {style}{{char1}{char2}{sep}}
\zstksymb #1#2}
\def \zstksymb #1#2#3#4{% {style}{char1}{char2}{sep}
\vcenter{\baselineskip = 0pt
\lineskiplimit = -\maxdimen
\setbox \zboxa = \hbox{$#1\mkern 1mu$}%
\muwidth = \wd\zboxa
\ialign{\hfil ##\hfil\cr
\raise #4\muwidth \hbox{$#1#2$}\cr
$#1#3$\cr}}}
% Character Styles
% --------- ------
\definecount{\zmstyfam}{0}
\def \setmathdigitstyle #1{% {style}
{\tcounta = "\the\classvarfam0
\advance \tcounta by \name{#1fam}%
\multiply \tcounta by 256
\advance \tcounta by `\0%
\tcountb = `0
\loop
\global\mathcode \tcountb = \tcounta
\increment \tcounta
\increment \tcountb
\if \lssp{\tcountb}{`\:}\repeat}}
\def \setmathletterstyle #1{% {\style}
{\tcounta = "\the\classvarfam0
\advance \tcounta by \name{#1fam}%
\multiply \tcounta by 256
\advance \tcounta by `\A%
\tcountb = `A
\loop
\global\mathcode \tcountb = \tcounta
\increment \tcounta
\increment \tcountb
\if \lssp{\tcountb}{`\[}\repeat
\advance \tcounta by 6
\tcountb = `\a
\loop
\global\mathcode \tcountb = \tcounta
\increment \tcounta
\increment \tcountb
\if \lssp{\tcountb}{`\{}\repeat}%
\if \zcommonencoding
\def \znext {#1}%
\def \zit {\it}%
\if \tokeqlp{\znext}{\zit}\setstyleskewchar{#1}{7}\fi
\fi}
\def \setmathucgreekstyle #1{% {style}
{\zmstyfam = \name{#1fam}%
\definemathchar \Alpha \classvarfam \rmfam {41}
\definemathchar \Beta \classvarfam \rmfam {42}
\definemathchar \Gamma \classvarfam \zmstyfam {00}
\definemathchar \Delta \classvarfam \zmstyfam {01}
\definemathchar \Epsilon \classvarfam \rmfam {45}
\definemathchar \Zeta \classvarfam \rmfam {5A}
\definemathchar \Eta \classvarfam \rmfam {48}
\definemathchar \Theta \classvarfam \zmstyfam {02}
\definemathchar \Iota \classvarfam \rmfam {49}
\definemathchar \Kappa \classvarfam \rmfam {4B}
\definemathchar \Lambda \classvarfam \zmstyfam {03}
\definemathchar \Mu \classvarfam \rmfam {4D}
\definemathchar \Nu \classvarfam \rmfam {4E}
\definemathchar \Xi \classvarfam \zmstyfam {04}
\definemathchar \Omicron \classvarfam \rmfam {4F}
\definemathchar \Pi \classvarfam \zmstyfam {05}
\definemathchar \Rho \classvarfam \rmfam {50}
\definemathchar \Sigma \classvarfam \zmstyfam {06}
\definemathchar \Tau \classvarfam \rmfam {54}
\definemathchar \Upsilon \classvarfam \zmstyfam {07}
\definemathchar \Phi \classvarfam \zmstyfam {08}
\definemathchar \Chi \classvarfam \rmfam {58}
\definemathchar \Psi \classvarfam \zmstyfam {09}
\definemathchar \Omega \classvarfam \zmstyfam {0A}}}
\def \zmtextstyle {\rm}
\def \zmtextfam {\rmfam}
\def \setmathtextstyle #1{% {style}
\gdef \zmtextstyle {#1}%
\xdef \zmtextfam {\name{#1fam}}}
\def \zmfunstyle {\rm}
\def \setmathfunctionstyle #1{% {style}
\gdef \zmfunstyle {#1}}
\def \zmvarstyle {\it}
\def \setmathmvarstyle #1{% {style}
\gdef \zmvarstyle {#1}}
\def \setmathpunctuationstyle #1{% {style}
{\zmstyfam = \name{#1fam}%
\definemathchar {`.} \classord \zmstyfam {2E}
\definemathchar {`,} \classpunc \zmstyfam {2C}
\definemathchar {`;} \classpunc \zmstyfam {3B}}}
% Characters
% ----------
\let \zmchar = \definemathchar
% Letters:
% INITEX does the following for each letter:
%
% \definemathchar{letter}{\classvarfam}{\mit}{xx}
%
% This can be changed using the \setmathletterstyle command above.
% Figures (digits):
% INITEX does the following for each digit:
%
% \definemathchar{digit}{\classvarfam}{\rm}{xx}
%
% This can be changed using the \setmathdigitstyle command above.
% Uppercase Greek letters:
% This can be changed using the \setmathucgreekstyle command above.
\setmathucgreekstyle{\rm}
% Lowercase Greek letters:
\zmchar \alpha \classord \mitfam {0B}
\zmchar \beta \classord \mitfam {0C}
\zmchar \gamma \classord \mitfam {0D}
\zmchar \delta \classord \mitfam {0E}
\zmchar \epsilon \classord \mitfam {0F}
\zmchar \zeta \classord \mitfam {10}
\zmchar \eta \classord \mitfam {11}
\zmchar \theta \classord \mitfam {12}
\zmchar \iota \classord \mitfam {13}
\zmchar \kappa \classord \mitfam {14}
\zmchar \lambda \classord \mitfam {15}
\zmchar \mu \classord \mitfam {16}
\zmchar \nu \classord \mitfam {17}
\zmchar \xi \classord \mitfam {18}
\zmchar \omicron \classord \mitfam {6F}
\zmchar \pi \classord \mitfam {19}
\zmchar \rho \classord \mitfam {1A}
\zmchar \sigma \classord \mitfam {1B}
\zmchar \tau \classord \mitfam {1C}
\zmchar \upsilon \classord \mitfam {1D}
\zmchar \phi \classord \mitfam {1E}
\zmchar \chi \classord \mitfam {1F}
\zmchar \psi \classord \mitfam {20}
\zmchar \omega \classord \mitfam {21}
\zmchar \varepsilon \classord \mitfam {22}
\zmchar \vartheta \classord \mitfam {23}
\zmchar \varpi \classord \mitfam {24}
\zmchar \varrho \classord \mitfam {25}
\zmchar \varsigma \classord \mitfam {26}
\zmchar \varphi \classord \mitfam {27}
% Ordinary symbols:
\zmchar {`.} \classord \rmfam {2E}
\zmchar {`/} \classord \mitfam {3D}
\zmchar \zmbackslash \classord \msyfam {6E}
\zmchar {`|} \classord \msyfam {6A}
\zmchar \aleph \classord \msyfam {40}
\zmchar \bot \classord \msyfam {3F}
\zmchar \clubsuit \classord \msyfam {7C}
\zmchar \diamondsuit \classord \msyfam {7D}
\zmchar \ell \classord \mitfam {60}
\zmchar \emptyset \classord \msyfam {3B}
\zmchar \exists \classord \msyfam {39}
\zmchar \flat \classord \mitfam {5B}
\zmchar \forall \classord \msyfam {38}
\zmchar \heartsuit \classord \msyfam {7E}
\zmchar \Im \classord \msyfam {3D}
\zmchar \imath \classord \mitfam {7B}
\zmchar \infinity \classord \msyfam {31}
\let \infty = \infinity
\zmchar \jmath \classord \mitfam {7C}
\zmchar \nabla \classord \msyfam {72}
\zmchar \natural \classord \mitfam {5C}
\zmchar \neg \classord \msyfam {3A}
\let \lnot = \neg
\zmchar \partial \classord \mitfam {40}
\zmchar \prime \classord \msyfam {30}
\zmchar \Re \classord \msyfam {3C}
\zmchar \sharp \classord \mitfam {5D}
\zmchar \spadesuit \classord \msyfam {7F}
\zmchar \surd \classord \msyfam {70}
\zmchar \top \classord \msyfam {3E}
\zmchar \triangle \classord \msyfam {34}
\zmchar \wp \classord \mitfam {7D}
% Large operations:
\zmchar \bigcap \classlargeop \mexfam {54}
\zmchar \bigcup \classlargeop \mexfam {53}
\zmchar \bigodot \classlargeop \mexfam {4A}
\zmchar \bigoplus \classlargeop \mexfam {4C}
\zmchar \bigotimes \classlargeop \mexfam {4E}
\zmchar \bigsqcup \classlargeop \mexfam {46}
\zmchar \biguplus \classlargeop \mexfam {55}
\zmchar \bigvee \classlargeop \mexfam {57}
\zmchar \bigwedge \classlargeop \mexfam {56}
\zmchar \coprod \classlargeop \mexfam {60}
\zmchar \intop \classlargeop \mexfam {52}
\zmchar \ointop \classlargeop \mexfam {48}
\zmchar \prod \classlargeop \mexfam {51}
\zmchar \smallint \classlargeop \msyfam {73}
\zmchar \sum \classlargeop \mexfam {50}
% Binary operations:
\zmchar {`*} \classbinop \msyfam {03}
\zmchar {`+} \classbinop \rmfam {2B}
\zmchar {`-} \classbinop \msyfam {00}
\zmchar \amalg \classbinop \msyfam {71}
\zmchar \ast \classbinop \msyfam {03}
\zmchar \bigcirc \classbinop \msyfam {0D}
\zmchar \bigtriangledown \classbinop \msyfam {35}
\zmchar \bigtriangleup \classbinop \msyfam {34}
\zmchar \zmbullet \classbinop \msyfam {0F}
\zmchar \cap \classbinop \msyfam {5C}
\zmchar \cdot \classbinop \msyfam {01}
\zmchar \circ \classbinop \msyfam {0E}
\let \compose = \circ
\zmchar \cup \classbinop \msyfam {5B}
\zmchar \zmdagger \classbinop \msyfam {79}
\zmchar \zmddagger \classbinop \msyfam {7A}
\zmchar \diamond \classbinop \msyfam {05}
\zmchar \div \classbinop \msyfam {04}
\zmchar \mp \classbinop \msyfam {07}
\zmchar \odot \classbinop \msyfam {0C}
\zmchar \ominus \classbinop \msyfam {09}
\zmchar \oplus \classbinop \msyfam {08}
\zmchar \oslash \classbinop \msyfam {0B}
\zmchar \otimes \classbinop \msyfam {0A}
\zmchar \pm \classbinop \msyfam {06}
\zmchar \setminus \classbinop \msyfam {6E}
\zmchar \sqcap \classbinop \msyfam {75}
\zmchar \sqcup \classbinop \msyfam {74}
\zmchar \star \classbinop \mitfam {3F}
\zmchar \times \classbinop \msyfam {02}
\let \cross = \times
\zmchar \triangleleft \classbinop \mitfam {2F}
\zmchar \triangleright \classbinop \mitfam {2E}
\zmchar \uplus \classbinop \msyfam {5D}
\zmchar \vee \classbinop \msyfam {5F}
\let \lor = \vee
\zmchar \wedge \classbinop \msyfam {5E}
\let \land = \wedge
\zmchar \wr \classbinop \msyfam {6F}
% Relations:
\zmchar {`:} \classrel \rmfam {3A}
\zmchar {`<} \classrel \mitfam {3C}
\zmchar {`=} \classrel \rmfam {3D}
\zmchar {`>} \classrel \mitfam {3E}
\zmchar \approx \classrel \msyfam {19}
\zmchar \asymp \classrel \msyfam {10}
\zmchar \dashv \classrel \msyfam {61}
\zmchar \equiv \classrel \msyfam {11}
\zmchar \frown \classrel \mitfam {5F}
\zmchar \geq \classrel \msyfam {15}
\let \ge = \geq
\let \gets = \leftarrow
\zmchar \gg \classrel \msyfam {1D}
\zmchar \in \classrel \msyfam {32}
\zmchar \Leftarrow \classrel \msyfam {28}
\zmchar \leftarrow \classrel \msyfam {20}
\zmchar \leftharpoondown \classrel \mitfam {29}
\zmchar \leftharpoonup \classrel \mitfam {28}
\zmchar \Leftrightarrow \classrel \msyfam {2C}
\zmchar \leftrightarrow \classrel \msyfam {24}
\zmchar \leq \classrel \msyfam {14}
\let \le = \leq
\zmchar \lhook \classrel \mitfam {2C}
\zmchar \ll \classrel \msyfam {1C}
\zmchar \mapstochar \classrel \msyfam {37}
\zmchar \mid \classrel \msyfam {6A}
\let \given = \mid
\zmchar \nearrow \classrel \msyfam {25}
\zmchar \ni \classrel \msyfam {33}
\zmchar \not \classrel \msyfam {36}
\zmchar \nwarrow \classrel \msyfam {2D}
\let \owns = \ni
\zmchar \parallel \classrel \msyfam {6B}
\zmchar \perp \classrel \msyfam {3F}
\zmchar \prec \classrel \msyfam {1E}
\zmchar \preceq \classrel \msyfam {16}
\zmchar \propto \classrel \msyfam {2F}
\zmchar \rhook \classrel \mitfam {2D}
\zmchar \Rightarrow \classrel \msyfam {29}
\zmchar \rightarrow \classrel \msyfam {21}
\zmchar \rightharpoondown \classrel \mitfam {2B}
\zmchar \rightharpoonup \classrel \mitfam {2A}
\zmchar \searrow \classrel \msyfam {26}
\zmchar \sim \classrel \msyfam {18}
\zmchar \simeq \classrel \msyfam {27}
\zmchar \smile \classrel \mitfam {5E}
\zmchar \subset \classrel \msyfam {1A}
\zmchar \subseteq \classrel \msyfam {12}
\zmchar \succ \classrel \msyfam {1F}
\zmchar \succeq \classrel \msyfam {17}
\zmchar \supset \classrel \msyfam {1B}
\zmchar \supseteq \classrel \msyfam {13}
\zmchar \swarrow \classrel \msyfam {2E}
\zmchar \sqsubseteq \classrel \msyfam {76}
\zmchar \sqsupseteq \classrel \msyfam {77}
\let \to = \rightarrow
\zmchar \vdash \classrel \msyfam {60}
% Openers:
\zmchar {`(} \classopen \rmfam {28}
\zmchar {`[} \classopen \rmfam {5B}
\zmchar {`\{} \classopen \msyfam {66}
% Closers:
\zmchar {`!} \classclose \rmfam {21}
\zmchar {`)} \classclose \rmfam {29}
\zmchar {`?} \classclose \rmfam {3F}
\zmchar {`]} \classclose \rmfam {5D}
\zmchar {`\}} \classclose \msyfam {67}
% Punctuation:
\zmchar {`,} \classpunc \rmfam {2C}
\zmchar {`;} \classpunc \rmfam {3B}
\zmchar \cdotp \classpunc \msyfam {01}
\zmchar \maps \classpunc \rmfam {3A}
\let \colon = \maps
\zmchar \ldotp \classpunc \mitfam {3A}
% Active characters:
\zmchar {` } \classactive \rmfam {00}
\zmchar {`'} \classactive \rmfam {00}
{\catcode`\' = \catactive
\gdef '{^\bgroup \zmprima}
} % \catcode
\def \zmprima {\prime \futurelet\znext \zmprimb}
\def \zmprimb {%
\if \tokeqlp{\znext}{'}%
\let \znext = \zmprimc
\else \if \tokeqlp{\znext}{^}%
\let \znext = \zmprimd
\else
\let \znext = \egroup
\fi\fi
\znext}
\def \zmprimc #1{\zmprima}
\def \zmprimd #1#2{#2\egroup}
% Delimiters
% ----------
% IniTeX does the following for each character:
%
% \delcode`x = -1
\definemathdelimiter{`(}{\classord}{\rmfam}{28}{\mexfam}{00}
\definemathdelimiter{`)}{\classord}{\rmfam}{29}{\mexfam}{01}
\definemathdelimiter{`/}{\classord}{\rmfam}{2F}{\mexfam}{0E}
\definemathdelimiter{`<}{\classord}{\msyfam}{68}{\mexfam}{0A}
\definemathdelimiter{`>}{\classord}{\msyfam}{69}{\mexfam}{0B}
\definemathdelimiter{`[}{\classord}{\rmfam}{5B}{\mexfam}{02}
\definemathdelimiter{`]}{\classord}{\rmfam}{5D}{\mexfam}{03}
\definemathdelimiter{`|}{\classord}{\msyfam}{6A}{\mexfam}{0C}
\definemathdelimiter{\Arrowvert}{\classord}{\mexfam}{3D}{\rmfam}{00}
\definemathdelimiter{\arrowvert}{\classord}{\mexfam}{3C}{\rmfam}{00}
\definemathdelimiter{\bracevert}{\classord}{\mexfam}{3E}{\rmfam}{00}
\definemathdelimiter{\Downarrow}{\classrel}{\msyfam}{2B}{\mexfam}{7F}
\definemathdelimiter{\downarrow}{\classrel}{\msyfam}{23}{\mexfam}{79}
\definemathdelimiter{\langle}{\classopen}{\msyfam}{68}{\mexfam}{0A}
\definemathdelimiter{\lceil}{\classopen}{\msyfam}{64}{\mexfam}{06}
\definemathdelimiter{\lfloor}{\classopen}{\msyfam}{62}{\mexfam}{04}
\definemathdelimiter{\lgroup}{\classopen}{\rmfam}{00}{\mexfam}{3A}
\definemathdelimiter{\lmoustache}{\classopen}{\rmfam}{00}{\mexfam}{40}
\definemathdelimiter{\rangle}{\classclose}{\msyfam}{69}{\mexfam}{0B}
\definemathdelimiter{\rceil}{\classclose}{\msyfam}{65}{\mexfam}{07}
\definemathdelimiter{\rfloor}{\classclose}{\msyfam}{63}{\mexfam}{05}
\definemathdelimiter{\rgroup}{\classclose}{\rmfam}{00}{\mexfam}{3B}
\definemathdelimiter{\rmoustache}{\classclose}{\rmfam}{00}{\mexfam}{41}
\definemathdelimiter{\Uparrow}{\classrel}{\msyfam}{2A}{\mexfam}{7E}
\definemathdelimiter{\uparrow}{\classrel}{\msyfam}{22}{\mexfam}{78}
\definemathdelimiter{\Updownarrow}{\classrel}{\msyfam}{6D}{\mexfam}{77}
\definemathdelimiter{\updownarrow}{\classrel}{\msyfam}{6C}{\mexfam}{3F}
\definemathdelimiter{\Vert}{\classord}{\msyfam}{6B}{\mexfam}{0D}
\definemathdelimiter{\vert}{\classord}{\msyfam}{6A}{\mexfam}{0C}
\definemathdelimiter{\zmbackslash}{\classord}{\msyfam}{6E}{\mexfam}{0F}
\definemathdelimiter{\zmlbrace}{\classopen}{\msyfam}{66}{\mexfam}{08}
\definemathdelimiter{\zmrbrace}{\classclose}{\msyfam}{67}{\mexfam}{09}
% Accents
% -------
\definemathaccent{\acute}{\classvarfam}{\rmfam}{13}
\definemathaccent{\bar}{\classvarfam}{\rmfam}{16}
\definemathaccent{\breve}{\classvarfam}{\rmfam}{15}
\definemathaccent{\check}{\classvarfam}{\rmfam}{14}
\definemathaccent{\ddot}{\classvarfam}{\rmfam}{7F}
\definemathaccent{\dot}{\classvarfam}{\rmfam}{5F}
\definemathaccent{\grave}{\classvarfam}{\rmfam}{12}
\definemathaccent{\zmhat}{\classvarfam}{\rmfam}{5E}
\definemathaccent{\zmtilde}{\classvarfam}{\rmfam}{7E}
\definemathaccent{\ring}{\classvarfam}{\rmfam}{17}
\definemathaccent{\widetilde}{\classord}{\mexfam}{65}
\definemathaccent{\widehat}{\classord}{\mexfam}{62}
\definemathaccent{\vec}{\classord}{\mitfam}{7E}
\def \widebar #1{% {math} %~ Wide bar accent. %^math_accent
\mathpalette\zwidebar{#1}}
\def \zwidebar #1#2{% {style}{math}
\rlap{\measuretextwidth{\tdimena}{$#1#2$}%
\kern .2\tdimena
$\overline{\vphantom{#1#2}\kern .6\tdimena}$}%
#2}
% Defined Characters
% ------- ----------
\def \angle {%
{\vbox{\ialign{$\scriptstyle##$\cr
\not \mathrel{\mkern 14mu}\cr
\noalign{\nointerlineskip}%
\mkern 2.5mu \leaders \hrule height .34pt \hfill
\mkern 2.5mu\cr}}}}
\definemathjoinedsymbol{\bowtie}{\mathrel}{\triangleright}{\triangleleft}{-3}
\definemathstackedsymbol{\cong}{\mathrel}{\sim}{=}{6}
\def \degree {^\circ}
\let \degrees = \degree
\def \defeq{%
\mathrel{\mathop{=}\limits^{\mathscriptscriptstyle{\roman{def}}}}}
\definemathstackedsymbol{\Deltaeq}{\mathrel}{\mathscriptscriptstyle{\Delta}}{=}{9}
\definemathstackedsymbol{\doteq}{\mathrel}{.}{=}{9}
\definemathstackedsymbol{\gel}{\mathrel}{\zge}{<}{11}
\definemathstackedsymbol{\zge}{\mathrel}{>}{=}{7.5}
\definemathstackedsymbol{\gl}{\mathrel}{>}{<}{5.5}
\def \hbar {\mathord{h \llap{$\mathchar"16 \mkern 3.5mu$}}}
\definemathjoinedsymbol{\hookleftarrow}{\mathrel}{\leftarrow}{\rhook}{-3}
\definemathjoinedsymbol{\hookrightarrow}{\mathrel}{\lhook}{\rightarrow}{-3}
\def \int {\intop\nolimits}
\def \iint {\zint2}
\def \iiint {\zint3}
\def \iiiint {\zint4}
\def \idotsint {\zint0}
\def \zint #1{%
\mkern -9mu \mathchoice{\mkern -5mu}{}{}{}%
\mathop{%
\mkern 9mu \mathchoice{\mkern 5mu}{}{}{}%
\intop
\ifcase #1%
\mkern -4mu \cdots \mkern -4mu
\or \relax \or
\zintkern
\or
\zintkern \intop \zintkern
\or
\zintkern \intop \zintkern \intop \zintkern
\fi}%
\intop\nolimits}
\def \zintkern {\mkern -8mu \mathchoice{\mkern -3mu}{}{}{}}
\let \join = \bowtie
\definemathstackedsymbol{\leftrightarrows}{\mathrel}{\leftarrow}{\rightarrow}{6}
\definemathstackedsymbol{\leftrightharpoons}{\mathrel}{\leftharpoonup}{\rightharpoondown}{4}
\definemathstackedsymbol{\ltgt}{\mathrel}{<}{>}{5.5}
\definemathjoinedsymbol{\Longleftarrow}{\mathrel}{\Leftarrow}{\Relbar}{-3}
\definemathjoinedsymbol{\longleftarrow}{\mathrel}{\leftarrow}{\relbar}{-3}
\definemathjoinedsymbol{\Longleftrightarrow}{\mathrel}{\Leftarrow}{\Rightarrow}{-3}
\let \iff = \Longleftrightarrow
\definemathjoinedsymbol{\longleftrightarrow}{\mathrel}{\leftarrow}{\rightarrow}{-3}
\def \longmapsto {\mapstochar \longrightarrow}
\definemathjoinedsymbol{\Longrightarrow}{\mathrel}{\Relbar}{\Rightarrow}{-3}
\definemathjoinedsymbol{\longrightarrow}{\mathrel}{\relbar}{\rightarrow}{-3}
\definemathjoinedsymbol{\longrightleftarrow}{\mathrel}{\rightarrow}{\leftarrow}{-3}
\def \oint {\ointop\nolimits}
\def \mapsto {\mapstochar \rightarrow}
\definemathjoinedsymbol{\models}{\mathrel}{|}{=}{-3}
\def \neq {\not=}
\let \ne = \neq
\def \nexists {\mathord{\raise .2ex \hbox{$\not\mkern 1.5mu$}\exists}}
\def \notin {\not\in}
\let \nin = \notin
\def \nparallel {\mathrel{\not\mkern 2mu\parallel}}
\definemathstackedsymbol{\rightleftarrows}{\mathrel}{\rightarrow}{\leftarrow}{6}
\definemathstackedsymbol{\rightleftharpoons}{\mathrel}{\rightharpoonup}{\leftharpoondown}{4}
\definemathjoinedsymbol{\semijoin}{\mathrel}{\triangleright}{<}{-4}
% Functions
% ---------
\def \definemathfunction #1#2#3{% {\name}{text}{limits}
\def #1{\mathop{\zmfunstyle #2}#3}}
\definemathfunction{\ad}{ad}{\nolimits} % adjoint
\definemathfunction{\Ai}{Ai}{\nolimits} % Airy function
\definemathfunction{\arccos}{arccos}{\nolimits} % arc cosine
\definemathfunction{\arccosh}{arccosh}{\nolimits} % hyperbolic arc cosine
\definemathfunction{\arccot}{arccot}{\nolimits} % arc cotangent
\definemathfunction{\arcsec}{arcsec}{\nolimits} % arc secant
\definemathfunction{\arcsin}{arcsin}{\nolimits} % arc sine
\definemathfunction{\arctan}{arctan}{\nolimits} % arc tangent
\definemathfunction{\arg}{arg}{\nolimits} % argument
\definemathfunction{\argmax}{arg\,max}{\displaylimits} % argument maximum
\definemathfunction{\argmin}{arg\,min}{\displaylimits} % argument maximum
\definemathfunction{\Bd}{Bd}{\nolimits} % Bound
\definemathfunction{\cl}{cl}{\nolimits} % closure
\definemathfunction{\codim}{codim}{\nolimits} % co-dimension
\definemathfunction{\coker}{coker}{\nolimits} % cokernel
\definemathfunction{\conj}{conj}{\nolimits} % conjugate
\definemathfunction{\cos}{cos}{\nolimits} % cosine
\definemathfunction{\cosec}{cos}{\nolimits} % cosecant
\definemathfunction{\cosh}{cosh}{\nolimits} % hyperbolic cosine
\definemathfunction{\cot}{cot}{\nolimits} % cotangent
\definemathfunction{\coth}{coth}{\nolimits} % hyperbolic cotangent
\definemathfunction{\csc}{csc}{\nolimits} % cosecant
\definemathfunction{\csch}{csch}{\nolimits} % hyperbolic cosecant
\definemathfunction{\curl}{curl}{\nolimits} % curl
\definemathfunction{\deg}{deg}{\nolimits} % degree
\definemathfunction{\det}{det}{\displaylimits} % determinant
\definemathfunction{\diag}{diag}{\nolimits} % diagonal
\definemathfunction{\dim}{dim}{\nolimits} % dimension
\definemathfunction{\dist}{dist}{\nolimits} % distance
\definemathfunction{\erf}{erf}{\nolimits} % error function
\definemathfunction{\erfc}{erfc}{\nolimits} % error function comp.
\definemathfunction{\exp}{exp}{\nolimits} % exponential
\definemathfunction{\gcd}{gcd}{\displaylimits} % greatest common div.
\definemathfunction{\GL}{GL}{\nolimits} % General Linear
\definemathfunction{\glb}{glb}{\nolimits} % greatest lower bound
\definemathfunction{\gr}{gr}{\nolimits} % group
\definemathfunction{\grad}{grad}{\nolimits} % gradient
\definemathfunction{\hom}{hom}{\nolimits} % homology
\definemathfunction{\id}{id}{\nolimits} % identity
\definemathfunction{\inf}{inf}{\displaylimits} % infinum
\definemathfunction{\injlim}{inj\,lim}{\displaylimits} % injected limit
\definemathfunction{\ker}{ker}{\nolimits} % kernel
\definemathfunction{\lcm}{lcm}{\displaylimits} % least common mult.
\definemathfunction{\length}{length}{\nolimits} % length
\definemathfunction{\lg}{lg}{\nolimits} % natural logarithm
\definemathfunction{\lim}{lim}{\displaylimits} % limit
\definemathfunction{\liminf}{lim\,inf}{\displaylimits} % limit infinum
\definemathfunction{\limsup}{lim\,sup}{\displaylimits} % limit supremum
\definemathfunction{\ln}{ln}{\nolimits} % natural logarithm
\definemathfunction{\Log}{Log}{\nolimits} % principal logarithm
\definemathfunction{\log}{log}{\nolimits} % logarithm
\definemathfunction{\lub}{lub}{\nolimits} % least upper bound
\definemathfunction{\max}{max}{\displaylimits} % maximum
\definemathfunction{\min}{min}{\displaylimits} % minimum
\definemathfunction{\mod}{mod}{\nolimits} % modulus
\definemathfunction{\Pr}{Pr}{\displaylimits} % Probability
\definemathfunction{\Prob}{Prob}{\displaylimits} % Probability
\definemathfunction{\projlim}{proj\,lim}{\displaylimits}% projected limit
\definemathfunction{\rank}{rank}{\nolimits} % rank
\definemathfunction{\sec}{sec}{\nolimits} % secant
\definemathfunction{\sech}{sech}{\nolimits} % hyperbolic secant
\definemathfunction{\sgn}{sgn}{\nolimits} % sign
\definemathfunction{\sign}{sign}{\nolimits} % sign
\definemathfunction{\sin}{sin}{\nolimits} % sine
\definemathfunction{\sinc}{sinc}{\nolimits} % cardinal sine
\definemathfunction{\sinh}{sinh}{\nolimits} % hyperbolic sine
\definemathfunction{\SL}{SL}{\nolimits} % Special Linear
\definemathfunction{\sup}{sup}{\displaylimits} % supremum
\definemathfunction{\Szg}{Sz(g)}{\nolimits} % Suzuki group
\definemathfunction{\tan}{tan}{\nolimits} % tangent
\definemathfunction{\tanh}{tanh}{\nolimits} % hyperbolic tangent
\definemathfunction{\tr}{tr}{\nolimits} % trace
\definemathfunction{\trace}{trace}{\nolimits} % trace
\definemathfunction{\wstar}{w*}{\nolimits} % weak star
% For the occasional one-timer:
\def \mathfunction #1{\mathop{\rm #1}\nolimits}
\let \mfun = \mathfunction
% Display/Text/Script Styles
% ------------------- ------
\def \mathdisplaystyle #1{{\displaystyle #1}}% {subequation}
\def \mathtextstyle #1{{\textstyle #1}}
\def \mathscriptstyle #1{{\scriptstyle #1}}
\def \mathscriptscriptstyle #1{{\scriptscriptstyle #1}}
\def \mathpalette #1#2{% {\macro}{text}
\mathchoice{#1\displaystyle{#2}}%
{#1\textstyle{#2}}%
{#1\scriptstyle{#2}}%
{#1\scriptscriptstyle{#2}}}
\def \mtext #1{%
{\mathchoice{\hbox{\zmtextstyle #1}}
{\hbox{\zmtextstyle #1}}
{\hbox{\the\scriptfont\zmtextfam #1}}
{\hbox{\the\scriptscriptfont\zmtextfam #1}}}}
\everymath = {\let\text=\mtext}%
% This is specifically designed to work in math or in text.
\def \mvar #1{{\zmvarstyle #1\if \textmodep \/\fi}}% {text}
% General Tools
% ------- -----
\def \aboverule #1{\above #1\relax}% {rule-height}
\def \abs #1{\left|#1\right|}% {expression}
\def \big #1{{\hbox{$\left#1\vbox to 8.5pt{}\right.\zmnosp$}}}
\def \Big #1{{\hbox{$\left#1\vbox to 11.5pt{}\right.\zmnosp$}}}
\def \bigg #1{{\hbox{$\left#1\vbox to 14.5pt{}\right.\zmnosp$}}}
\def \Bigg #1{{\hbox{$\left#1\vbox to 17.5pt{}\right.\zmnosp$}}}
\def \zmnosp {\nulldelimiterspace = 0pt}
\def \bigl {\mathopen\big}
\def \Bigl {\mathopen\Big}
\def \bigm {\mathrel\big}
\def \Bigm {\mathrel\Big}
\def \bigr {\mathclose\big}
\def \Bigr {\mathclose\Big}
\def \biggl {\mathopen\bigg}
\def \Biggl {\mathopen\Bigg}
\def \biggm {\mathrel\bigg}
\def \Biggm {\mathrel\Bigg}
\def \biggr {\mathclose\bigg}
\def \Biggr {\mathclose\Bigg}
\def \binomial #1#2{{{#1} \atopwithdelims() {#2}}}
\let \binom = \binomial
\def \bmod {\mathbin{\rm mod}}
\def \bordermatrix #1{%
{\setbox \zboxa = \hbox{\mex B}%
\tdimena = \wd\zboxa
\setbox \zboxa = \vbox{%
\def \cr {\crcr \noalign{\kern 0pt \global\let \cr = \completerow}}%
\ialign{$##$\hfil \kern 2pt \kern \tdimena&
\thinspace \hfil $##$\hfil&&
\quad \hfil $##$\hfil \crcr
\omit \strut \hfil \crcr
\noalign{\kern -\baselineskip}%
#1\crcr
\omit \strut \cr}}%
\setbox \zboxc = \vbox{%
\unvcopy \zboxa \global\setbox \zboxb = \lastbox}%
\setbox \zboxc = \hbox{%
\unhbox \zboxb \unskip \global\setbox \zboxb = \lastbox}%
\setbox \zboxc = \hbox{%
$\kern \wd\zboxb \kern -\tdimena \left(\kern -\wd\zboxb
\global\setbox \zboxb = \vbox{\box\zboxb \kern 8pt}%
\vcenter{\kern -\ht\zboxb \unvbox\zboxa \kern -\baselineskip}\,%
\right)$}%
\null\;\vbox{\kern \ht\zboxb \box\zboxc}}}
\def \brace {\atopwithdelims\{\}}
\def \bracematrix #1{% {row...}
\left\{ \matrix{#1} \right\}}
\def \brack {\atopwithdelims[]}
\def \bracketmatrix #1{% {row...}
\left[ \matrix{#1} \right]}
\def \bracketmatrixfl #1{% {row...}
\left[ \matrixfl{#1} \right]}
\def \bracketmatrixfr #1{% {row...}
\left[ \matrixfr{#1} \right]}
\def \cases #1{% {row...}
\left\{ \,%
\vcenter{\matrixbaselines
\ialign{$##$\hfil&
\quad {\rm ##}\hfil \crcr
#1\crcr}}%
\right.}
% This version of \cases has math in both columns.
\def \mcases #1{% {row...}
\left\{ \,%
\vcenter{\matrixbaselines
\ialign{$##$\hfil&
\quad $##$\hfil \crcr
#1\crcr}}%
\right.}
\def \cdots {\mathinner{\cdotp\cdotp\cdotp}}
\def \ddots {%
\if \newdots
\vbox{\baselineskip = 4pt \lineskiplimit = 0pt
\hbox{.}
\hbox{\kern .4em .}
\hbox{\kern .8em .}}%
\else
\mathinner{\mkern 1mu \raise 7pt \vbox{\kern 7pt \hbox{.}}%
\mkern 2mu \raise 4pt \hbox{.}%
\mkern 2mu \raise 1pt \hbox{.}%
\mkern 1mu}%
\fi}
\def \detmatrix #1{% {row...}
\left| \matrix{#1} \right|}
\def \displayfrac #1#2{% {numerator}{denominator}
{\displaystyle \frac{#1}{#2}}}
\def \displaylines #1{% {row...}
\openup \jot
\global\setflag \zdtop = \true
\everycr = {\noalign{\if \zdtop
\vskip -\lineskiplimit
\vskip \normallineskiplimit
\global\setflag \zdtop = \false
\else
\penalty \interdisplaylinepenalty
\fi}}%
\halign{\hbox to \displaywidth{$\tabskip = 0pt \everycr = {}%
\hfil \displaystyle ##\hfil$}\cr
#1\crcr}}
\def \eqalign #1{% {row...}
\vcenter{%
\ialign{&\mathstrut \hfil $\displaystyle ##{}$&
$\displaystyle {}##$\hfil\cr
#1\crcr}}}
\def \equalfill {%
$\mathord =\mkern -6mu
\cleaders \hbox{$\mkern -2mu \mathord =\mkern -2mu$}\hfill
\mkern -6mu \mathord =$}
% All other fraction macros should use \frac.
\def \frac #1#2{% {numerator}{denominator}
{{\mskip\fracbarhang #1\mskip\fracbarhang} \over
{\mskip\fracbarhang #2\mskip\fracbarhang}}}
\def \fromunder #1{% {math}
\mathrel{\mathop{\longleftarrow}\limits^{#1}}}
\def \hphantom {%
\setflag \zhphant = \true
\setflag \zvphant = \false
\zphanta}
\def \joinrel {\mathrel{\mkern -3mu}}
\def \largefrac #1#2{% {numerator}{denominator}
{\mathchoice{\mathdisplaystyle{\frac{#1}{#2}}}
{\mathdisplaystyle{\frac{#1}{#2}}}
{\mathtextstyle{\frac{#1}{#2}}}
{\mathscriptstyle{\frac{#1}{#2}}}}}
\def \ldots {\mathinner{\ldotp\ldotp\ldotp}}
\def \leftarrowfill {\zleftarrowfill{\textstyle}}
\def \leftrightarrowfill {\zleftrightarrowfill{\textstyle}}
\def \rightarrowfill {\zrightarrowfill{\textstyle}}
\def \Rightarrowfill {\zRightarrowfill{\textstyle}}
\def \zleftarrowfill #1{% {style}
\setbox\zboxa = \hbox{$#1-$}%
\ht\zboxa = 0pt
$#1\mathord\leftarrow \mkern -6mu
\cleaders \hbox{$#1\mkern -2mu \copy\zboxa \mkern -2mu$}\hfill
\mkern -6mu \box\zboxa$}
\def \zleftrightarrowfill #1{% {style}
\setbox\zboxa = \hbox{$#1-$}%
\ht\zboxa = 0pt
$#1\mathord\leftarrow \mkern -6mu
\cleaders \hbox{$#1\mkern -2mu \box\zboxa \mkern -2mu$}\hfill
\mkern -6mu \mathord\rightarrow$}
\def \zRightarrowfill #1{% {style}
\setbox\zboxa = \hbox{$#1=$}%
\ht\zboxa = 0pt
$#1\copy\zboxa \mkern -6mu
\cleaders \hbox{$#1\mkern -2mu \box\zboxa \mkern -2mu$}\hfill
\mkern -6mu \mathord\Rightarrow$}
\def \zrightarrowfill #1{% {style}
\setbox\zboxa = \hbox{$#1-$}%
\ht\zboxa = 0pt
$#1\copy\zboxa \mkern -6mu
\cleaders \hbox{$#1\mkern -2mu \box\zboxa \mkern -2mu$}\hfill
\mkern -6mu \mathord\rightarrow$}
\let \leqalignno = \eqalignno
\def \mathstrut {\vphantom(}
\def \matrix #1{% {row...}
\null\nonscript\,%
\vcenter{\matrixbaselines
\ialign{\hfil $##$\hfil&& \quad \hfil $##$\hfil \crcr
\mathstrut\crcr
\noalign{\kern -\baselineskip}%
#1\crcr
\mathstrut\crcr
\noalign{\kern -\baselineskip}}}%
\nonscript\,}
\let \adjustmatrix = \noalign
\def \matrixfl #1{% {row...}
\null\nonscript\,%
\vcenter{\matrixbaselines
\ialign{$##$\hfil && \quad $##$\hfil \crcr
\mathstrut\crcr
\noalign{\kern -\baselineskip}%
#1\crcr
\mathstrut\crcr
\noalign{\kern -\baselineskip}}}%
\nonscript\,}
\def \matrixfr #1{% {row...}
\null\nonscript\,%
\vcenter{\matrixbaselines
\ialign{\hfil $##$&& \quad \hfil $##$\crcr
\mathstrut\crcr
\noalign{\kern -\baselineskip}%
#1\crcr
\mathstrut\crcr
\noalign{\kern -\baselineskip}}}%
\nonscript\,}
\def \matrixbaselines {%
\baselineskip = \the\matrixspread\normalbaselineskip
\lineskiplimit = \normallineskiplimit
\lineskip = \normallineskip}
\def \ontopof #1#2{{{#1} \atop {#2}}}% {numerator}{denominator}
\def \openup {\afterassignment\zopenup \tdimena=}
\def \zopenup {%
\advance \baselineskip by \tdimena
\advance \lineskiplimit by \tdimena
\advance \lineskip by \tdimena}
\def \overbrace #1{%
\mathop{%
\vbox{\ialign{##\cr
\noalign{\kern 3pt}%
\downbracefill\cr
\noalign{\kern 3pt \nointerlineskip}%
$\hfil \displaystyle{#1}\hfil$\cr}}}\limits}
\def \overleftarrow {\mathpalette\zoverleftarrow}
\def \overleftrightarrow {\mathpalette\zoverleftrightarrow}
\def \overRightarrow {\mathpalette\zoverRightarrow}
\def \overrightarrow {\mathpalette\zoverrightarrow}
\def \zoverleftarrow #1#2{% {style}{math}
\vbox{\ialign{##\cr
\zleftarrowfill{\scriptscriptstyle}\cr
\noalign{\nointerlineskip}%
$\hfil #1#2\hfil$\crcr}}}
\def \zoverleftrightarrow #1#2{% {style}{math}
\vbox{\ialign{##\cr
\zleftrightarrowfill{\scriptscriptstyle}\cr
\noalign{\nointerlineskip}%
$\hfil #1#2\hfil$\crcr}}}
\def \zoverRightarrow #1#2{% {style}{math}
\vbox{\ialign{##\cr
\zRightarrowfill{\scriptscriptstyle}\cr
\noalign{\nointerlineskip}%
$\hfil #1#2\hfil$\crcr}}}
\def \zoverrightarrow #1#2{% {style}{math}
\vbox{\ialign{##\cr
\zrightarrowfill{\scriptscriptstyle}\cr
\noalign{\nointerlineskip}%
$\hfil #1#2\hfil$\crcr}}}
\def \overset #1#2{
\mathbin{\mathop{#2}\limits^{#1}}}
\def \parenmatrix #1{% {row...}
\left( \matrix{#1} \right)}
\let \pmatrix = \parenmatrix
\def \parenmatrixfl #1{% {row...}
\left( \matrixfl{#1} \right)}
\def \parenmatrixfr #1{% {row...}
\left( \matrixfr{#1} \right)}
\def \phantom {%
\setflag \zhphant = \true
\setflag \zvphant = \true
\zphanta}
\def \zphanta {%
\if \mathmodep
\def \znext {\mathpalette\zphantb}%
\else
\let \znext = \zphantc
\fi
\znext}
\def \zphantb #1#2{%
\setbox \zboxa = \hbox{$#1{#2}$}%
\zphantd}
\def \zphantc #1{%
\setbox \zboxa = \hbox{#1}%
\zphantd}
\def \zphantd {%
\setbox \zboxb = \hbox{}%
\if \zhphant \wd\zboxb = \wd\zboxa \fi
\if \zvphant \ht\zboxb = \ht\zboxa \dp\zboxb = \dp\zboxa \fi
\box \zboxb}
\def \plainTeXmathdisplay {%
\global\everydisplay = {}}
\def \pmod #1{\allowbreak \,({\rm mod}\,#1)}
\def \Relbar {\mathrel =}
\def \relbar {\mathrel{\smash -}}
\definebox{\zrootbox}
\def \nthroot #1{% {n}
\setbox\zrootbox = \hbox{$\scriptscriptstyle{#1}$}%
\mathpalette\zroot}
\def \zroot #1#2{% {\style}{radicand}
\setbox\zboxa = \hbox{$#1\sqrt{#2}$}%
\tdimena = \ht\zboxa
\advance \tdimena by -\dp\zboxa
\mkern 5mu \raise .6\tdimena \copy\zrootbox \mkern -10mu \box\zboxa}
\def \skew #1#2#3{% {amount}{accent}{char}
{\zmuskipa = #1mu
\divide \zmuskipa by 2
\mkern \zmuskipa
#2{\mkern -\zmuskipa{#3}\mkern \zmuskipa}%
\mkern -\zmuskipa}{}}
\def \smallfrac #1#2{% {numerator}{denominator}
{\mathchoice{\mathtextstyle{\frac{#1}{#2}}}
{\mathscriptstyle{\frac{#1}{#2}}}
{\mathscriptscriptstyle{\frac{#1}{#2}}}
{\mathscriptscriptstyle{\frac{#1}{#2}}}}}
\def \smash {%
\relax
\if \mathmodep
\def \znext {\mathpalette\zsmasha}%
\else
\let \znext = \zsmashb
\fi
\znext}
\def \zsmasha #1#2{%
\setbox \zboxa = \hbox{$#1{#2}$}%
\zsmashc}
\def \zsmashb #1{%
\setbox \zboxa = \hbox{#1}%
\zsmashc}
\def \zsmashc {%
\ht\zboxa = 0pt
\dp\zboxa = 0pt
\box \zboxa}
\def \sqrt {\radical"270370 }
\let \sub = _
\let \super = ^
\def \Tounder #1{% {math}
\mathrel{\mathop{\Longrightarrow}\limits^{#1}}}
\def \tounder #1{% {math}
\mathrel{\mathop{\longrightarrow}\limits^{#1}}}
\def \underbrace #1{% {text}
\mathop{%
\vtop{\ialign{##\cr
$\hfil \displaystyle{#1}\hfil$\cr
\noalign{\kern 3pt \nointerlineskip}%
\upbracefill\cr
\noalign{\kern 3pt}}}}\limits}
\def \underset #1#2{
\mathbin{\mathop{#2}\limits_{#1}}}
\def \unit #1{% {text}
\if \mathmodep
{\nonscript\,\mtext{#1}}%
\else
\,#1%
\fi}
\def \vdots {%
\if \newdots
\vbox{\baselineskip = 4pt \lineskiplimit = 0pt
\hbox{.}
\hbox{.}
\hbox{.}}%
\else
\vbox{\baselineskip = 4pt \lineskiplimit = 0pt
\kern 6pt
\hbox{.}
\hbox{.}
\hbox{.}}%
\fi}
\def \vphantom {%
\setflag \zhphant = \false
\setflag \zvphant = \true
\zphanta}
% Block Matrices
% ----- --------
\def \blockmatrix #1{% {rows}
\zblockmatrix{\false}{#1}}
\def \blockmatrixvr #1{% {rows}
\zblockmatrix{\true}{#1}}
\def \zblockmatrix #1#2{% {verticals?}{rows}
\left[
\vcenter{%
\defineatsigncommand @R{\colrule}%
\defineatsigncommand @N{\nocolrule}%
\offinterlineskip
\tdimena = \ht\strutbox \advance \tdimena by .2ex
\tdimenb = \dp\strutbox \advance \tdimenb by .4ex
\setbox \strutbox \hbox{\vrule width 0pt height \tdimena depth \tdimenb}%
\ialign{\hfil \strut \thirdspace $##$\thirdspace \hfil&&
\hspace{.35em}%
\vrule \if #1\colrule \else \nocolrule \fi
##\relax
\hspace{.35em}&
\hfil \strut \thirdspace $##$\thirdspace \hfil\crcr
#2\crcr}}%
\right]}
\def \rowrule {%
\noalign{%
\vskip .5ex
\hrule height .1ex\relax
\vskip .7ex}}
\def \colrule {%
width .1ex }
% Math Displays
% ---- --------
\defineblock{\mathdisplay}{\endmathdisplay}{\true}{}
%~block mathdisplay
% \abovepenalty = integer % Penalty above display.
% \aboveskip = glue % Visual space above display.
% \belowpenalty = integer % Penalty below display.
% \belowskip = glue % Visual space below display.
% \bodyfont = {...} % Font for display.
% \def \comptextformat {...} % Composite number text formatter.
% \diagramdiagarrowstyle = {...} % Style for diagonal arrows in diagrams.
% \diagramgutter = dimen % Gutter between diagram columns.
% \diagraminterrowskip = glue % Interrowskip for diagrams.
% \diagramminarrow = dimen % Minimum length of arrow in diagram.
% \hfuzz = dimen % Overhang allowed at end of line.
% \interrowskip = glue % Extra visual space between equations.
% \leftindent = dimen % Left indentation for \alignleft.
% \matrixspread = {decimal} % Spread factor for matrices.
% \def \numberformat {...} % Equation number formatter.
% \position = {...} % Positioning options.
% \rightindent = dimen % Right indentation for \alignright.
% \textcolor = {...} % Color of text.
%~end
\definetoks{\diagramdiagarrowstyle}
\definedimen{\diagramgutter}{0pt}
\defineskip{\diagraminterrowskip}{0pt}
\definedimen{\diagramminarrow}{0pt}
% Positioning options are:
% \alignleft Left aligned, with \leftindent.
% \alignright Right aligned, with \rightindent.
% \center Centered.
% \numberleft Equation number on left.
% \numberright Equation number on right.
% These parameters are calculated:
\definetoks{\mathdisplayeqno} % Text following \eqno marker.
\definecount{\mathdisplayprevgraf}{-1} % Previous display's ending \prevgraf.
\definecount{\mathdisplayprevpenalty}{0}% Previous display's \belowpenalty.
\defineskip{\mathdisplayprevskip}{0pt} % Previous display's \belowskip.
\declareeverypar{\global\mathdisplayprevgraf=-1}
\zdeclareeveryvcontext{\zsavevcontext{\mathdisplayprevgraf=-1}}
%~ This marker specifies that the following text is the equation number
%~ for the math display.
\definemarker{\eqno}
\everydisplay = {\mathdisplay}
\def \mathdisplay #1$${% equation $$
\advance \displayindent by \leftskip
\advance \displaywidth by -\leftskip
\advance \displaywidth by -\rightskip
% \beginblockscope is unnecessary.
\global\increment \mathdisplaydepth
\abovepenalty = 5000 %~default hard
\belowpenalty = \breakallowed %~default hard
\hfuzz = 1pt %~default hard
\leftindent = 0pt %~default soft
\matrixspread = {1.0} %~default soft
\rightindent = 0pt %~default soft
\textcolor = {}% %~default soft
\processdesign{\mathdisplay}{}%
% \mathdisplaynumber is incremented by \eqno, if appropriate.
\if \eqlp{\prevgraf}{\mathdisplayprevgraf}%
\aboveskip = -\belowskip
\advance \aboveskip by \interrowskip
\fi
\let \text = \mtext
\zmdparams
\settaginfo{}{}% % No tag info so far.
\if \notp{\emptytoksp{\textcolor}}\color{\the\textcolor}\fi
\mathdisplayformat{#1}%
\endmathdisplay}
\def \endmathdisplay {%
\global\mathdisplayprevgraf = \prevgraf
\global\advance \mathdisplayprevgraf by 3
\global\mathdisplayprevpenalty = \belowpenalty
\global\mathdisplayprevskip = \belowskip
\global\decrement \mathdisplaydepth
\if \notp{\emptytoksp{\textcolor}}\endcolor \fi%
% \endblockscope is unnecessary.
$$}
\definecount{\zmdhpos}{0}
\def \zmdparams {%
\abovedisplayskip = \aboveskip
\abovedisplayshortskip = \aboveskip
\belowdisplayskip = \belowskip
\belowdisplayshortskip = \belowskip
\predisplaypenalty = \abovepenalty
\postdisplaypenalty = \belowpenalty
\zmdhpos = 0
\let \center = \relax
\def \alignleft {\zmdhpos = 1}%
\def \alignright {\zmdhpos = 2}%
\setflag \zmdnumleft = \false
\def \numberleft {\setflag \zmdnumleft = \true}%
\let \numberright = \relax
\the\position}
\def \mathdisplayformat #1{% {display}
\the\bodyfont
\zmdparse#1\eqno\eqno\zmark
{\lineskiplimit = \maxdimen % Force \interrowskip between
\lineskip = \interrowskip % each row of multi-line display.
\ifcase \zmdhpos
\if \zmdnumleft % Centered display.
\hbox to \displaywidth {%
\rlap{\hspace{-1\leftskip}\zmdeqno}%
\hfil $\displaystyle \zmdeq$\hfil}%
\else
\hbox to \displaywidth {%
\hfil $\displaystyle \zmdeq$\hfil
\llap{\zmdeqno\hspace{-1\rightskip}}}%
\fi
\or
\if \zmdnumleft % Left-aligned display.
\hbox to \displaywidth {%
\hbox to \leftindent{\hspace{-1\leftskip}\zmdeqno\hss}%
$\displaystyle \zmdeq$\hfil}%
\else
\hbox to \displaywidth{%
\kern \leftindent $\displaystyle \zmdeq$\hfil
\llap{\zmdeqno\hspace{-1\rightskip}}}%
\fi
\or
\if \zmdnumleft % Right-aligned display.
\hbox to \displaywidth {%
\rlap{\hspace{-1\leftskip}\zmdeqno}%
\hfil $\displaystyle \zmdeq$\kern \rightindent}%
\else
\hbox to \displaywidth{%
\hfil $\displaystyle \zmdeq$%
\hbox to \rightindent{\hss\zmdeqno\hspace{-1\rightskip}}}%
\fi
\fi}}
\def \zmdparse #1\eqno#2\eqno#3\zmark{% equation\eqno number\eqno ???\zmark
\def \zmdeq {#1}%
\if \andp{\emptyargp{#2}}{\emptyargp{#3}}%
\let \zmdeqno = \relax
\else
\def \zmdeqno {\zmdformeqno#2\tag\tag\zmark}%
\fi}
% This macro is invoked to format equation numbers in both positions:
% at the end of the display and at the end of \eqaligned rows.
\def \zmdformeqno #1\tag#2\tag#3\zmark{% number\tag{xxx}\tag ???\zmark
\if \emptyargp{#1}%
\global\increment \mathdisplaynumber
\mathdisplayeqno = \expandafter{\number\mathdisplaynumber}%
\setcomptext{\mathdisplaycomptext}%
\else
\zmdexpliciteqno #1 \zmark
\fi
\settaginfo{\the\mathdisplaycomptext}{???}%
\hbox{\numberformat}%
\if \notp{\emptyargp{#3}}\zmdtageqno#2\zmark \fi}
\def \zmdexpliciteqno #1#2 #3\zmark{%
\if \codeeqlp{#1}{!}%
\mathdisplayeqno = {#2}%
\mathdisplaycomptext = {#2}%
\else\if \codeeqlp{#1}{+}%
\global\increment \mathdisplaynumber
\mathdisplayeqno = \expandafter{\number\mathdisplaynumber #2}%
\setcomptext{\mathdisplaycomptext}%
\else\if \codeeqlp{#1}{,}%
\mathdisplayeqno = \expandafter{\number\mathdisplaynumber #2}%
\setcomptext{\mathdisplaycomptext}%
\else\if \codeeqlp{#1}{:}%
\global\increment \mathdisplaynumber
\mathdisplayeqno = {#2}%
\setcomptext{\mathdisplaycomptext}%
\else\if \codeeqlp{#1}{=}%
\zmdseteqno #2\zmark
\setcomptext{\mathdisplaycomptext}%
\else\if \codeeqlp{#1}{>}%
\zmdrefeqno #2;;\zmark
%%% \mathdisplayeqno = {\ref{#2}}%
%%% \mathdisplaycomptext = {\ref{#2}}%
\else
\mathdisplayeqno = {#1#2}%
\setcomptext{\mathdisplaycomptext}%
\fi\fi\fi\fi\fi\fi}
\def \zmdseteqno #1;#2\zmark{%
\global\mathdisplaynumber = #1\relax
\mathdisplayeqno = \expandafter{\number\mathdisplaynumber #2}}
\def \zmdrefeqno #1;#2;#3\zmark{%
\if \emptyargp{#2}%
\mathdisplayeqno = {\ref{#1}}%
\mathdisplaycomptext = {\ref{#1}}%
\else
\mathdisplayeqno = {\ref{#1}\,#2}%
\mathdisplaycomptext = {\ref{#1}\,#2}%
\fi}
\def \zmdtageqno #1#2\zmark{%
\def \znext { }%
\if \znext#2\tag{#1}\else \tag{#1#2}\fi}
\def \setmathdisplaynumber #1{%
\global\mathdisplaynumber = #1\relax
\global\decrement \mathdisplaynumber}
%~ This modifier for |$$| is used when the display is the first thing
%~ after a head, the first thing in a list item, the first thing in
%~ a float, etc. It eliminates the vertical space above the display.
\def \immediatemathdisplay {% %^modifier
\with{\abovepenalty = \breaknever
\aboveskip = 0pt}}
% Aligned Equations
% ------- ---------
% This tool can only be used inside a math display.
\defineskip{\zeqaltabskip}{0pt}
\definedimen{\zeqnoshift}{0pt}
\def \eqaligned #1{% {rows...}
\vcenter{%
\zeqalinit
\halign to \tdimena {%
\hfil $\displaystyle ##{}$\tabskip = 0pt&
$\displaystyle {}##$\hfil \tabskip = \zeqaltabskip&
\relax \zeqaleqno ##\zmark% \relax prevents expansion of \zeqaleqno.
\tabskip = \if \zmdnumleft \displaywidth \else 0pt \fi \cr
#1\crcr}}}
\def \eqalignedpairs #1{% {rows...}
\vcenter{%
\zeqalinit
\halign to \tdimena {%
\hfil $\displaystyle ##{}$\tabskip = 0pt&
$\displaystyle {}##$\hfil&
\hfil $\displaystyle ##{}$&
$\displaystyle {}##$\hfil \tabskip = \zeqaltabskip&
\relax \zeqaleqno ##\zmark% \relax prevents expansion of \zeqaleqno.
\tabskip = \if \zmdnumleft \displaywidth \else 0pt \fi \cr
#1\crcr}}}
\def \eqalignedtriples #1{% {rows...}
\vcenter{%
\zeqalinit
\halign to \tdimena {%
\hfil $\displaystyle ##{}$\tabskip = 0pt&
$\displaystyle {}##$\hfil&
\hfil $\displaystyle ##{}$&
$\displaystyle {}##$\hfil&
\hfil $\displaystyle ##{}$&
$\displaystyle {}##$\hfil \tabskip = \zeqaltabskip&
\relax \zeqaleqno ##\zmark% \relax prevents expansion of \zeqaleqno.
\tabskip = \if \zmdnumleft \displaywidth \else 0pt \fi \cr
#1\crcr}}}
\def \eqalignedquadruples #1{% {rows...}
\vcenter{%
\zeqalinit
\halign to \tdimena {%
\hfil $\displaystyle ##{}$\tabskip = 0pt&
$\displaystyle {}##$\hfil&
\hfil $\displaystyle ##{}$&
$\displaystyle {}##$\hfil&
\hfil $\displaystyle ##{}$&
$\displaystyle {}##$\hfil&
\hfil $\displaystyle ##{}$&
$\displaystyle {}##$\hfil \tabskip = \zeqaltabskip&
\relax \zeqaleqno ##\zmark% \relax prevents expansion of \zeqaleqno.
\tabskip = \if \zmdnumleft \displaywidth \else 0pt \fi \cr
#1\crcr}}}
\def \zeqalinit {%
\def \eqno {&\relax}% \relax prevents expansion of stuff after \eqno.
\tdimena = \displaywidth
\advance \tdimena by -\leftindent
\advance \tdimena by -\rightindent
\zeqaltabskip = \if \eqlp{\zmdhpos}{2}0pt \else \centerindent \fi
\if \zmdnumleft
\zeqnoshift = \leftskip \advance \zeqnoshift by \leftindent
\else
\zeqnoshift = \rightskip \advance \zeqnoshift by \rightindent
\fi
\tabskip = \if \eqlp{\zmdhpos}{1}0pt \else \centerindent \fi}
\def \zeqaleqno \relax#1\zmark{% \relax [\eqno [text]][\tag]\zmark
\if \zmdnumleft
\kern -\displaywidth
\rlap{\zmdformeqno#1\tag\tag\zmark}%
\else
\llap{\zmdformeqno#1\tag\tag\zmark \hspace{-\zeqnoshift}}%
\fi}
\let \adjustmathdisplay = \noalign
% Diagrams
% --------
% This tool can only be used inside a math display.
\def \diagram #1{% {rows...}
\zdiagcmds
\null\,%
\vcenter{%
\lineskip = \diagraminterrowskip
\lineskiplimit = \lineskip
\tabskip = -\diagramgutter
\halign{%
&\kern \diagramgutter \hfil $\displaystyle ##$\hfil \tabskip = 0pt \cr
#1\crcr}}%
\,}
\def \zdiagcmds {%
\defineatsigncommand @>##1>##2>{\zdiagra{##1}{##2}}%
\defineatsigncommand @<##1<##2<{\zdiagla{##1}{##2}}%
\defineatsigncommand @X##1X##2X{\zdiaglra{##1}{##2}}%
\defineatsigncommand @=##1=##2={\zdiaghb{##1}{##2}}%
\defineatsigncommand @V##1V##2V{%
\zdiagva{c}{}{\hbox}{\big\downarrow}{##1}{##2}}%
\defineatsigncommand @A##1A##2A{%
\zdiagva{c}{}{\hbox}{\big\uparrow}{##1}{##2}}%
\defineatsigncommand @|##1|##2|{%
\zdiagva{c}{}{\hbox}{\big|}{##1}{##2}}%
\defineatsigncommand @H##1|##2|{%
\zdiagva{c}{}{\hbox}{\big\Vert}{##1}{##2}}%
\defineatsigncommand @1##11##21##31{%
\zdiagva{##1}{l}{r}{\the\diagramdiagarrowstyle \mathchar "7025}{##2}{##3}}%
\defineatsigncommand @3##13##23##33{%
\zdiagva{##1}{l}{r}{\the\diagramdiagarrowstyle \mathchar "7026}{##2}{##3}}%
\defineatsigncommand @5##15##25##35{%
\zdiagva{##1}{r}{l}{\the\diagramdiagarrowstyle \mathchar "702E}{##2}{##3}}%
\defineatsigncommand @7##17##27##37{%
\zdiagva{##1}{r}{l}{\the\diagramdiagarrowstyle \mathchar "702D}{##2}{##3}}%
\defineatsigncommand @"##1"##2"{\zdiagwd{##1}{##2}}}
\def \zdiagra #1#2{%
{\setbox \zboxa = \hbox{$\scriptstyle \;{#1}\;\;\;$}%
\setbox \zboxb = \hbox{$\scriptstyle \;{#2}\;\;\;$}%
\setbox \zboxc = \hbox{$#2$}%
\tdimena = \diagramminarrow
\if \dimgtrp{\wd\zboxa}{\tdimena}\tdimena = \wd\zboxa \fi
\if \dimgtrp{\wd\zboxb}{\tdimena}\tdimena = \wd\zboxb \fi
\mathrel{\mathop{\hbox to \tdimena {\rightarrowfill}}%
\limits^{#1}\if \dimposp{\wd\zboxc}_{#2}\fi}}}
\def \zdiagla #1#2{%
{\setbox \zboxa = \hbox{$\scriptstyle \;\;\;{#1}\;$}%
\setbox \zboxb = \hbox{$\scriptstyle \;\;\;{#2}\;$}%
\setbox \zboxc = \hbox{$#2$}%
\tdimena = \diagramminarrow
\if \dimgtrp{\wd\zboxa}{\tdimena}\tdimena = \wd\zboxa \fi
\if \dimgtrp{\wd\zboxb}{\tdimena}\tdimena = \wd\zboxb \fi
\mathrel{\mathop{\hbox to \tdimena {\leftarrowfill}}%
\limits^{#1}\if \dimposp{\wd\zboxc}_{#2}\fi}}}
\def \zdiaglra #1#2{%
{\setbox \zboxa = \hbox{$\scriptstyle \;\;\;{#1}\;\;\;$}%
\setbox \zboxb = \hbox{$\scriptstyle \;\;\;{#2}\;\;\;$}%
\setbox \zboxc = \hbox{$#2$}%
\tdimena = \diagramminarrow
\if \dimgtrp{\wd\zboxa}{\tdimena}\tdimena = \wd\zboxa \fi
\if \dimgtrp{\wd\zboxb}{\tdimena}\tdimena = \wd\zboxb \fi
\mathrel{\mathop{\hbox to \tdimena {\leftrightarrowfill}}%
\limits^{#1}\if \dimposp{\wd\zboxc}_{#2}\fi}}}
\def \zdiaghb #1#2{%
{\setbox \zboxa = \hbox{$\scriptstyle \;{#1}\;$}%
\setbox \zboxb = \hbox{$\scriptstyle \;{#2}\;$}%
\setbox \zboxc = \hbox{$#2$}%
\tdimena = \diagramminarrow
\if \dimgtrp{\wd\zboxa}{\tdimena}\tdimena = \wd\zboxa \fi
\if \dimgtrp{\wd\zboxb}{\tdimena}\tdimena = \wd\zboxb \fi
\mathrel{\mathop{\hbox to \tdimena {\equalfill}}%
\limits^{#1}\if \dimposp{\wd\zboxc}_{#2}\fi}}}
\def \zdiagva #1#2#3#4#5#6{% {centering}{h-overlap}{t-overlap}
% {arrow}{left-label}{right-label}
\if \codeeqlp{#1}{h}%
\if \codeeqlp{#2}{l}%
\llap{$\scriptstyle{#5}\mkern 2mu{#4}$}%
\rlap{$\mkern 2mu \scriptstyle #6$}%
\else
\llap{$\scriptstyle{#5}\mkern 2mu$}%
\rlap{${#4}\mkern 2mu \scriptstyle{#6}$}%
\fi
\else\if \codeeqlp{#1}{t}%
\if \codeeqlp{#3}{l}%
\llap{$\scriptstyle{#5}\mkern 2mu{#4}$}
\rlap{$\mkern 2mu \scriptstyle #6$}%
\else
\llap{$\scriptstyle{#5}\mkern 2mu$}
\rlap{${#4}\mkern 2mu \scriptstyle #6$}%
\fi
\else
\llap{$\scriptstyle{#5}\mkern 2mu$}{#4}%
\rlap{$\mkern 2mu \scriptstyle #6$}%
\fi\fi}
\def \zdiagwd #1#2{%
\setbox \zboxa = \hbox{$\scriptstyle #2$}%
\hbox to \wd\zboxa {\hfil $\scriptstyle #1$\hfil}}
% Enunciation Definition
% ----------- ----------
\setlist \zenuntypelist = {}
\def \defineenunciationtype #1#2{% {type}{association}
\if \emptyargp{#2}%
\if \withname\undefinedp{\enunciation#1number}%
\withname\definecount{\enunciation#1number}{0}%
\withname\declaresnapitem{\enunciation#1number}%
\fi
\else
\defineenunciationtype{#2}{}%
\edef \znext {%
\global\withname\let{\enunciation#1number}=\name{\enunciation#2number}}%
\znext
\fi
\append{#1}{\zenuntypelist}}
%~ Use this command to define a new type of enunciation.
\def \defineenunciation #1#2#3{% {type}{association}{design}
\defineenunciationtype{#1}{#2}%
\withname\def {\enunciation#1design}{#3}}
% This is deprecated in favor of \defineenunciation.
\def \defineenunciationtypedesign #1#2#3{% {type}{assocation}{design}
\defineenunciationtype{#1}{#2}%
\withname\def {\enunciation#1design}{#3}}
\def \resetenunciationnumbers {%
\maplist{\global\name{\enunciation##1number}=0\relax}{\zenuntypelist}}
% Enunciation Block
% ----------- -----
\defineblock{\enunciation}{\endenunciation}{\false}{}
%~block enunciation Type
% \abovepenalty = integer % Penalty above block
% \aboveskip = glue % Space b/b above block.
% \setflag \allowclubline = flag % True if club allowed below.
% \setflag \allownesting = flag % True if blocks can be nested.
% \attribution = {...} % Attribution text (no longer used).
% \setflag \attributionarg = flag % True if \enunciation takes attribution argument.
% \autoqed = {,,,} % Automatic QED at end.
% \belowpenalty = integer % Penalty below block.
% \belowskip = glue % Space b/b below block.
% \bodyfont = {...} % Font for text.
% \def \comptextformat {...} % Composite number text formatter.
% \continue = integer % Continued or continuation.
% \difficulty = integer % Level of difficulty.
% \def \endformat {...} % End of enunciation formatter.
% \def \labelformat ##1{...} % Enunciation label formatter.
% \leftindent = glue % Left indentation.
% \parindent = dimen % Paragraph indent.
% \parrag = dimen % Paragraph raggedness.
% \parskip = glue % Paragraph skip.
% \rightindent = glue % Right indentation.
% \width = dimen % Width of text.
%~end
\definetoks{\attribution}
\definecount{\attributiontype}{0} % 0: none; 1: attribution; 2: new title
\definetoks{\autoqed}
\setflag \zautoqeddone = \false
\def \enunciation #1{% {type}{optional-attribution}
\beginblockscope{enunciation}%
\global\increment \enunciationdepth
\abovepenalty = \breakgood %~default hard
\setflag \allowclubline = \false %~default soft
\setflag \allownesting = \false %~default soft
\attribution = {}% %~default with
\setflag \attributionarg = \false %~default soft
\autoqed = {}% %~default soft
\belowpenalty = \breakgood %~default hard
\continue = 0 %~default with
\setflag \continuation = \false % Deprecated
\difficulty = 0 %~default with
\def \endformat {}% %~default soft
\processdesign{\enunciation}{#1}%
\zsetcontinue % Handle old \continuation.
\if \andp{\notp{\allownesting}}{\gtrp{\enunciationdepth}{1}}%
\error{blkcantnest}
{An enunciation cannot be nested inside itself}%
\fi
\if \attributionarg
\let \znext = \enunciationarg
\else
\let \znext = \enunciationb
\fi
\znext{#1}}
\def \enunciationarg #1#2{% {type}{attribution}
\if \notp{\emptyargp{#2}}\attribution = {#2}\fi
\enunciationb{#1}}
\def \enunciationb #1{% {type}
\attributiontype = 0\relax
\global\setflag \zautoqeddone = \false
\if \notp{\emptytoksp{\attribution}}%
\expandafter\zparseenunattr \the\attribution \zmark
\fi
\if \notp{\continuationp}%
\global\withname\increment{\enunciation#1number}%
\fi
\global\withname\enunciationnumber{\enunciation#1number}%
\setcomptext{\enunciationcomptext}%
\enunciationformat
\settaginfo{\the\enunciationcomptext}{???}%
\ignorespaces}
\def \endenunciation {%
\futurelet\nexttoken \zendenunciation}
\def \zendenunciation {%
\endenunciationformat
\global\decrement \enunciationdepth
\endblockscope{enunciation}%
\parnext}
\def \enunciationformat {%
\endgraf
\the\bodyfont
\bbskipabove{\abovepenalty}{\aboveskip}%
\alterindentation{\leftindent}{\rightindent}%
\settextwidth{\width}%
\setparrag{\parrag}%
\expandafter\labelformat\expandafter{\the\attribution}%
\if \notp{\allowclubline}\overrideclubpenalty{\breaknever}\fi}
\def \endenunciationformat{%
\if \notp{\zautoqeddone}\the\autoqed \fi
\endgraf
\endformat
\bbskipbelowblockpar{\nexttoken}{\belowpenalty}{\belowskip}}
%~ This marker indicates that the enunciation title completely
%~ replaces the default title.
\definemarker{\title}
\def \zparseenunattr #1#2\zmark{%
\def \znext {#1}%
\def \ztitle {\title}%
\if \tokeqlp{\znext}{\ztitle}%
\attribution = {#2}%
\attributiontype = 2\relax
\else
\attributiontype = 1\relax
\fi}
%~ This command is used in enunciation design macros to select the
%~ title format based on the |\enunciation| *attribution* argument.
\long\def \attributiontypecase #1#2#3{% {format1}{format2}{format3}
\ifcase \attributiontype
#1% no attribution
\or
#2% normal attribution
\or
#3% title override
\fi}%
% QED Definition
% --- ----------
%~ This command defines an end-of-enunciation dingbat for use
%~ with enunciations.
\def \defineeoedingbat #1#2#3{% {name}{text}{space}
\withname\gdef {#1dingbat}{#2}%
\gdef #1{\zformateoe{#2}#3\zmark}%
\withname\gdef {\no\expandafter\discardtok\string#1}{%
\global\setflag \zautoqeddone = \true}}
\def \zformateoe #1#2#3\zmark{%
{\def \znext {#2}%
\def \zfr {\flushright}%
\if \tokeqlp{\znext}{\zfr}%
\if \vmodep
\rightline{#1}%
\else\if \mathmodep
\hskip #3{#1}%
\else
\hskip #3\retain \nobreak \hfill {#1}%
\fi\fi
\else
\if \vmodep
\rightline{#1}%
\else\if \mathmodep
\hskip #2#3{#1}%
\else
\unskip \hskip #2#3\hskip 0pt plus -1fill \retain \nobreak \hfill {#1}%
\fi\fi
\fi
\global\setflag \zautoqeddone = \true}}
%~ This command is deprecated in favor of |\defineeoedingbat|.
\def \defineqed #1#2#3#4{% {\name}{text}{space}{min-space}
\withname\gdef {#1dingbat}{#2}%
\gdef #1{\zformatqed{#2}{#3}{#4}}%
\withname\gdef{\no\expandafter\discardtok\string#1}{%
\global\setflag \zautoqeddone = \true}}
\def \zformatqed #1#2#3{% {text}{space}{min-space}
{\def \znext {#2}%
\def \zfr {\flushright}%
\if \tokeqlp{\znext}{\zfr}%
\hspace{#3}\retain \nobreak \hfill {#1}%
\else
\if \vmodep
\noindent #1\par
\else
\hspace{#2}{#1}%
\fi
\fi
\global\setflag \zautoqeddone = \true}}