% AMRMathMacros.TeX --- Stolfi    May 11, 1984 3:00:02 pm PDT

% Macros and \mathcodes that apply when standard TeX fonts (of any size)
% are being used for math

% These definitions assume the math fonts
%  (\textfont, \scriptfont, and \scriptscriptfont)
%  of families 0, 1, 2 and 3 have been set respectively to STANDARD TeX fonts,
%  respectively roman, math italic, symbol, and extension. 

% MACROS FOR CONSTRUCTING NEW OPERATORS

\message{operator twiddling ...}

% abuts a mathrel to the previous one

\def\joinrel{\mathrel{\mkern-3mu}}

% Same as \not, but with steeper slash. Use with \mathpalette

\def\c@ncel#1#2{\overlap{$\hfil#1\mkern1mu/\hfil$\crcr$#1#2$}}

% Puts #2 over equal sign.  Use with \mathpalette.

\def\@vereq#1#2{\lower.5\p@  % bug! should vary with font size
   \vbox{\baselinesep\z@glue\linesep-.5\p@
      \ialign{$\m@th#1\hfil##\hfil$\crcr
        #2\crcr
        =\crcr}}}

% MATH CODES FOR SPECIAL CHARACTERS

\message{mathcodes ...}

% Definition of math characters

% INITEX sets up \mathcode x=x, for x=0..127, except that
% \mathcode x=x+"7100, for x = `A to `Z and `a to `z;
% \mathcode x=x+"7000, for x = `0 to `9.

\mathcode`\="3214 % Ascii '034 = \le
\mathcode`\="3215 % Ascii '035 = \ge
\mathcode`\="3220 % Ascii '030 = \leftarrow
\mathcode`\="3221 % Ascii '031 = \rightarrow
\mathcode`\ ="8000 % \space
\mathcode`\!="5021
\mathcode`\'="8000 % ^\prime
\mathcode`\(="4028
\mathcode`\)="5029
\mathcode`\*="2203 % \ast
\mathcode`\+="202B
\mathcode`\,="613B
\mathcode`\-="2200
\mathcode`\.="013A
\mathcode`\/="013D
\mathcode`\:="303A
\mathcode`\;="603B
\mathcode`\<="313C
\mathcode`\=="303D
\mathcode`\>="313E
\mathcode`\?="503F
\mathcode`\[="405B
\mathcode`\]="505D
\mathcode`\|="026A

% GREEK LETTERS

\message{greek ...}

\mathchardef\alpha="010B
\mathchardef\beta="010C
\mathchardef\gamma="010D
\mathchardef\delta="010E
\mathchardef\epsilon="0122 % exchanged with \varepsilon
\mathchardef\zeta="0110
\mathchardef\eta="0111
\mathchardef\theta="0112
\mathchardef\iota="0113
\mathchardef\kappa="0114
\mathchardef\lambda="0115
\mathchardef\mu="0116
\mathchardef\nu="0117
\mathchardef\xi="0118
\mathchardef\pi="0119
\mathchardef\rho="011A
\mathchardef\sigma="011B
\mathchardef\tau="011C
\mathchardef\upsilon="011D
\mathchardef\phi="0127 % exchanged with \varphi
\mathchardef\chi="011F
\mathchardef\psi="0120
\mathchardef\omega="0121
\mathchardef\varepsilon="010F % exchanged with \epsilon
\mathchardef\vartheta="0123
\mathchardef\varpi="0124
\mathchardef\varrho="0125
\mathchardef\varsigma="0126
\mathchardef\varphi="011E % exchanged with \phi
\mathchardef\Gamma="7000
\mathchardef\Delta="7001
\mathchardef\Theta="7002
\mathchardef\Lambda="7003
\mathchardef\Xi="7004
\mathchardef\Pi="7005
\mathchardef\Sigma="7006
\mathchardef\Upsilon="7007
\mathchardef\Phi="7008
\mathchardef\Psi="7009
\mathchardef\Omega="700A

% SPECIAL MATH STYLES

\message{special styles ...}

% Old style digits (work also in text mode)

\def\oldstyle{\mit}

% Calligraphic letters (work also in text mode)

\def\cal{\sy}

% Italic greek capitals

\def\itgreek{\it}

% DELIMITERS

\message{delimiters ...}

% delcodes  

% INITEX sets all \delcode values to -1, except  \delcode`.=0

\delcode`\(="028300
\delcode`\)="029301
\delcode`\[="05B302
\delcode`\]="05D303
\delcode`\<="26830A
\delcode`\>="26930B
\delcode`\/="02F30E
\delcode`\|="26A30C
\delcode`\\="20430F

% Named delimiters  

\def\lmoustache{\delimiter"4000340 } % top from (, bottom from )
\def\rmoustache{\delimiter"5000341 } % top from ), bottom from (
\def\lgroup{\delimiter"400033A } % extensible ( with sharper tips
\def\rgroup{\delimiter"500033B } % extensible ) with sharper tips
\def\arrowvert{\delimiter"33C } % arrow without arrowheads
\def\Arrowvert{\delimiter"33D } % double arrow without arrowheads
\def\bracevert{\delimiter"33E } % the vertical bar that extends braces
\def\Vert{\delimiter"26B30D } \let\|=\Vert
\def\vert{\delimiter"26A30C }
\def\uparrow{\delimiter"3222378 }
\def\downarrow{\delimiter"3223379 }
\def\updownarrow{\delimiter"326C33F }
\def\Uparrow{\delimiter"322A37E }
\def\Downarrow{\delimiter"322B37F }
\def\Updownarrow{\delimiter"326D377 }
\def\backslash{\delimiter"26E30F } % for double coset G\backslash H
\def\rangle{\delimiter"526930B }
\def\langle{\delimiter"426830A }
\def\rbrace{\delimiter"5267309 } \let\}=\rbrace
\def\lbrace{\delimiter"4266308 } \let\{=\lbrace
\def\rceil{\delimiter"5265307 }
\def\lceil{\delimiter"4264306 }
\def\rfloor{\delimiter"5263305 }
\def\lfloor{\delimiter"4262304 }

%  Combinatorics ops and such 

\def\choose{\atopwithdelims()}
\def\brack{\atopwithdelims[]}
\def\brace{\atopwithdelims\{\}}

%  Extensible delimiter factor 

\delimiterfactor=901

% OTHER SYMBOLS AND OPERATORS

\message{operators ...}

%  Named math characters 

\mathchardef\aleph="0240

\mathchardef\imath="017B
\mathchardef\jmath="017C
\mathchardef\ell="0160
\mathchardef\wp="017D
\mathchardef\Re="023C
\mathchardef\Im="023D
\mathchardef\partial="0140
\mathchardef\infty="0231
\mathchardef\prime="0230
\mathchardef\varemptyset="023B % Knuth's empty set
\mathchardef\nabla="0272
\def\surd{{\mathchar"1270}}
\mathchardef\top="023E
\mathchardef\bot="023F

\mathchardef\triangle="0234
\mathchardef\forall="0238
\mathchardef\exists="0239

\mathchardef\coprod="1360
\mathchardef\bigvee="1357
\mathchardef\bigwedge="1356
\mathchardef\biguplus="1355
\mathchardef\bigcap="1354
\mathchardef\bigcup="1353
\mathchardef\intop="1352 \def\int{\intop\nolimits}
\mathchardef\prod="1351
\mathchardef\sum="1350
\mathchardef\bigotimes="134E
\mathchardef\bigoplus="134C
\mathchardef\bigodot="134A
\mathchardef\ointop="1348 \def\oint{\ointop\nolimits}
\mathchardef\bigsqcup="1346
\mathchardef\smallint="1273

\mathchardef\neg="023A \let\lnot=\neg

\mathchardef\triangleleft="212F  \let\lpoint=\triangleleft
\mathchardef\triangleright="212E  \let\rpoint=\triangleright
\mathchardef\bigtriangleup="2234
\mathchardef\bigtriangledown="2235
\mathchardef\wedge="225E   \let\land=\wedge
\mathchardef\vee="225F   \let\lor=\vee
\mathchardef\cap="225C   \let\inte=\cap % infix intersection
\mathchardef\cup="225B   \let\uni=\cup % infix union
\mathchardef\ddagger="227A
\mathchardef\dagger="2279
\mathchardef\sqcap="2275
\mathchardef\sqcup="2274
\mathchardef\uplus="225D
\mathchardef\amalg="2271
\mathchardef\diamond="2205
\mathchardef\bullet="220F
\mathchardef\wr="226F
\mathchardef\div="2204
\mathchardef\odot="220C
\mathchardef\oslash="220B
\mathchardef\otimes="220A
\mathchardef\ominus="2209
\mathchardef\oplus="2208   \let\xor=\oplus % boolean exclusive or
\mathchardef\mp="2207
\mathchardef\pm="2206
\mathchardef\circ="220E
\mathchardef\bigcirc="220D
\mathchardef\setminus="226E % for set difference A\setminus B
\mathchardef\cdot="2201
\mathchardef\ast="2203
\mathchardef\times="2202
\mathchardef\pentagram="213F % \star in Plain.TeX

\mathchardef\propto="322F
\mathchardef\sqsubseteq="3276
\mathchardef\sqsupseteq="3277
\mathchardef\parallel="326B
\mathchardef\mid="326A \let\st=\mid % \st = `such that' for \rset
\mathchardef\dashv="3261
\mathchardef\vdash="3260

\mathchardef\leq="3214 \let\le=\leq
\mathchardef\geq="3215 \let\ge=\geq

\mathchardef\succ="321F
\mathchardef\prec="321E
\mathchardef\approx="3219  \let\simil=\approx % double squiggle
\mathchardef\succeq="3217
\mathchardef\preceq="3216
\mathchardef\supset="321B
\mathchardef\subset="321A
\mathchardef\supseteq="3213
\mathchardef\subseteq="3212
\mathchardef\in="3232
\mathchardef\ni="3233 \let\owns=\ni
\mathchardef\gg="321D
\mathchardef\ll="321C

\mathchardef\not="3236

\mathchardef\sim="3218  \let\iso=\sim % single squiggle
\mathchardef\simeq="3227
\mathchardef\perp="323F
\mathchardef\equiv="3211
\mathchardef\asymp="3210
\mathchardef\smile="315E
\mathchardef\frown="315F

% Varous arrows

% mostly horizontal or fixed-size; for vertical extensible ones look 
%  at the "delimiters" section. 

\mathchardef\nearrow="3225
\mathchardef\searrow="3226
\mathchardef\nwarrow="322D
\mathchardef\swarrow="322E
\mathchardef\Leftrightarrow="322C
\mathchardef\Leftarrow="3228
\mathchardef\Rightarrow="3229

\let\up=\uparrow 
\let\down=\downarrow

\mathchardef\leftrightarrow="3224
\mathchardef\leftarrow="3220  \let\gets=\leftarrow
\mathchardef\rightarrow="3221  \let\to=\rightarrow
\mathchardef\mapstochar="3237

\mathchardef\leftharpoonup="3128
\mathchardef\leftharpoondown="3129
\mathchardef\rightharpoonup="312A
\mathchardef\rightharpoondown="312B

\mathchardef\lhook="312C \def\hookrightarrow{\lhook\joinrel\rightarrow}
\mathchardef\rhook="312D \def\hookleftarrow{\leftarrow\joinrel\rhook}

\def\rightleftharpoons{\mathrel{\mathpalette\rlh@{}}}
\def\rlh@#1{\vcenter{\hbox{\overlap{
   \raise2pt\hbox{$#1\rightharpoonup$}\crcr
   $#1\leftharpoondown$}}}}

\def\relbar{\mathrel{\smash-}} % because - has the same height as +
\def\Relbar{\mathrel=}

\def\Longrightarrow{\Relbar\joinrel\Rightarrow}
\def\longrightarrow{\relbar\joinrel\rightarrow}
\def\longleftarrow{\leftarrow\joinrel\relbar}
\def\Longleftarrow{\Leftarrow\joinrel\Relbar}

\def\longmapsto{\mapstochar\longrightarrow}

\def\longleftrightarrow{\leftarrow\joinrel\rightarrow}
\def\Longleftrightarrow{\Leftarrow\joinrel\Rightarrow}

\def\iff{\;\Longleftrightarrow\;}

% Pieces used in constructing `brace leaders'

\mathchardef\braceld="37A \mathchardef\bracerd="37B
\mathchardef\bracelu="37C \mathchardef\braceru="37D

% Musical symbols 

\mathchardef\flat="015B
\mathchardef\natural="015C
\mathchardef\sharp="015D

% Card suits 

\mathchardef\clubsuit="027C
\mathchardef\diamondsuit="027D
\mathchardef\heartsuit="027E
\mathchardef\spadesuit="027F

% Roots 

\def\sqrt{\radical"270370 }

\def\root#1\of{\setbox\rootbox\hbox{$\m@th\scriptscriptstyle{#1}$}
  \mathpalette\r@@t}
\def\r@@t#1#2{\setbox\z@\hbox{$\m@th#1\sqrt{#2}$}
  \dimen@\ht\z@ \advance\dimen@-\dp\z@
  \mskip5mu\raise.6\dimen@\copy\rootbox \mskip-10mu \box\z@}

% Fancy primes:

{\catcode`\'=\active \gdef'{^\bgroup\prim@s}}

\def\prim@s{\prime\futurelet\next\pr@m@s}
\def\pr@m@s{\ifx'\next \let\next\pr@@@s \else\let\next\egroup\fi \next}
\def\pr@@@s#1{\prim@s}

% Sets, sequences, absolute value:  

\def\set#1{{\lbrace{#1}\rbrace}}  % set defined by enumeration
\def\rset#1{{\lbrace \,{#1}\,\rbrace}} % set defined by \relv
\def\seq#1{{\langle{#1}\rangle}}  % sequence
\def\abs#1{\left\leftv{#1}\right\rightv} % absolute value or set size

%  Other constructed math symbols 

\def\emptyset{\big\varphi} % bug! should vary with size
  \let\ety=\emptyset

\def\hbar{{\mathchar'26\mskip-9muh}}

\def\models{\mathrel|\joinrel=}

\def\sp{\mathbin{\,}} % to denote continuous intervals (segs, arcs, etc)
\def\isp{\mathbin{.\,.}} % to denote integer intervals (as in Pascal)

\def\mapsto{\mapstochar\rightarrow}

\def\doteq{\buildrel\textstyle.\over=}

\def\*{\discretionary
  {\thinspace\edef\next{\the\textfont2}\next\char2}{}{}}

\def\cong{\mathrel{\mathpalette\@vereq\sim}} % congruence sign

\def\neq{\not=} \let\ne=\neq

\def\nequiv{\not\equiv}

\def\notin{\mathrel{\mathpalette\c@ncel\in}}

\def\doubleint{\int\!\!\!\int} % double integral

\def\bowtie{\mathrel\triangleright\joinrel\mathrel\triangleleft}

\def\deg{^\circ} % degrees
\def\star{^\ast} % asterisk in superscript position.

\def\angle{{\vbox{\ialign
   {$\m@th\scriptstyle##$\cr\not\mathrel{\mkern14mu}\cr
    \noalign{\nointerlineskip}
    \mkern2.5mu\leaders\hrule height.34pt\hfill\mkern2.5mu\cr}}}}

% BIGGGER SYMBOLS

\message{biggger symbols ...}

%  Simply big ones (just enlarge the mathtext fonts) 

\def\big#1{\hbox{$\biggermathfonts  #1 $}}

%  Really big ones (delimiters only; use the normal extension machinery): 

\def\Big#1{
  {\hbox{$\left#1\vbox to1.35ht\strutbox{}\right.\n@space$}}}
\def\bigg#1{
  {\hbox{$\left#1\vbox to1.70ht\strutbox{}\right.\n@space$}}}
\def\Bigg#1{
  {\hbox{$\left#1\vbox to2.25ht\strutbox{}\right.\n@space$}}}

\def\n@space{\nulldelimiterspace\z@ \m@th}

% Biggger delimiters  

\def\bigl#1{\mathopen{\big#1}}
\def\bigm#1{\mathrel{\big#1}}
\def\bigr#1{\mathclose{\big#1}}
\def\Bigl#1{\mathopen{\Big#1}}
\def\Bigm#1{\mathrel{\Big#1}}
\def\Bigr#1{\mathclose{\Big#1}}
\def\biggl#1{\mathopen{\bigg#1}}
\def\biggm#1{\mathrel{\bigg#1}}
\def\biggr#1{\mathclose{\bigg#1}}
\def\Biggl#1{\mathopen{\Bigg#1}}
\def\Biggm#1{\mathrel{\Bigg#1}}
\def\Biggr#1{\mathclose{\Bigg#1}}

% DOTS

\message{dots ...}

\mathchardef\ldotp="602E % ldot as a punctuation mark
\mathchardef\cdotp="6201 % cdot as a punctuation mark

\mathchardef\colon="603A % colon as a punctuation mark

\def\ldots{\mathinner{\ldotp\ldotp\ldotp}}
\def\cdots{\mathinner{\cdotp\cdotp\cdotp}}

% Note: the height of \vdots and \ddots does not change in \script,
%    \scriptscript, and \bigmath modes.   

\def\vdots{\vbox{\baselinesep0.5ex \lineseplimit\maxdimen
    \kern0.5ex\hbox{.}\hbox{.}\hbox{.}}}

\def\ddots{\mathinner{
  \mskip1mu\raise1ex\vbox{\kern0.5ex\hbox{.}}
  \mskip2mu\raise0.5ex\hbox{.}
  \mskip2mu\hbox{.}\mskip1mu}}

% LEADERS 

\message{leaders ...}

% with rules  

\def\hrulefill{\leaders\hrule\hfill}

% with dots  

\def\dotfill{\cleaders\hbox{$\m@th \mkern1.5mu.\mkern1.5mu$}\hfill}

% with braces  

\def\downbracefill{$\m@th\braceld\leaders\vrule\hfill\braceru
  \bracelu\leaders\vrule\hfill\bracerd$}

\def\upbracefill{$\m@th\bracelu\leaders\vrule\hfill\bracerd
  \braceld\leaders\vrule\hfill\braceru$}

% with arrows  

\def\rightarrowfill{$\m@th\mathord-\mkern-6mu%
  \cleaders\hbox{$\mkern-2mu\mathord-\mkern-2mu$}\hfill
  \mkern-6mu\mathord\rightarrow$}

\def\leftarrowfill{$\m@th\mathord\leftarrow\mkern-6mu%
  \cleaders\hbox{$\mkern-2mu\mathord-\mkern-2mu$}\hfill
  \mkern-6mu\mathord-$}

% MATH ACCENTS

\message{accents ...}

% Accents proper   

\def\acute{\mathaccent"7013 }
\def\grave{\mathaccent"7012 }
\def\ddot{\mathaccent"707F }
\def\tilde{\mathaccent"707E }
\def\bar{\mathaccent"7016 }
\def\breve{\mathaccent"7015 }
\def\check{\mathaccent"7014 }
\def\hat{\mathaccent"705E }
\def\vec{\mathaccent"717E }
\def\dot{\mathaccent"705F }
\def\widetilde{\mathaccent"0365 }
\def\widehat{\mathaccent"0362 }

\def\skew#1#2#3{{#2{#3\mkern#1mu}\mkern-#1mu}{}}

% Fancy overlines/underlines   

\def\overbrace#1{\mathop{\vbox{\ialign{##\crcr
  \noalign{\kern3\p@}
  \downbracefill\crcr
  \noalign{\kern3\p@\nointerlineskip}
  $\hfil\displaystyle{#1}\hfil$\crcr}}}\limits}

\def\underbrace#1{\mathop{\vtop{\ialign{##\crcr
  $\hfil\displaystyle{#1}\hfil$\crcr
  \noalign{\kern3\p@\nointerlineskip}
  \upbracefill\crcr
  \noalign{\kern3\p@}}}}\limits}

\def\overrightarrow#1{\vbox{\ialign{##\crcr
  \rightarrowfill\crcr
  \noalign{\kern-\p@\nointerlineskip}
  $\hfil\displaystyle{#1}\hfil$\crcr}}}

\def\overleftarrow#1{\vbox{\ialign{##\crcr
  \leftarrowfill\crcr
  \noalign{\kern-\p@\nointerlineskip}
  $\hfil\displaystyle{#1}\hfil$\crcr}}}

% Special characters

\def\dag{\mathhexbox279}
\def\ddag{\mathhexbox27A}

\def\sectionmark{\mathhexbox278} % was \S in plain.tex
\def\paragmark{\mathhexbox27B}   % was \P in plain.tex

% END

\message{done.}
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