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alltt.sty
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applemac.def
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fontenc.sty
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fontmath.cfg
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fontmath.ltx
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fonttext.cfg
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graphpap.sty
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idx.tex
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inputenc.sty
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latex209.def
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latexrelease.sty
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latexsym.sty
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sample2e.tex
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sfonts.def
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shortvrb.sty
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showidx.sty
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Code Editor : fontmath.ltx
%% %% This is file `fontmath.ltx', %% generated with the docstrip utility. %% %% The original source files were: %% %% fontdef.dtx (with options: `math') %% %% This is a generated file. %% %% Copyright (C) 1993-2021 %% The LaTeX Project and any individual authors listed elsewhere %% in this file. %% %% This file was generated from file(s) of the LaTeX base system. %% -------------------------------------------------------------- %% %% It may be distributed and/or modified under the %% conditions of the LaTeX Project Public License, either version 1.3c %% of this license or (at your option) any later version. %% The latest version of this license is in %% https://www.latex-project.org/lppl.txt %% and version 1.3c or later is part of all distributions of LaTeX %% version 2008 or later. %% %% This file may only be distributed together with a copy of the LaTeX %% base system. You may however distribute the LaTeX base system without %% such generated files. %% %% The list of all files belonging to the LaTeX base distribution is %% given in the file `manifest.txt'. See also `legal.txt' for additional %% information. %% %% Details of how to use a configuration file to modify this part of %% the system are in the document `cfgguide.tex'. %% %% %%% From File: fontdef.dtx \ProvidesFile{fontmath.ltx} [2021/01/15 v3.0i LaTeX Kernel (Math font setup)] \typeout{=== Don't modify this file, use a .cfg file instead ===^^J} \DeclareFontEncoding{OML}{}{} \DeclareFontEncoding{OMS}{}{} \DeclareFontEncoding{OMX}{}{} \DeclareFontEncoding{U}{}{\noaccents@} \DeclareFontSubstitution{OML}{cmm}{m}{it} \DeclareFontSubstitution{OMS}{cmsy}{m}{n} \DeclareFontSubstitution{OMX}{cmex}{m}{n} \DeclareFontSubstitution{U}{cmr}{m}{n} \begingroup \nfss@catcodes \input {omlcmm.fd} \input {omscmsy.fd} \input {omxcmex.fd} \input {ucmr.fd} \endgroup \DeclareSymbolFont{operators} {OT1}{cmr} {m}{n} \DeclareSymbolFont{letters} {OML}{cmm} {m}{it} \DeclareSymbolFont{symbols} {OMS}{cmsy}{m}{n} \DeclareSymbolFont{largesymbols}{OMX}{cmex}{m}{n} \SetSymbolFont{operators}{bold}{OT1}{cmr} {bx}{n} \SetSymbolFont{letters} {bold}{OML}{cmm} {b}{it} \SetSymbolFont{symbols} {bold}{OMS}{cmsy}{b}{n} \DeclareSymbolFontAlphabet{\mathrm} {operators} \DeclareSymbolFontAlphabet{\mathnormal}{letters} \DeclareSymbolFontAlphabet{\mathcal} {symbols} \DeclareMathAlphabet {\mathbf}{OT1}{cmr}{bx}{n} \DeclareMathAlphabet {\mathsf}{OT1}{cmss}{m}{n} \DeclareMathAlphabet {\mathit}{OT1}{cmr}{m}{it} \DeclareMathAlphabet {\mathtt}{OT1}{cmtt}{m}{n} \SetMathAlphabet\mathsf{bold}{OT1}{cmss}{bx}{n} \SetMathAlphabet\mathit{bold}{OT1}{cmr}{bx}{it} \DeclareMathSizes{5}{5}{5}{5} \DeclareMathSizes{6}{6}{5}{5} \DeclareMathSizes{7}{7}{5}{5} \DeclareMathSizes{8}{8}{6}{5} \DeclareMathSizes{9}{9}{6}{5} \DeclareMathSizes{\@xpt}{\@xpt}{7}{5} \DeclareMathSizes{\@xipt}{\@xipt}{8}{6} \DeclareMathSizes{\@xiipt}{\@xiipt}{8}{6} \DeclareMathSizes{\@xivpt}{\@xivpt}{\@xpt}{7} \DeclareMathSizes{\@xviipt}{\@xviipt}{\@xiipt}{\@xpt} \DeclareMathSizes{\@xxpt}{\@xxpt}{\@xivpt}{\@xiipt} \DeclareMathSizes{\@xxvpt}{\@xxvpt}{\@xxpt}{\@xviipt} \DeclareMathSymbol{a}{\mathalpha}{letters}{`a} \DeclareMathSymbol{b}{\mathalpha}{letters}{`b} \DeclareMathSymbol{c}{\mathalpha}{letters}{`c} \DeclareMathSymbol{d}{\mathalpha}{letters}{`d} \DeclareMathSymbol{e}{\mathalpha}{letters}{`e} \DeclareMathSymbol{f}{\mathalpha}{letters}{`f} \DeclareMathSymbol{g}{\mathalpha}{letters}{`g} \DeclareMathSymbol{h}{\mathalpha}{letters}{`h} \DeclareMathSymbol{i}{\mathalpha}{letters}{`i} \DeclareMathSymbol{j}{\mathalpha}{letters}{`j} \DeclareMathSymbol{k}{\mathalpha}{letters}{`k} \DeclareMathSymbol{l}{\mathalpha}{letters}{`l} \DeclareMathSymbol{m}{\mathalpha}{letters}{`m} \DeclareMathSymbol{n}{\mathalpha}{letters}{`n} \DeclareMathSymbol{o}{\mathalpha}{letters}{`o} \DeclareMathSymbol{p}{\mathalpha}{letters}{`p} \DeclareMathSymbol{q}{\mathalpha}{letters}{`q} \DeclareMathSymbol{r}{\mathalpha}{letters}{`r} \DeclareMathSymbol{s}{\mathalpha}{letters}{`s} \DeclareMathSymbol{t}{\mathalpha}{letters}{`t} \DeclareMathSymbol{u}{\mathalpha}{letters}{`u} \DeclareMathSymbol{v}{\mathalpha}{letters}{`v} \DeclareMathSymbol{w}{\mathalpha}{letters}{`w} \DeclareMathSymbol{x}{\mathalpha}{letters}{`x} \DeclareMathSymbol{y}{\mathalpha}{letters}{`y} \DeclareMathSymbol{z}{\mathalpha}{letters}{`z} \DeclareMathSymbol{A}{\mathalpha}{letters}{`A} \DeclareMathSymbol{B}{\mathalpha}{letters}{`B} \DeclareMathSymbol{C}{\mathalpha}{letters}{`C} \DeclareMathSymbol{D}{\mathalpha}{letters}{`D} \DeclareMathSymbol{E}{\mathalpha}{letters}{`E} \DeclareMathSymbol{F}{\mathalpha}{letters}{`F} \DeclareMathSymbol{G}{\mathalpha}{letters}{`G} \DeclareMathSymbol{H}{\mathalpha}{letters}{`H} \DeclareMathSymbol{I}{\mathalpha}{letters}{`I} \DeclareMathSymbol{J}{\mathalpha}{letters}{`J} \DeclareMathSymbol{K}{\mathalpha}{letters}{`K} \DeclareMathSymbol{L}{\mathalpha}{letters}{`L} \DeclareMathSymbol{M}{\mathalpha}{letters}{`M} \DeclareMathSymbol{N}{\mathalpha}{letters}{`N} \DeclareMathSymbol{O}{\mathalpha}{letters}{`O} \DeclareMathSymbol{P}{\mathalpha}{letters}{`P} \DeclareMathSymbol{Q}{\mathalpha}{letters}{`Q} \DeclareMathSymbol{R}{\mathalpha}{letters}{`R} \DeclareMathSymbol{S}{\mathalpha}{letters}{`S} \DeclareMathSymbol{T}{\mathalpha}{letters}{`T} \DeclareMathSymbol{U}{\mathalpha}{letters}{`U} \DeclareMathSymbol{V}{\mathalpha}{letters}{`V} \DeclareMathSymbol{W}{\mathalpha}{letters}{`W} \DeclareMathSymbol{X}{\mathalpha}{letters}{`X} \DeclareMathSymbol{Y}{\mathalpha}{letters}{`Y} \DeclareMathSymbol{Z}{\mathalpha}{letters}{`Z} \DeclareMathSymbol{0}{\mathalpha}{operators}{`0} \DeclareMathSymbol{1}{\mathalpha}{operators}{`1} \DeclareMathSymbol{2}{\mathalpha}{operators}{`2} \DeclareMathSymbol{3}{\mathalpha}{operators}{`3} \DeclareMathSymbol{4}{\mathalpha}{operators}{`4} \DeclareMathSymbol{5}{\mathalpha}{operators}{`5} \DeclareMathSymbol{6}{\mathalpha}{operators}{`6} \DeclareMathSymbol{7}{\mathalpha}{operators}{`7} \DeclareMathSymbol{8}{\mathalpha}{operators}{`8} \DeclareMathSymbol{9}{\mathalpha}{operators}{`9} \DeclareMathSymbol{!}{\mathclose}{operators}{"21} \DeclareMathSymbol{*}{\mathbin}{symbols}{"03} % \ast \DeclareMathSymbol{+}{\mathbin}{operators}{"2B} \DeclareMathSymbol{,}{\mathpunct}{letters}{"3B} \DeclareMathSymbol{-}{\mathbin}{symbols}{"00} \DeclareMathSymbol{.}{\mathord}{letters}{"3A} \DeclareMathSymbol{:}{\mathrel}{operators}{"3A} \DeclareMathSymbol{;}{\mathpunct}{operators}{"3B} \DeclareMathSymbol{=}{\mathrel}{operators}{"3D} \DeclareMathSymbol{?}{\mathclose}{operators}{"3F} \mathcode`\ ="8000 % \space \mathcode`\'="8000 % ^\prime \mathcode`\_="8000 % \_ \DeclareMathDelimiter{(}{\mathopen} {operators}{"28}{largesymbols}{"00} \DeclareMathDelimiter{)}{\mathclose}{operators}{"29}{largesymbols}{"01} \DeclareMathDelimiter{[}{\mathopen} {operators}{"5B}{largesymbols}{"02} \DeclareMathDelimiter{]}{\mathclose}{operators}{"5D}{largesymbols}{"03} \DeclareMathDelimiter{<}{\mathopen}{symbols}{"68}{largesymbols}{"0A} \DeclareMathDelimiter{>}{\mathclose}{symbols}{"69}{largesymbols}{"0B} \DeclareMathSymbol{<}{\mathrel}{letters}{"3C} \DeclareMathSymbol{>}{\mathrel}{letters}{"3E} \DeclareMathDelimiter{/}{\mathord}{operators}{"2F}{largesymbols}{"0E} \DeclareMathSymbol{/}{\mathord}{letters}{"3D} \DeclareMathDelimiter{|}{\mathord}{symbols}{"6A}{largesymbols}{"0C} \expandafter\DeclareMathDelimiter\@backslashchar {\mathord}{symbols}{"6E}{largesymbols}{"0F} \DeclareMathSymbol{\alpha}{\mathord}{letters}{"0B} \DeclareMathSymbol{\beta}{\mathord}{letters}{"0C} \DeclareMathSymbol{\gamma}{\mathord}{letters}{"0D} \DeclareMathSymbol{\delta}{\mathord}{letters}{"0E} \DeclareMathSymbol{\epsilon}{\mathord}{letters}{"0F} \DeclareMathSymbol{\zeta}{\mathord}{letters}{"10} \DeclareMathSymbol{\eta}{\mathord}{letters}{"11} \DeclareMathSymbol{\theta}{\mathord}{letters}{"12} \DeclareMathSymbol{\iota}{\mathord}{letters}{"13} \DeclareMathSymbol{\kappa}{\mathord}{letters}{"14} \DeclareMathSymbol{\lambda}{\mathord}{letters}{"15} \DeclareMathSymbol{\mu}{\mathord}{letters}{"16} \DeclareMathSymbol{\nu}{\mathord}{letters}{"17} \DeclareMathSymbol{\xi}{\mathord}{letters}{"18} \DeclareMathSymbol{\pi}{\mathord}{letters}{"19} \DeclareMathSymbol{\rho}{\mathord}{letters}{"1A} \DeclareMathSymbol{\sigma}{\mathord}{letters}{"1B} \DeclareMathSymbol{\tau}{\mathord}{letters}{"1C} \DeclareMathSymbol{\upsilon}{\mathord}{letters}{"1D} \DeclareMathSymbol{\phi}{\mathord}{letters}{"1E} \DeclareMathSymbol{\chi}{\mathord}{letters}{"1F} \DeclareMathSymbol{\psi}{\mathord}{letters}{"20} \DeclareMathSymbol{\omega}{\mathord}{letters}{"21} \DeclareMathSymbol{\varepsilon}{\mathord}{letters}{"22} \DeclareMathSymbol{\vartheta}{\mathord}{letters}{"23} \DeclareMathSymbol{\varpi}{\mathord}{letters}{"24} \DeclareMathSymbol{\varrho}{\mathord}{letters}{"25} \DeclareMathSymbol{\varsigma}{\mathord}{letters}{"26} \DeclareMathSymbol{\varphi}{\mathord}{letters}{"27} \DeclareMathSymbol{\Gamma}{\mathalpha}{operators}{"00} \DeclareMathSymbol{\Delta}{\mathalpha}{operators}{"01} \DeclareMathSymbol{\Theta}{\mathalpha}{operators}{"02} \DeclareMathSymbol{\Lambda}{\mathalpha}{operators}{"03} \DeclareMathSymbol{\Xi}{\mathalpha}{operators}{"04} \DeclareMathSymbol{\Pi}{\mathalpha}{operators}{"05} \DeclareMathSymbol{\Sigma}{\mathalpha}{operators}{"06} \DeclareMathSymbol{\Upsilon}{\mathalpha}{operators}{"07} \DeclareMathSymbol{\Phi}{\mathalpha}{operators}{"08} \DeclareMathSymbol{\Psi}{\mathalpha}{operators}{"09} \DeclareMathSymbol{\Omega}{\mathalpha}{operators}{"0A} \DeclareMathSymbol{\aleph}{\mathord}{symbols}{"40} \DeclareMathSymbol{\imath}{\mathord}{letters}{"7B} \DeclareMathSymbol{\jmath}{\mathord}{letters}{"7C} \DeclareMathSymbol{\ell}{\mathord}{letters}{"60} \DeclareMathSymbol{\wp}{\mathord}{letters}{"7D} \DeclareMathSymbol{\Re}{\mathord}{symbols}{"3C} \DeclareMathSymbol{\Im}{\mathord}{symbols}{"3D} \DeclareMathSymbol{\partial}{\mathord}{letters}{"40} \DeclareMathSymbol{\infty}{\mathord}{symbols}{"31} \DeclareMathSymbol{\prime}{\mathord}{symbols}{"30} \DeclareMathSymbol{\emptyset}{\mathord}{symbols}{"3B} \DeclareMathSymbol{\nabla}{\mathord}{symbols}{"72} \DeclareMathSymbol{\top}{\mathord}{symbols}{"3E} \DeclareMathSymbol{\bot}{\mathord}{symbols}{"3F} \DeclareMathSymbol{\triangle}{\mathord}{symbols}{"34} \DeclareMathSymbol{\forall}{\mathord}{symbols}{"38} \DeclareMathSymbol{\exists}{\mathord}{symbols}{"39} \DeclareMathSymbol{\neg}{\mathord}{symbols}{"3A} \DeclareMathSymbol{\lnot}{\mathord}{symbols}{"3A} \DeclareMathSymbol{\flat}{\mathord}{letters}{"5B} \DeclareMathSymbol{\natural}{\mathord}{letters}{"5C} \DeclareMathSymbol{\sharp}{\mathord}{letters}{"5D} \DeclareMathSymbol{\clubsuit}{\mathord}{symbols}{"7C} \DeclareMathSymbol{\diamondsuit}{\mathord}{symbols}{"7D} \DeclareMathSymbol{\heartsuit}{\mathord}{symbols}{"7E} \DeclareMathSymbol{\spadesuit}{\mathord}{symbols}{"7F} \DeclareRobustCommand\hbar{{\mathchar'26\mkern-9muh}} \DeclareRobustCommand\surd{{\mathchar"1270}} \DeclareRobustCommand\angle{{\vbox{\ialign{$\m@th\scriptstyle##$\crcr \not\mathrel{\mkern14mu}\crcr \noalign{\nointerlineskip} \mkern2.5mu\leaders\hrule \@height.34pt\hfill\mkern2.5mu\crcr}}}} \DeclareMathSymbol{\coprod}{\mathop}{largesymbols}{"60} \DeclareMathSymbol{\bigvee}{\mathop}{largesymbols}{"57} \DeclareMathSymbol{\bigwedge}{\mathop}{largesymbols}{"56} \DeclareMathSymbol{\biguplus}{\mathop}{largesymbols}{"55} \DeclareMathSymbol{\bigcap}{\mathop}{largesymbols}{"54} \DeclareMathSymbol{\bigcup}{\mathop}{largesymbols}{"53} \DeclareMathSymbol{\intop}{\mathop}{largesymbols}{"52} \DeclareRobustCommand\int{\intop\nolimits} \DeclareMathSymbol{\prod}{\mathop}{largesymbols}{"51} \DeclareMathSymbol{\sum}{\mathop}{largesymbols}{"50} \DeclareMathSymbol{\bigotimes}{\mathop}{largesymbols}{"4E} \DeclareMathSymbol{\bigoplus}{\mathop}{largesymbols}{"4C} \DeclareMathSymbol{\bigodot}{\mathop}{largesymbols}{"4A} \DeclareMathSymbol{\ointop}{\mathop}{largesymbols}{"48} \DeclareRobustCommand\oint{\ointop\nolimits} \DeclareMathSymbol{\bigsqcup}{\mathop}{largesymbols}{"46} \DeclareMathSymbol{\smallint}{\mathop}{symbols}{"73} \DeclareMathSymbol{\triangleleft}{\mathbin}{letters}{"2F} \DeclareMathSymbol{\triangleright}{\mathbin}{letters}{"2E} \DeclareMathSymbol{\bigtriangleup}{\mathbin}{symbols}{"34} \DeclareMathSymbol{\bigtriangledown}{\mathbin}{symbols}{"35} \DeclareMathSymbol{\varbigtriangleup}{\mathbin}{symbols}{"34} \DeclareMathSymbol{\varbigtriangledown}{\mathbin}{symbols}{"35} \DeclareMathSymbol{\wedge}{\mathbin}{symbols}{"5E} \DeclareMathSymbol{\vee}{\mathbin}{symbols}{"5F} \DeclareMathSymbol{\land}{\mathbin}{symbols}{"5E} \DeclareMathSymbol{\lor}{\mathbin}{symbols}{"5F} \DeclareMathSymbol{\cap}{\mathbin}{symbols}{"5C} \DeclareMathSymbol{\cup}{\mathbin}{symbols}{"5B} \DeclareMathSymbol{\ddagger}{\mathbin}{symbols}{"7A} \DeclareMathSymbol{\dagger}{\mathbin}{symbols}{"79} \DeclareMathSymbol{\sqcap}{\mathbin}{symbols}{"75} \DeclareMathSymbol{\sqcup}{\mathbin}{symbols}{"74} \DeclareMathSymbol{\uplus}{\mathbin}{symbols}{"5D} \DeclareMathSymbol{\amalg}{\mathbin}{symbols}{"71} \DeclareMathSymbol{\diamond}{\mathbin}{symbols}{"05} \DeclareMathSymbol{\bullet}{\mathbin}{symbols}{"0F} \DeclareMathSymbol{\wr}{\mathbin}{symbols}{"6F} \DeclareMathSymbol{\div}{\mathbin}{symbols}{"04} \DeclareMathSymbol{\odot}{\mathbin}{symbols}{"0C} \DeclareMathSymbol{\oslash}{\mathbin}{symbols}{"0B} \DeclareMathSymbol{\otimes}{\mathbin}{symbols}{"0A} \DeclareMathSymbol{\ominus}{\mathbin}{symbols}{"09} \DeclareMathSymbol{\oplus}{\mathbin}{symbols}{"08} \DeclareMathSymbol{\mp}{\mathbin}{symbols}{"07} \DeclareMathSymbol{\pm}{\mathbin}{symbols}{"06} \DeclareMathSymbol{\circ}{\mathbin}{symbols}{"0E} \DeclareMathSymbol{\bigcirc}{\mathbin}{symbols}{"0D} \DeclareMathSymbol{\setminus}{\mathbin}{symbols}{"6E} \DeclareMathSymbol{\cdot}{\mathbin}{symbols}{"01} \DeclareMathSymbol{\ast}{\mathbin}{symbols}{"03} \DeclareMathSymbol{\times}{\mathbin}{symbols}{"02} \DeclareMathSymbol{\star}{\mathbin}{letters}{"3F} \DeclareMathSymbol{\propto}{\mathrel}{symbols}{"2F} \DeclareMathSymbol{\sqsubseteq}{\mathrel}{symbols}{"76} \DeclareMathSymbol{\sqsupseteq}{\mathrel}{symbols}{"77} \DeclareMathSymbol{\parallel}{\mathrel}{symbols}{"6B} \DeclareMathSymbol{\mid}{\mathrel}{symbols}{"6A} \DeclareMathSymbol{\dashv}{\mathrel}{symbols}{"61} \DeclareMathSymbol{\vdash}{\mathrel}{symbols}{"60} \DeclareMathSymbol{\nearrow}{\mathrel}{symbols}{"25} \DeclareMathSymbol{\searrow}{\mathrel}{symbols}{"26} \DeclareMathSymbol{\nwarrow}{\mathrel}{symbols}{"2D} \DeclareMathSymbol{\swarrow}{\mathrel}{symbols}{"2E} \DeclareMathSymbol{\Leftrightarrow}{\mathrel}{symbols}{"2C} \DeclareMathSymbol{\Leftarrow}{\mathrel}{symbols}{"28} \DeclareMathSymbol{\Rightarrow}{\mathrel}{symbols}{"29} \DeclareRobustCommand\neq{\not=} \DeclareRobustCommand\ne{\not=} \DeclareMathSymbol{\leq}{\mathrel}{symbols}{"14} \DeclareMathSymbol{\geq}{\mathrel}{symbols}{"15} \DeclareMathSymbol{\le}{\mathrel}{symbols}{"14} \DeclareMathSymbol{\ge}{\mathrel}{symbols}{"15} \DeclareMathSymbol{\succ}{\mathrel}{symbols}{"1F} \DeclareMathSymbol{\prec}{\mathrel}{symbols}{"1E} \DeclareMathSymbol{\approx}{\mathrel}{symbols}{"19} \DeclareMathSymbol{\succeq}{\mathrel}{symbols}{"17} \DeclareMathSymbol{\preceq}{\mathrel}{symbols}{"16} \DeclareMathSymbol{\supset}{\mathrel}{symbols}{"1B} \DeclareMathSymbol{\subset}{\mathrel}{symbols}{"1A} \DeclareMathSymbol{\supseteq}{\mathrel}{symbols}{"13} \DeclareMathSymbol{\subseteq}{\mathrel}{symbols}{"12} \DeclareMathSymbol{\in}{\mathrel}{symbols}{"32} \DeclareMathSymbol{\ni}{\mathrel}{symbols}{"33} \DeclareMathSymbol{\owns}{\mathrel}{symbols}{"33} \DeclareMathSymbol{\gg}{\mathrel}{symbols}{"1D} \DeclareMathSymbol{\ll}{\mathrel}{symbols}{"1C} \DeclareMathSymbol{\not}{\mathrel}{symbols}{"36} \DeclareMathSymbol{\leftrightarrow}{\mathrel}{symbols}{"24} \DeclareMathSymbol{\leftarrow}{\mathrel}{symbols}{"20} \DeclareMathSymbol{\rightarrow}{\mathrel}{symbols}{"21} \DeclareMathSymbol{\gets}{\mathrel}{symbols}{"20} \DeclareMathSymbol{\to}{\mathrel}{symbols}{"21} \DeclareMathSymbol{\mapstochar}{\mathrel}{symbols}{"37} \DeclareRobustCommand\mapsto{\mapstochar\rightarrow} \DeclareMathSymbol{\sim}{\mathrel}{symbols}{"18} \DeclareMathSymbol{\simeq}{\mathrel}{symbols}{"27} \DeclareMathSymbol{\perp}{\mathrel}{symbols}{"3F} \DeclareMathSymbol{\equiv}{\mathrel}{symbols}{"11} \DeclareMathSymbol{\asymp}{\mathrel}{symbols}{"10} \DeclareMathSymbol{\smile}{\mathrel}{letters}{"5E} \DeclareMathSymbol{\frown}{\mathrel}{letters}{"5F} \DeclareMathSymbol{\leftharpoonup}{\mathrel}{letters}{"28} \DeclareMathSymbol{\leftharpoondown}{\mathrel}{letters}{"29} \DeclareMathSymbol{\rightharpoonup}{\mathrel}{letters}{"2A} \DeclareMathSymbol{\rightharpoondown}{\mathrel}{letters}{"2B} \DeclareRobustCommand \cong{\mathrel{\mathpalette\@vereq\sim}} % congruence sign \def\@vereq#1#2{\lower.5\p@\vbox{\lineskiplimit\maxdimen\lineskip-.5\p@ \ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}} \DeclareRobustCommand \notin{\mathrel{\m@th\mathpalette\c@ncel\in}} \def\c@ncel#1#2{\m@th\ooalign{$\hfil#1\mkern1mu/\hfil$\crcr$#1#2$}} \DeclareRobustCommand \rightleftharpoons{\mathrel{\mathpalette\rlh@{}}} \def\rlh@#1{\vcenter{\m@th\hbox{\ooalign{\raise2pt \hbox{$#1\rightharpoonup$}\crcr $#1\leftharpoondown$}}}} \DeclareRobustCommand \doteq{\buildrel\textstyle.\over=} \DeclareRobustCommand \joinrel{\mathrel{\mkern-3mu}} \DeclareRobustCommand \relbar{\mathrel{\smash-}} % \smash, because - % has the same height as + \DeclareRobustCommand \Relbar{\mathrel{=}} \DeclareMathSymbol{\lhook}{\mathrel}{letters}{"2C} \DeclareRobustCommand\hookrightarrow{\lhook\joinrel\rightarrow} \DeclareMathSymbol{\rhook}{\mathrel}{letters}{"2D} \DeclareRobustCommand\hookleftarrow{\leftarrow\joinrel\rhook} \DeclareRobustCommand \bowtie{\mathrel\triangleright\joinrel\mathrel\triangleleft} \DeclareRobustCommand \models{\mathrel{|}\joinrel\Relbar} \DeclareRobustCommand \Longrightarrow{\Relbar\joinrel\Rightarrow} \DeclareRobustCommand\longrightarrow {\relbar\joinrel\rightarrow} \DeclareRobustCommand\longleftarrow {\leftarrow\joinrel\relbar} \DeclareRobustCommand \Longleftarrow{\Leftarrow\joinrel\Relbar} \DeclareRobustCommand \longmapsto{\mapstochar\longrightarrow} \DeclareRobustCommand \longleftrightarrow{\leftarrow\joinrel\rightarrow} \DeclareRobustCommand \Longleftrightarrow{\Leftarrow\joinrel\Rightarrow} \DeclareRobustCommand \iff{\;\Longleftrightarrow\;} \DeclareMathSymbol{\ldotp}{\mathpunct}{letters}{"3A} \DeclareMathSymbol{\cdotp}{\mathpunct}{symbols}{"01} \DeclareMathSymbol{\colon}{\mathpunct}{operators}{"3A} \DeclareRobustCommand \cdots{\mathinner{\cdotp\cdotp\cdotp}} \DeclareRobustCommand \vdots{\vbox{\baselineskip4\p@ \lineskiplimit\z@ \kern6\p@\hbox{.}\hbox{.}\hbox{.}}} \DeclareRobustCommand \ddots{\mathinner{\mkern1mu\raise7\p@ \vbox{\kern7\p@\hbox{.}}\mkern2mu \raise4\p@\hbox{.}\mkern2mu\raise\p@\hbox{.}\mkern1mu}} \DeclareMathAccent{\acute}{\mathalpha}{operators}{"13} \DeclareMathAccent{\grave}{\mathalpha}{operators}{"12} \DeclareMathAccent{\ddot}{\mathalpha}{operators}{"7F} \DeclareMathAccent{\tilde}{\mathalpha}{operators}{"7E} \DeclareMathAccent{\bar}{\mathalpha}{operators}{"16} \DeclareMathAccent{\breve}{\mathalpha}{operators}{"15} \DeclareMathAccent{\check}{\mathalpha}{operators}{"14} \DeclareMathAccent{\hat}{\mathalpha}{operators}{"5E} \DeclareMathAccent{\vec}{\mathord}{letters}{"7E} \DeclareMathAccent{\dot}{\mathalpha}{operators}{"5F} \DeclareMathAccent{\widetilde}{\mathord}{largesymbols}{"65} \DeclareMathAccent{\widehat}{\mathord}{largesymbols}{"62} \DeclareMathAccent{\mathring}{\mathalpha}{operators}{"17} \DeclareMathRadical{\sqrtsign}{symbols}{"70}{largesymbols}{"70} \DeclareRobustCommand\overrightarrow[1]{\vbox{\m@th\ialign{##\crcr \rightarrowfill\crcr\noalign{\kern-\p@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}} \DeclareRobustCommand\overleftarrow[1]{\vbox{\m@th\ialign{##\crcr \leftarrowfill\crcr\noalign{\kern-\p@\nointerlineskip}% $\hfil\displaystyle{#1}\hfil$\crcr}}} \DeclareRobustCommand\overbrace[1] {\mathop{\vbox{\m@th\ialign{##\crcr\noalign{\kern3\p@}% \downbracefill\crcr\noalign{\kern3\p@\nointerlineskip}% $\hfil\displaystyle{#1}\hfil$\crcr}}}\limits} \DeclareRobustCommand\underbrace[1]{\mathop{\vtop{\m@th\ialign{##\crcr $\hfil\displaystyle{#1}\hfil$\crcr \noalign{\kern3\p@\nointerlineskip}% \upbracefill\crcr\noalign{\kern3\p@}}}}\limits} \DeclareRobustCommand\skew[3] {{\muskip\z@#1mu\divide\muskip\z@\tw@ \mkern\muskip\z@ #2{\mkern-\muskip\z@{#3}\mkern\muskip\z@}\mkern-\muskip\z@}{}} \DeclareRobustCommand\rightarrowfill{$\m@th\smash-\mkern-7mu% \cleaders\hbox{$\mkern-2mu\smash-\mkern-2mu$}\hfill \mkern-7mu\mathord\rightarrow$} \DeclareRobustCommand\leftarrowfill{$\m@th\mathord\leftarrow\mkern-7mu% \cleaders\hbox{$\mkern-2mu\smash-\mkern-2mu$}\hfill \mkern-7mu\smash-$} \DeclareMathSymbol{\braceld}{\mathord}{largesymbols}{"7A} \DeclareMathSymbol{\bracerd}{\mathord}{largesymbols}{"7B} \DeclareMathSymbol{\bracelu}{\mathord}{largesymbols}{"7C} \DeclareMathSymbol{\braceru}{\mathord}{largesymbols}{"7D} \DeclareRobustCommand\downbracefill{$\m@th \setbox\z@\hbox{$\braceld$}% \braceld\leaders\vrule \@height\ht\z@ \@depth\z@\hfill\braceru \bracelu\leaders\vrule \@height\ht\z@ \@depth\z@\hfill\bracerd$} \DeclareRobustCommand\upbracefill{$\m@th \setbox\z@\hbox{$\braceld$}% \bracelu\leaders\vrule \@height\ht\z@ \@depth\z@\hfill\bracerd \braceld\leaders\vrule \@height\ht\z@ \@depth\z@\hfill\braceru$} \DeclareMathDelimiter{\lmoustache} % top from (, bottom from ) {\mathopen}{largesymbols}{"7A}{largesymbols}{"40} \DeclareMathDelimiter{\rmoustache} % top from ), bottom from ( {\mathclose}{largesymbols}{"7B}{largesymbols}{"41} \DeclareMathDelimiter{\arrowvert} % arrow without arrowheads {\mathord}{symbols}{"6A}{largesymbols}{"3C} \DeclareMathDelimiter{\Arrowvert} % double arrow without arrowheads {\mathord}{symbols}{"6B}{largesymbols}{"3D} \DeclareMathDelimiter{\Vert} {\mathord}{symbols}{"6B}{largesymbols}{"0D} \DeclareMathDelimiter{\|} {\mathord}{symbols}{"6B}{largesymbols}{"0D} \DeclareMathDelimiter{\vert} {\mathord}{symbols}{"6A}{largesymbols}{"0C} \DeclareMathDelimiter{\uparrow} {\mathrel}{symbols}{"22}{largesymbols}{"78} \DeclareMathDelimiter{\downarrow} {\mathrel}{symbols}{"23}{largesymbols}{"79} \DeclareMathDelimiter{\updownarrow} {\mathrel}{symbols}{"6C}{largesymbols}{"3F} \DeclareMathDelimiter{\Uparrow} {\mathrel}{symbols}{"2A}{largesymbols}{"7E} \DeclareMathDelimiter{\Downarrow} {\mathrel}{symbols}{"2B}{largesymbols}{"7F} \DeclareMathDelimiter{\Updownarrow} {\mathrel}{symbols}{"6D}{largesymbols}{"77} \DeclareMathDelimiter{\backslash} % for double coset G\backslash H {\mathord}{symbols}{"6E}{largesymbols}{"0F} \DeclareMathDelimiter{\rangle} {\mathclose}{symbols}{"69}{largesymbols}{"0B} \DeclareMathDelimiter{\langle} {\mathopen}{symbols}{"68}{largesymbols}{"0A} \DeclareMathDelimiter{\rbrace} {\mathclose}{symbols}{"67}{largesymbols}{"09} \DeclareMathDelimiter{\lbrace} {\mathopen}{symbols}{"66}{largesymbols}{"08} \DeclareMathDelimiter{\rceil} {\mathclose}{symbols}{"65}{largesymbols}{"07} \DeclareMathDelimiter{\lceil} {\mathopen}{symbols}{"64}{largesymbols}{"06} \DeclareMathDelimiter{\rfloor} {\mathclose}{symbols}{"63}{largesymbols}{"05} \DeclareMathDelimiter{\lfloor} {\mathopen}{symbols}{"62}{largesymbols}{"04} \DeclareMathDelimiter{\lgroup} % extensible ( with sharper tips {\mathopen}{largesymbols}{"3A}{largesymbols}{"3A} \DeclareMathDelimiter{\rgroup} % extensible ) with sharper tips {\mathclose}{largesymbols}{"3B}{largesymbols}{"3B} \DeclareMathDelimiter{\bracevert} % the vertical bar that extends braces {\mathord}{largesymbols}{"3E}{largesymbols}{"3E} \DeclareMathSymbol{\mathparagraph}{\mathord}{symbols}{"7B} \DeclareMathSymbol{\mathsection}{\mathord}{symbols}{"78} \DeclareMathSymbol{\mathdollar}{\mathord}{operators}{"24} \DeclareRobustCommand\mathsterling{\mathit{\mathchar"7024}} \DeclareRobustCommand\mathunderscore{\kern.06em\vbox{\hrule\@width.3em}} \DeclareRobustCommand\mathellipsis{\mathinner{\ldotp\ldotp\ldotp}}% \DeclareRobustCommand\big[1]{\leavevmode@ifvmode {\hbox{$\left#1\vbox to8.5\p@{}\right.\n@space$}}} \DeclareRobustCommand\Big[1]{\leavevmode@ifvmode {\hbox{$\left#1\vbox to11.5\p@{}\right.\n@space$}}} \DeclareRobustCommand\bigg[1]{\leavevmode@ifvmode {\hbox{$\left#1\vbox to14.5\p@{}\right.\n@space$}}} \DeclareRobustCommand\Bigg[1]{\leavevmode@ifvmode {\hbox{$\left#1\vbox to17.5\p@{}\right.\n@space$}}} \def\n@space{\nulldelimiterspace\z@ \m@th} \def\operator@font{\mathgroup\symoperators} \thinmuskip=3mu \medmuskip=4mu plus 2mu minus 4mu \thickmuskip=5mu plus 5mu \endinput %% %% End of file `fontmath.ltx'.
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