%% 
%% This is file `lucbmath.sty', generated 
%% on <1995/2/23> with the docstrip utility (1.1).
%% 
%% The original source files were:
%% 
%% lucida.dtx  (with options: `lucbmath')
%% Copyright (C) 1993 Sebastian Rahtz. All rights reserved. 
%% This is a generated file for *PSNFSS2e*. Permission is granted to to 
%% customize the declarations in this file to serve the needs of your 
%% installation. However, no permission is granted to distribute a 
%% modified version of this file under its original name. 
%% 
\def\fileversion{3.2}
\def\filedate{1995/01/27}
\def\docdate {1995/01/27}
\DeclareOption{kb}{% this is for Berry-type font names
\def\Lucida@names{0}}
\DeclareOption{yy}{% this is for Y\&Y font names
\def\Lucida@names{1}}
\ExecuteOptions{kb} 
\ProcessOptions
\ifnum\Lucida@names=0
 \DeclareFontEncoding{LMR}{}{}
 \DeclareFontSubstitution{LMR}{hlcm}{m}{n}
 \DeclareSymbolFont{letters}{OML}{hlcm}{m}{it}
 \DeclareSymbolFont{symbols}{OMS}{hlcy}{m}{n}
 \DeclareSymbolFont{largesymbols}{OMX}{hlcv}{m}{n}
 \SetSymbolFont{letters}{bold}{OML}{hlcm}{b}{it}
 \SetSymbolFont{symbols}{bold}{OMS}{hlcy}{b}{n}
 \DeclareSymbolFont{italics}{\encodingdefault}{\rmdefault}{m}{it}
 \DeclareSymbolFont{arrows}{LMR}{hlcm}{m}{n}
\else
 \DeclareFontEncoding{LMR}{}{}
 \DeclareFontSubstitution{LMR}{lbm}{m}{n}
 \DeclareSymbolFont{letters}{OML}{lbm}{m}{it}
 \DeclareSymbolFont{symbols}{OMS}{lby}{m}{n}
 \DeclareSymbolFont{largesymbols}{OMX}{lbv}{m}{n}
 \SetSymbolFont{letters}{bold}{OML}{lbm}{b}{it}
 \SetSymbolFont{symbols}{bold}{OMS}{lby}{b}{n}
 \DeclareSymbolFont{italics}{\encodingdefault}{\rmdefault}{m}{it}
 \DeclareSymbolFont{arrows}{LMR}{lbm}{m}{n}
\fi
\def\Lucidasizes{%
  \def\@vpt{5.2}%
  \def\@vipt{6.1}%
  \def\@viipt{6.9}%
  \def\@viiipt{7.8}%
  \def\@ixpt{8.6}%
  \def\@xpt{9.5}%
  \def\@xipt{10.4}%
  \def\@xiipt{11.2}%
  \def\@xivpt{12.9}%
  \def\@xviipt{15.5}%
  \def\@xxpt{18.1}%
  \def\@xxvpt{22.4}%
 \DeclareMathSizes{5.2}{5.2}{5.2}{5.2}
 \DeclareMathSizes{6.1}{6.1}{5.2}{5.2}
 \DeclareMathSizes{6.9}{6.9}{5.2}{5.2}
 \DeclareMathSizes{7.8}{7.8}{6.1}{5.2}
 \DeclareMathSizes{8.6}{8.6}{6.1}{5.2}
 \DeclareMathSizes{9.5}{9.5}{6.9}{5.2}
 \DeclareMathSizes{10.95}{10.95}{6.9}{5.2}
 \DeclareMathSizes{11.2}{11.2}{7.8}{6.1}
 \DeclareMathSizes{12.9}{12.9}{9.5}{6.9}
 \DeclareMathSizes{15.5}{15.5}{11.2}{9.5}
 \DeclareMathSizes{18.1}{18.1}{12.9}{11.2}
 \DeclareMathSizes{22.4}{22.4}{18.1}{15.5}
}%
\def\CMRsizes{%
 \def\@vpt{5}%
 \def\@vipt{6}%
 \def\@viipt{7}%
 \def\@viiipt{8}%
 \def\@ixpt{9}%
 \def\@xpt{10}%
 \def\@xipt{11}%
 \def\@xiipt{12}%
 \def\@xivpt{14}%
 \def\@xviipt{17}%
 \def\@xxpt{20}%
 \def\@xxvpt{25}%
}%
\AtEndOfPackage{\Lucidasizes}
\DeclareSymbolFont{operators}{OT1}{\rmdefault}{m}{n}
\SetSymbolFont{operators}{bold}{OT1}{\rmdefault}{b}{n}%
\SetSymbolFont{operators}{normal}{OT1}{\rmdefault}{m}{n}%
\DeclareMathAlphabet      {\mathbf}{\encodingdefault}{\rmdefault}{b}{n}%
\DeclareMathAlphabet      {\mathrm}{\encodingdefault}{\rmdefault}{m}{n}%
\DeclareMathAlphabet      {\mathsf}{\encodingdefault}{\sfdefault}{m}{n}%
\DeclareMathAlphabet      {\mathit}{\encodingdefault}{\rmdefault}{m}{it}%
\DeclareMathAlphabet      {\mathtt}{\encodingdefault}{\ttdefault}{m}{n}%
\SetMathAlphabet{\mathbf}{bold}{\encodingdefault}{\rmdefault}{b}{n}%
\SetMathAlphabet{\mathsf}{bold}{\encodingdefault}{\sfdefault}{b}{n}%
\SetMathAlphabet{\mathrm}{bold}{\encodingdefault}{\rmdefault}{b}{n}%
\SetMathAlphabet{\mathit}{bold}{\encodingdefault}{\rmdefault}{b}{it}%
\SetMathAlphabet{\mathtt}{bold}{\encodingdefault}{\ttdefault}{b}{n}%
\DeclareSymbolFontAlphabet{\bbold}{arrows}
\ifnum\Lucida@names=0
 \DeclareMathAccent\vec  {\mathord}{letters}{"7E}
\else
 \DeclareMathAccent\vec  {\mathord}{letters}{"7E}
 \DeclareMathAccent\dot  {\mathalpha}{operators}{"C7}
\fi
\@ifpackageloaded{amsfonts}{%
  \def\biggg{\bBigg@\thr@@} 
  \def\Biggg{\bBigg@{3.5}}
}{% 
  \def\big#1{{\hbox{$\left#1\vbox to8.20\p@{}\right.\n@space$}}}
  \def\Big#1{{\hbox{$\left#1\vbox to10.80\p@{}\right.\n@space$}}}
  \def\bigg#1{{\hbox{$\left#1\vbox to13.42\p@{}\right.\n@space$}}}
  \def\Bigg#1{{\hbox{$\left#1\vbox to16.03\p@{}\right.\n@space$}}}
  \def\biggg#1{{\hbox{$\left#1\vbox to17.72\p@{}\right.\n@space$}}}
  \def\Biggg#1{{\hbox{$\left#1\vbox to21.25\p@{}\right.\n@space$}}}
  \def\n@space{\nulldelimiterspace\z@ \m@th}
}
\def\bigggl{\mathopen\biggg}
\def\bigggr{\mathclose\biggg}
\def\Bigggl{\mathopen\Biggg}
\def\Bigggr{\mathclose\Biggg}
\mathcode`\[="4186 \delcode`\[="186302 
\mathcode`\]="5187 \delcode`\]="187303
\mathcode`\(="4184 \delcode`\(="184300
\mathcode`\)="5185 \delcode`\)="185301
\mathcode`\=="3283 
\mathcode`\+="2282
\mathcode`\/="013D \delcode`\/="13D30E
\def\ldbrack{\delimiter"4182382 }
\def\rdbrack{\delimiter"5183383 }
\DeclareMathSymbol{\surfintop}{1}{largesymbols}{"90}
\def\surfint{\surfintop\nolimits}
\DeclareMathSymbol{\midintop}{1}{largesymbols}{"92} 
\def\midint{\midintop\nolimits}
\DeclareMathSymbol{\midointop}{1}{largesymbols}{"93}
\def\midoint{\midointop\nolimits}
\DeclareMathSymbol{\midsurfintop}{1}{largesymbols}{"94}
\def\midsurfint{\midsurfintop\nolimits}
\def\largeint{\delimiter"135A395 }
\def\joinrel{\mathrel{\mkern-4mu}} % \def\joinrel{\mathrel{\mkern-3mu}}
\def\relbar{\mathrel{\smash{\mathchar"3\hexnumber@\symarrows 2D}}\mathrel{\mkern-2.5mu}}
\def\Relbar{\mathrel{\mathchar"3\hexnumber@\symarrows 3D}\mathrel{\mkern-2.5mu}}
\def\longleftarrow{\leftarrow\relbar\mathrel{\mkern4mu}}
\def\longrightarrow{\mathrel{\mkern4mu}\relbar\rightarrow}
\def\Longleftarrow{\Leftarrow\Relbar\mathrel{\mkern4mu}}
\def\Longrightarrow{\mathrel{\mkern4mu}\Relbar\Rightarrow}
\let\bowtie\undefined
\let\models\undefined
\let\doteq\undefined
\let\cong\undefined
\let\angle\undefined
\DeclareMathSymbol{\bowtie}{3}{letters}{"F6}
\DeclareMathSymbol{\models}{3}{symbols}{"EE}
\DeclareMathSymbol{\doteq}{3}{symbols}{"C9}
\DeclareMathSymbol{\cong}{3}{symbols}{"9B}
\DeclareMathSymbol{\angle}{0}{symbols}{"8B}
\let\Box\undefined
\let\Diamond\undefined
\let\leadsto\undefined
\let\neq\undefined
\let\hookleftarrow\undefined
\let\hookrightarrow\undefined
\let\mapsto\undefined
\let\notin\undefined
\let\iff\undefined
\let\rightleftharpoons\undefined
\DeclareMathSymbol{\neq}{3}{arrows}{"94}
\DeclareMathSymbol{\rightleftharpoons}{3}{arrows}{"7A}
\DeclareMathSymbol{\leftrightharpoons}{3}{arrows}{"79}
\DeclareMathSymbol{\hookleftarrow}{3}{arrows}{"3C}
\DeclareMathSymbol{\hookrightarrow}{3}{arrows}{"3E}
\DeclareMathSymbol{\mapsto}{3}{arrows}{"2C}
\def\longmapsto{\mapstochar\longrightarrow}
\let\Join\undefined
\let\rhd\undefined
\let\lhd\undefined
\let\unrhd\undefined
\let\unlhd\undefined
\DeclareMathSymbol{\Join}{3}{letters}{"F6}
\DeclareMathSymbol{\rhd}{3}{letters}{"2E}
\DeclareMathSymbol{\lhd}{3}{letters}{"2F}
\DeclareMathSymbol{\unlhd}{3}{symbols}{"F4}
\DeclareMathSymbol{\unrhd}{3}{symbols}{"F5}
\DeclareMathSymbol{\Box}{0}{arrows}{"02} 
\DeclareMathSymbol{\Diamond}{0}{arrows}{"08}
\DeclareMathSymbol{\leadsto}{3}{arrows}{"8E} 
\DeclareMathSymbol{\leadsfrom}{3}{arrows}{"8D}
\def\mathstrut{\vphantom{f}}
\@ifpackageloaded{amstex}{}{%
  \def\matrix#1{\null\,\vcenter{\normalbaselines\m@th
    \ialign{\hfil$##$\hfil&&\quad\hfil$##$\hfil\crcr
      \mathstrut\crcr\noalign{\kern-0.9\baselineskip}
     #1\crcr\mathstrut\crcr\noalign{\kern-0.9\baselineskip}}}\,}
}
\def\r@@t#1#2{\setbox\z@\hbox{$\m@th#1\sqrt{#2}$}
  \dimen@\ht\z@ \advance\dimen@-\dp\z@
  \mkern5mu\raise.6\dimen@\copy\rootbox \mkern-7.5mu \box\z@}
\DeclareMathSymbol{\defineequal}{3}{symbols}{"D6}
\DeclareMathSymbol{\notleq}{3}{arrows}{"9C}
\DeclareMathSymbol{\notgeq}{3}{arrows}{"9D}
\DeclareMathSymbol{\notequiv}{3}{arrows}{"95}
\DeclareMathSymbol{\notprec}{3}{arrows}{"E5}
\DeclareMathSymbol{\notsucc}{3}{arrows}{"E6}
\DeclareMathSymbol{\notapprox}{3}{arrows}{"98}
\DeclareMathSymbol{\notpreceq}{3}{arrows}{"E7}
\DeclareMathSymbol{\notsucceq}{3}{arrows}{"E8}
\DeclareMathSymbol{\notasymp}{3}{arrows}{"F3}
\DeclareMathSymbol{\notsubset}{3}{arrows}{"C6}
\DeclareMathSymbol{\notsupset}{3}{arrows}{"C7}
\DeclareMathSymbol{\notsim}{3}{arrows}{"96}
\DeclareMathSymbol{\notsubseteq}{3}{arrows}{"C8}
\DeclareMathSymbol{\notsupseteq}{3}{arrows}{"C9}
\DeclareMathSymbol{\notsimeq}{3}{arrows}{"97}
\DeclareMathSymbol{\notsqsubseteq}{3}{arrows}{"D4}
\DeclareMathSymbol{\notsqsupseteq}{3}{arrows}{"D5}
\DeclareMathSymbol{\notcong}{3}{arrows}{"99}
\DeclareMathSymbol{\notin}{3}{arrows}{"1D}
\DeclareMathSymbol{\notni}{3}{arrows}{"1F}
\DeclareMathSymbol{\notvdash}{3}{arrows}{"F8}
\DeclareMathSymbol{\notmodels}{3}{arrows}{"F9}
\DeclareMathSymbol{\notparallel}{3}{arrows}{"F7}
\DeclareMathSymbol{\noteq}{3}{arrows}{"94}
\DeclareMathSymbol{\notless}{3}{arrows}{"9A}
\DeclareMathSymbol{\notgreater}{3}{arrows}{"9B}
\DeclareMathSymbol{\notmid}{3}{arrows}{"F6}
\@ifpackageloaded{amsfonts}{}{% from MJD
  \def\nonmatherr@#1{\errmessage{\string#1\space allowed only in math mode}}
  \def\Bbb{\relax\ifmmode\expandafter\Bbb@\else
   \expandafter\nonmatherr@\expandafter\Bbb\fi}
}
\let\Bbb@\bbold
\DeclareMathSymbol{\Gamma}{0}{largesymbols}{'320}
\DeclareMathSymbol{\Delta}{0}{largesymbols}{'321}
\DeclareMathSymbol{\Theta}{0}{largesymbols}{'322}
\DeclareMathSymbol{\Lambda}{0}{largesymbols}{'323}
\DeclareMathSymbol{\Xi}{0}{largesymbols}{'324}
\DeclareMathSymbol{\Pi}{0}{largesymbols}{'325}
\DeclareMathSymbol{\Sigma}{0}{largesymbols}{'326}
\DeclareMathSymbol{\Upsilon}{0}{largesymbols}{'327}
\DeclareMathSymbol{\Phi}{0}{largesymbols}{'330}
\DeclareMathSymbol{\Psi}{0}{largesymbols}{'331}
\DeclareMathSymbol{\Omega}{0}{largesymbols}{'332}
\DeclareMathSymbol{\varGamma}{0}{letters}{"00}
\DeclareMathSymbol{\varDelta}{0}{letters}{"01}
\DeclareMathSymbol{\varTheta}{0}{letters}{"02}
\DeclareMathSymbol{\varLambda}{0}{letters}{"03}
\DeclareMathSymbol{\varXi}{0}{letters}{"04}
\DeclareMathSymbol{\varPi}{0}{letters}{"05}
\DeclareMathSymbol{\varSigma}{0}{letters}{"06}
\DeclareMathSymbol{\varUpsilon}{0}{letters}{"07}
\DeclareMathSymbol{\varPhi}{0}{letters}{"08}
\DeclareMathSymbol{\varPsi}{0}{letters}{"09}
\DeclareMathSymbol{\varOmega}{0}{letters}{"0A}
\DeclareMathSymbol{\boxdot}{2}{symbols}{"ED}
\DeclareMathSymbol{\boxplus}{2}{symbols}{"EA}
\DeclareMathSymbol{\boxtimes}{2}{symbols}{"EC}
\DeclareMathSymbol{\square}{0}{arrows}{"02}
\DeclareMathSymbol{\blacksquare}{0}{arrows}{"03}
\DeclareMathSymbol{\centerdot}{2}{arrows}{"E1}
\DeclareMathSymbol{\lozenge}{0}{arrows}{"08}
\DeclareMathSymbol{\blacklozenge}{0}{arrows}{"09}
\DeclareMathSymbol{\circlearrowright}{3}{arrows}{"8C}
\DeclareMathSymbol{\circlearrowleft}{3}{arrows}{"8B}
\DeclareMathSymbol{\rightleftharpoons}{3}{arrows}{"7A}
\DeclareMathSymbol{\leftrightharpoons}{3}{arrows}{"79}
\DeclareMathSymbol{\boxminus}{2}{symbols}{"EB}
\DeclareMathSymbol{\Vdash}{3}{symbols}{"F0}
\DeclareMathSymbol{\Vvdash}{3}{letters}{"D3}
\DeclareMathSymbol{\vDash}{3}{symbols}{"EE}
\DeclareMathSymbol{\twoheadrightarrow}{3}{arrows}{"25}
\DeclareMathSymbol{\twoheadleftarrow}{3}{arrows}{"23}
\DeclareMathSymbol{\leftleftarrows}{3}{arrows}{"71}
\DeclareMathSymbol{\rightrightarrows}{3}{arrows}{"73}
\DeclareMathSymbol{\upuparrows}{3}{arrows}{"72}
\DeclareMathSymbol{\downdownarrows}{3}{arrows}{"74}
\DeclareMathSymbol{\upharpoonright}{3}{arrows}{"75}
\DeclareMathSymbol{\downharpoonright}{3}{arrows}{"77}
\DeclareMathSymbol{\upharpoonleft}{3}{arrows}{"76}
\DeclareMathSymbol{\downharpoonleft}{3}{arrows}{"78}
\DeclareMathSymbol{\rightarrowtail}{3}{arrows}{"29}
\DeclareMathSymbol{\leftarrowtail}{3}{arrows}{"28}
\DeclareMathSymbol{\leftrightarrows}{3}{arrows}{"6E}
\DeclareMathSymbol{\rightleftarrows}{3}{arrows}{"6D}
\DeclareMathSymbol{\Lsh}{3}{arrows}{"7B}
\DeclareMathSymbol{\Rsh}{3}{arrows}{"7D}
\DeclareMathSymbol{\rightsquigarrow}{3}{arrows}{"8E}
\DeclareMathSymbol{\leftsquigarrow}{3}{arrows}{"8D}
\DeclareMathSymbol{\leftrightsquigarrow}{3}{arrows}{"91}
\DeclareMathSymbol{\looparrowleft}{3}{arrows}{"3F}
\DeclareMathSymbol{\looparrowright}{3}{arrows}{"40}
\DeclareMathSymbol{\circeq}{3}{symbols}{"D0}
\DeclareMathSymbol{\succsim}{3}{symbols}{"E1}
\DeclareMathSymbol{\gtrsim}{3}{symbols}{"DD}
\DeclareMathSymbol{\gtrapprox}{3}{letters}{"DB}
\DeclareMathSymbol{\multimap}{3}{letters}{"C7}
\DeclareMathSymbol{\image}{3}{letters}{"C6}
\DeclareMathSymbol{\original}{3}{letters}{"C5}
\DeclareMathSymbol{\therefore}{3}{symbols}{"90}
\DeclareMathSymbol{\because}{3}{symbols}{"91}
\DeclareMathSymbol{\doteqdot}{3}{symbols}{"CA}
\DeclareMathSymbol{\triangleq}{3}{symbols}{"D5}
\DeclareMathSymbol{\precsim}{3}{symbols}{"E0}
\DeclareMathSymbol{\lesssim}{3}{symbols}{"DC}
\DeclareMathSymbol{\lessapprox}{3}{letters}{"DA}
\DeclareMathSymbol{\eqslantless}{3}{letters}{"E2}
\DeclareMathSymbol{\eqslantgtr}{3}{letters}{"E3}
\DeclareMathSymbol{\curlyeqprec}{3}{letters}{"E6}
\DeclareMathSymbol{\curlyeqsucc}{3}{letters}{"E7}
\DeclareMathSymbol{\preccurlyeq}{3}{letters}{"E4}
\DeclareMathSymbol{\leqq}{3}{symbols}{"DA}
\DeclareMathSymbol{\leqslant}{3}{letters}{"E0}
\DeclareMathSymbol{\lessgtr}{3}{symbols}{"DE}
\DeclareMathSymbol{\backprime}{0}{letters}{"C8}
\DeclareMathSymbol{\axisshort}{0}{arrows}{"39}
\DeclareMathSymbol{\risingdotseq}{3}{symbols}{"CC}
\DeclareMathSymbol{\fallingdotseq}{3}{symbols}{"CB}
\DeclareMathSymbol{\succcurlyeq}{3}{letters}{"E5}
\DeclareMathSymbol{\geqq}{3}{symbols}{"DB}
\DeclareMathSymbol{\geqslant}{3}{letters}{"E1}
\DeclareMathSymbol{\gtrless}{3}{symbols}{"DF}
\let\sqsubset\undefined
\let\sqsupset\undefined
\DeclareMathSymbol{\sqsubset}{3}{symbols}{"E4}
\DeclareMathSymbol{\sqsupset}{3}{symbols}{"E5}
\DeclareMathSymbol{\vartriangleright}{3}{letters}{"2E}
\DeclareMathSymbol{\vartriangleleft}{3}{letters}{"2F}
\DeclareMathSymbol{\trianglerighteq}{3}{symbols}{"F5}
\DeclareMathSymbol{\trianglelefteq}{3}{symbols}{"F4}
\DeclareMathSymbol{\bigstar}{0}{arrows}{"AB}
\DeclareMathSymbol{\between}{3}{letters}{"F2}
\DeclareMathSymbol{\blacktriangledown}{0}{arrows}{"07}
\DeclareMathSymbol{\blacktriangleright}{3}{letters}{"F1}
\DeclareMathSymbol{\blacktriangleleft}{3}{letters}{"F0}
\DeclareMathSymbol{\arrowaxisright}{0}{arrows}{"37}
\DeclareMathSymbol{\arrowaxisleft}{0}{arrows}{"36}
\DeclareMathSymbol{\vartriangle}{3}{arrows}{"04}
\DeclareMathSymbol{\blacktriangle}{0}{arrows}{"05}
\DeclareMathSymbol{\triangledown}{0}{arrows}{"06}
\DeclareMathSymbol{\eqcirc}{3}{symbols}{"CF}
\DeclareMathSymbol{\lesseqgtr}{3}{letters}{"E8}
\DeclareMathSymbol{\gtreqless}{3}{letters}{"E9}
\DeclareMathSymbol{\lesseqqgtr}{3}{letters}{"EA}
\DeclareMathSymbol{\gtreqqless}{3}{letters}{"EB}
\DeclareMathSymbol{\Rrightarrow}{3}{arrows}{"6C}
\DeclareMathSymbol{\Lleftarrow}{3}{arrows}{"6A}
\DeclareMathSymbol{\veebar}{2}{letters}{"D2}
\DeclareMathSymbol{\barwedge}{2}{symbols}{"F6}
\DeclareMathSymbol{\angle}{0}{symbols}{"8B}
\DeclareMathSymbol{\measuredangle}{0}{symbols}{"8C}
\DeclareMathSymbol{\sphericalangle}{0}{symbols}{"8D}
\DeclareMathSymbol{\varpropto}{3}{symbols}{"2F} % ?
\DeclareMathSymbol{\smallsmile}{3}{letters}{"5E} % ? 
\DeclareMathSymbol{\smallfrown}{3}{letters}{"5F} % ?       
\DeclareMathSymbol{\Subset}{3}{symbols}{"F8}
\DeclareMathSymbol{\Supset}{3}{symbols}{"F9}
\DeclareMathSymbol{\Cup}{2}{symbols}{"FA}
\DeclareMathSymbol{\Cap}{2}{symbols}{"FB}
\DeclareMathSymbol{\curlywedge}{2}{symbols}{"84}
\DeclareMathSymbol{\curlyvee}{2}{symbols}{"85}
\DeclareMathSymbol{\leftthreetimes}{2}{letters}{"D0}
\DeclareMathSymbol{\rightthreetimes}{2}{letters}{"D1}
\DeclareMathSymbol{\subseteqq}{3}{letters}{"EE}
\DeclareMathSymbol{\supseteqq}{3}{letters}{"EF}
\DeclareMathSymbol{\bumpeq}{3}{symbols}{"C8}
\DeclareMathSymbol{\Bumpeq}{3}{symbols}{"C7}
\DeclareMathSymbol{\lll}{3}{letters}{"DE}
\DeclareMathSymbol{\ggg}{3}{letters}{"DF}
\DeclareMathSymbol{\circledS}{0}{letters}{"CA}
\DeclareMathSymbol{\pitchfork}{3}{letters}{"F3}
\DeclareMathSymbol{\dotplus}{2}{symbols}{"89}
\DeclareMathSymbol{\backsim}{3}{letters}{"F8}
\DeclareMathSymbol{\backsimeq}{3}{letters}{"F9}
\DeclareMathSymbol{\complement}{0}{letters}{"94}
\DeclareMathSymbol{\intercal}{2}{letters}{"D9}
\DeclareMathSymbol{\circledcirc}{2}{symbols}{"E6}
\DeclareMathSymbol{\circledast}{2}{symbols}{"E7}
\DeclareMathSymbol{\circleddash}{2}{letters}{"CC}
\DeclareMathSymbol{\lvertneqq}{3}{arrows}{"DE}
\DeclareMathSymbol{\gvertneqq}{3}{arrows}{"DF}
\DeclareMathSymbol{\nleq}{3}{arrows}{"9C}
\DeclareMathSymbol{\ngeq}{3}{arrows}{"9D}
\DeclareMathSymbol{\nless}{3}{arrows}{"9A}
\DeclareMathSymbol{\ngtr}{3}{arrows}{"9B}
\DeclareMathSymbol{\nprec}{3}{arrows}{"E5}
\DeclareMathSymbol{\nsucc}{3}{arrows}{"E6}
\DeclareMathSymbol{\lneqq}{3}{arrows}{"DC}
\DeclareMathSymbol{\gneqq}{3}{arrows}{"DD}
\DeclareMathSymbol{\nleqslant}{3}{arrows}{"D6}
\DeclareMathSymbol{\ngeqslant}{3}{arrows}{"D7}
\DeclareMathSymbol{\lneq}{3}{arrows}{"DA}
\DeclareMathSymbol{\gneq}{3}{arrows}{"DB}
\DeclareMathSymbol{\npreceq}{3}{arrows}{"E7}
\DeclareMathSymbol{\nsucceq}{3}{arrows}{"E8}
\DeclareMathSymbol{\precnsim}{3}{arrows}{"EB}
\DeclareMathSymbol{\succnsim}{3}{arrows}{"EC}
\DeclareMathSymbol{\lnsim}{3}{arrows}{"E0}
\DeclareMathSymbol{\gnsim}{3}{arrows}{"E2}
\DeclareMathSymbol{\nleqq}{3}{arrows}{"D8}
\DeclareMathSymbol{\ngeqq}{3}{arrows}{"D9}
\DeclareMathSymbol{\precneqq}{3}{arrows}{"E9}
\DeclareMathSymbol{\succneqq}{3}{arrows}{"EA}
\DeclareMathSymbol{\precnapprox}{3}{arrows}{"ED}
\DeclareMathSymbol{\succnapprox}{3}{arrows}{"EE}
\DeclareMathSymbol{\lnapprox}{3}{arrows}{"E3}
\DeclareMathSymbol{\gnapprox}{3}{arrows}{"E4}
\DeclareMathSymbol{\nsim}{3}{arrows}{"96}
\DeclareMathSymbol{\ncong}{3}{arrows}{"99}
\DeclareMathSymbol{\diagup}{3}{arrows}{"0B}
\DeclareMathSymbol{\diagdown}{3}{arrows}{"0C}
\DeclareMathSymbol{\varsubsetneq}{3}{arrows}{"D0}
\DeclareMathSymbol{\varsupsetneq}{3}{arrows}{"D1}
\DeclareMathSymbol{\nsubseteqq}{3}{arrows}{"CA}
\DeclareMathSymbol{\nsupseteqq}{3}{arrows}{"CB}
\DeclareMathSymbol{\subsetneqq}{3}{arrows}{"CE}
\DeclareMathSymbol{\supsetneqq}{3}{arrows}{"CF}
\DeclareMathSymbol{\varsubsetneqq}{3}{arrows}{"D2}
\DeclareMathSymbol{\varsupsetneqq}{3}{arrows}{"D3}
\DeclareMathSymbol{\subsetneq}{3}{arrows}{"CC}
\DeclareMathSymbol{\supsetneq}{3}{arrows}{"CD}
\DeclareMathSymbol{\nsubseteq}{3}{arrows}{"C8}
\DeclareMathSymbol{\nsupseteq}{3}{arrows}{"C9}
\DeclareMathSymbol{\nparallel}{3}{arrows}{"F7}
\DeclareMathSymbol{\nmid}{3}{arrows}{"F6}
\DeclareMathSymbol{\nshortmid}{3}{arrows}{"F4}
\DeclareMathSymbol{\nshortparallel}{3}{arrows}{"F5}
\DeclareMathSymbol{\nvdash}{3}{arrows}{"F8}
\DeclareMathSymbol{\nVdash}{3}{arrows}{"FA}
\DeclareMathSymbol{\nvDash}{3}{arrows}{"F9}
\DeclareMathSymbol{\nVDash}{3}{arrows}{"FB}
\DeclareMathSymbol{\ntrianglerighteq}{3}{arrows}{"F2}
\DeclareMathSymbol{\ntrianglelefteq}{3}{arrows}{"F1}
\DeclareMathSymbol{\ntriangleleft}{3}{arrows}{"EF}
\DeclareMathSymbol{\ntriangleright}{3}{arrows}{"F0}
\DeclareMathSymbol{\nleftarrow}{3}{arrows}{"32}
\DeclareMathSymbol{\nrightarrow}{3}{arrows}{"33}
\DeclareMathSymbol{\nLeftarrow}{3}{arrows}{"66}
\DeclareMathSymbol{\nRightarrow}{3}{arrows}{"68}
\DeclareMathSymbol{\nLeftrightarrow}{3}{arrows}{"67}
\DeclareMathSymbol{\nleftrightarrow}{3}{arrows}{"34}
\DeclareMathSymbol{\divideontimes}{2}{letters}{"F7}
\DeclareMathSymbol{\varnothing}{0}{letters}{"9C}
\DeclareMathSymbol{\nexists}{0}{arrows}{"20}
\DeclareMathSymbol{\Finv}{0}{letters}{"90}
\DeclareMathSymbol{\Game}{0}{letters}{"91}
\let\mho\undefined
\DeclareMathSymbol{\mho}{0}{letters}{"92}
\DeclareMathSymbol{\simeq}{3}{symbols}{"27}
\DeclareMathSymbol{\eqsim}{3}{symbols}{"99}
\DeclareMathSymbol{\beth}{0}{letters}{"95}
\DeclareMathSymbol{\gimel}{0}{letters}{"96}
\DeclareMathSymbol{\daleth}{0}{letters}{"97}
\DeclareMathSymbol{\lessdot}{3}{letters}{"DC}
\DeclareMathSymbol{\gtrdot}{3}{letters}{"DD}
\DeclareMathSymbol{\ltimes}{2}{letters}{"CE}
\DeclareMathSymbol{\rtimes}{2}{letters}{"CF}
\DeclareMathSymbol{\shortmid}{3}{letters}{"F4}
\DeclareMathSymbol{\shortparallel}{3}{letters}{"F5}
\DeclareMathSymbol{\smallsetminus}{2}{letters}{"D8} %?
\DeclareMathSymbol{\thicksim}{3}{symbols}{"18} %?
\DeclareMathSymbol{\thickapprox}{3}{symbols}{"19} %?      
\DeclareMathSymbol{\approxeq}{3}{symbols}{"9D}
\DeclareMathSymbol{\succapprox}{3}{letters}{"ED}
\DeclareMathSymbol{\precapprox}{3}{letters}{"EC}
\DeclareMathSymbol{\curvearrowleft}{3}{arrows}{"87}
\DeclareMathSymbol{\curvearrowright}{3}{arrows}{"88}
\DeclareMathSymbol{\digamma}{0}{letters}{"46} %?
\DeclareMathSymbol{\varkappa}{0}{letters}{"9B}
\DeclareMathSymbol{\Bbbk}{0}{arrows}{"6B}
\DeclareMathSymbol{\hslash}{0}{letters}{"9D}
\DeclareMathSymbol{\hbar}{0}{arrows}{"1B}
\DeclareMathSymbol{\backepsilon}{3}{letters}{"FB} %?
\DeclareMathSymbol{\dashrightarrow}{0}{arrows}{"3A}
\DeclareMathSymbol{\dashleftarrow}{0}{arrows}{"38}
\DeclareMathSymbol{\dashuparrow}{0}{arrows}{"39}
\DeclareMathSymbol{\dashdownarrow}{0}{arrows}{"3B}
\DeclareMathDelimiter\ulcorner{4}{arrows}{"70}{arrows}{"70}
\DeclareMathDelimiter\urcorner{5}{arrows}{"71}{arrows}{"71}
\DeclareMathDelimiter\llcorner{4}{arrows}{"78}{arrows}{"78}
\DeclareMathDelimiter\lrcorner{5}{arrows}{"79}{arrows}{"79}
\newif\iffirstchoice@\firstchoice@true
\@ifpackageloaded{amstext}{}{%
  \def\RIfM@{\relax\ifmmode}
  \def\DN@{\def\next@}
  \def\eat@#1{}
  \firstchoice@true
  \def\text@#1{\mathchoice
   {\hbox{\everymath{\displaystyle}\def\textfonti{\the\textfont\@ne}%
    \def\textfontii{\the\textfont\tw@}\textdef@@ T#1}}
   {\hbox{\firstchoice@false
    \everymath{\textstyle}\def\textfonti{\the\textfont\@ne}%
    \def\textfontii{\the\textfont\tw@}\textdef@@ T#1}}
   {\hbox{\firstchoice@false
    \everymath{\scriptstyle}\def\textfonti{\the\scriptfont\@ne}%
    \def\textfontii{\the\scriptfont\tw@}\textdef@@ S\rm#1}}
   {\hbox{\firstchoice@false
    \everymath{\scriptscriptstyle}\def\textfonti
    {\the\scriptscriptfont\@ne}%
    \def\textfontii{\the\scriptscriptfont\tw@}\textdef@@ s\rm#1}}}
  \def\textdef@@#1{\textdef@#1\rm\textdef@#1\bf\textdef@#1\sl\textdef@#1\it}
  \def\text@@#1{\leavevmode\hbox{#1}}
  \def\rmfam{0}
  \def\textdef@#1#2{%
   \DN@{\csname\expandafter\eat@\string#2fam\endcsname}%
   \if S#1\edef#2{\the\scriptfont\next@\relax}%
   \else\if s#1\edef#2{\the\scriptscriptfont\next@\relax}%
   \else\edef#2{\the\textfont\next@\relax}\fi\fi}
  \def\text{\RIfM@\expandafter\text@\else\expandafter\text@@\fi}
  \def\mathhexbox@#1#2#3{\text{$\m@th\mathchar"#1#2#3$}}
}
\xdef\checkmark{\noexpand\mathhexbox\hexnumber@\symarrows 58 }
\def\lmathhexbox#1#2#3{\leavevmode
  \hbox{$\m@th \mathchar"#1#2#3$}}
\def \circledR  {\lmathhexbox1C9 }
\def \maltese   {\lmathhexbox1CB }
\let\Leftrightarrow\undefined
\DeclareMathSymbol{\Leftrightarrow}{3}{arrows}{"61}
\def\AmS{{\protect\usefont{OMS}{hlcy}{m}{n}%
  A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
\endinput
%% 
%% End of file `lucbmath.sty'.