%%
%% This is file `amssymb.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% amssymb.dtx
%%% ====================================================================
%%% @LaTeX-file{
%%% filename = "amssymb.dtx",
%%% version = "2.2b",
%%% date = "1996/11/03",
%%% time = "12:11:39 EST",
%%% author = "American Mathematical Society",
%%% copyright = "Copyright (C) 1996 American Mathematical Society,
%%% all rights reserved. Copying of this file is
%%% authorized only if either:
%%% (1) you make absolutely no changes to your copy,
%%% including name; OR
%%% (2) if you do make changes, you first rename it
%%% to some other name.",
%%% address = "American Mathematical Society,
%%% Technical Support,
%%% Electronic Products and Services,
%%% P. O. Box 6248,
%%% Providence, RI 02940,
%%% USA",
%%% telephone = "401-455-4080 or (in the USA and Canada)
%%% 800-321-4AMS (321-4267)",
%%% FAX = "401-331-3842",
%%% checksum = "31124 351 1075 17689",
%%% email = "tech-support@ams.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "latex, amslatex, ams-latex, math symbol,
%%% amsfonts, msam, msbm",
%%% supported = "yes",
%%% abstract = "This is part of the AMSFonts distribution.
%%% It is a \LaTeX{} option that defines symbol
%%% names for all the math symbols in the fonts
%%% MSAM and MSBM, of the AMSFonts (2.0+) package.",
%%% docstring = "The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
[1994/12/01]% LaTeX date must December 1994 or later
\ProvidesPackage{amssymb}[1996/11/03 v2.2b]
\DeclareOption{psamsfonts}{\PassOptionsToPackage{psamsfonts}{amsfonts}}
\ProcessOptions\relax
\RequirePackage{amsfonts}[1995/01/01]
\let\square\relax \let\rightsquigarrow\square \let\lozenge\square
\let\vartriangleright\square \let\vartriangleleft\square
\let\trianglerighteq\square \let\trianglelefteq\square
\DeclareMathSymbol{\boxdot} {\mathbin}{AMSa}{"00}
\DeclareMathSymbol{\boxplus} {\mathbin}{AMSa}{"01}
\DeclareMathSymbol{\boxtimes} {\mathbin}{AMSa}{"02}
\DeclareMathSymbol{\square} {\mathord}{AMSa}{"03}
\DeclareMathSymbol{\blacksquare} {\mathord}{AMSa}{"04}
\DeclareMathSymbol{\centerdot} {\mathbin}{AMSa}{"05}
\DeclareMathSymbol{\lozenge} {\mathord}{AMSa}{"06}
\DeclareMathSymbol{\blacklozenge} {\mathord}{AMSa}{"07}
\DeclareMathSymbol{\circlearrowright} {\mathrel}{AMSa}{"08}
\DeclareMathSymbol{\circlearrowleft} {\mathrel}{AMSa}{"09}
%% In amsfonts.sty:
%%\DeclareMathSymbol{\rightleftharpoons}{\mathrel}{AMSa}{"0A}
\DeclareMathSymbol{\leftrightharpoons} {\mathrel}{AMSa}{"0B}
\DeclareMathSymbol{\boxminus} {\mathbin}{AMSa}{"0C}
\DeclareMathSymbol{\Vdash} {\mathrel}{AMSa}{"0D}
\DeclareMathSymbol{\Vvdash} {\mathrel}{AMSa}{"0E}
\DeclareMathSymbol{\vDash} {\mathrel}{AMSa}{"0F}
\DeclareMathSymbol{\twoheadrightarrow} {\mathrel}{AMSa}{"10}
\DeclareMathSymbol{\twoheadleftarrow} {\mathrel}{AMSa}{"11}
\DeclareMathSymbol{\leftleftarrows} {\mathrel}{AMSa}{"12}
\DeclareMathSymbol{\rightrightarrows} {\mathrel}{AMSa}{"13}
\DeclareMathSymbol{\upuparrows} {\mathrel}{AMSa}{"14}
\DeclareMathSymbol{\downdownarrows} {\mathrel}{AMSa}{"15}
\DeclareMathSymbol{\upharpoonright} {\mathrel}{AMSa}{"16}
\let\restriction\upharpoonright
\DeclareMathSymbol{\downharpoonright} {\mathrel}{AMSa}{"17}
\DeclareMathSymbol{\upharpoonleft} {\mathrel}{AMSa}{"18}
\DeclareMathSymbol{\downharpoonleft}{\mathrel}{AMSa}{"19}
\DeclareMathSymbol{\rightarrowtail} {\mathrel}{AMSa}{"1A}
\DeclareMathSymbol{\leftarrowtail} {\mathrel}{AMSa}{"1B}
\DeclareMathSymbol{\leftrightarrows}{\mathrel}{AMSa}{"1C}
\DeclareMathSymbol{\rightleftarrows}{\mathrel}{AMSa}{"1D}
\DeclareMathSymbol{\Lsh} {\mathrel}{AMSa}{"1E}
\DeclareMathSymbol{\Rsh} {\mathrel}{AMSa}{"1F}
\DeclareMathSymbol{\rightsquigarrow} {\mathrel}{AMSa}{"20}
\DeclareMathSymbol{\leftrightsquigarrow}{\mathrel}{AMSa}{"21}
\DeclareMathSymbol{\looparrowleft} {\mathrel}{AMSa}{"22}
\DeclareMathSymbol{\looparrowright} {\mathrel}{AMSa}{"23}
\DeclareMathSymbol{\circeq} {\mathrel}{AMSa}{"24}
\DeclareMathSymbol{\succsim} {\mathrel}{AMSa}{"25}
\DeclareMathSymbol{\gtrsim} {\mathrel}{AMSa}{"26}
\DeclareMathSymbol{\gtrapprox} {\mathrel}{AMSa}{"27}
\DeclareMathSymbol{\multimap} {\mathrel}{AMSa}{"28}
\DeclareMathSymbol{\therefore} {\mathrel}{AMSa}{"29}
\DeclareMathSymbol{\because} {\mathrel}{AMSa}{"2A}
\DeclareMathSymbol{\doteqdot} {\mathrel}{AMSa}{"2B}
\let\Doteq\doteqdot
\DeclareMathSymbol{\triangleq} {\mathrel}{AMSa}{"2C}
\DeclareMathSymbol{\precsim} {\mathrel}{AMSa}{"2D}
\DeclareMathSymbol{\lesssim} {\mathrel}{AMSa}{"2E}
\DeclareMathSymbol{\lessapprox} {\mathrel}{AMSa}{"2F}
\DeclareMathSymbol{\eqslantless} {\mathrel}{AMSa}{"30}
\DeclareMathSymbol{\eqslantgtr} {\mathrel}{AMSa}{"31}
\DeclareMathSymbol{\curlyeqprec} {\mathrel}{AMSa}{"32}
\DeclareMathSymbol{\curlyeqsucc} {\mathrel}{AMSa}{"33}
\DeclareMathSymbol{\preccurlyeq} {\mathrel}{AMSa}{"34}
\DeclareMathSymbol{\leqq} {\mathrel}{AMSa}{"35}
\DeclareMathSymbol{\leqslant} {\mathrel}{AMSa}{"36}
\DeclareMathSymbol{\lessgtr} {\mathrel}{AMSa}{"37}
\DeclareMathSymbol{\backprime} {\mathord}{AMSa}{"38}
\DeclareMathSymbol{\risingdotseq} {\mathrel}{AMSa}{"3A}
\DeclareMathSymbol{\fallingdotseq}{\mathrel}{AMSa}{"3B}
\DeclareMathSymbol{\succcurlyeq} {\mathrel}{AMSa}{"3C}
\DeclareMathSymbol{\geqq} {\mathrel}{AMSa}{"3D}
\DeclareMathSymbol{\geqslant} {\mathrel}{AMSa}{"3E}
\DeclareMathSymbol{\gtrless} {\mathrel}{AMSa}{"3F}
%% in amsfonts.sty
%% \DeclareMathSymbol{\sqsubset} {\mathrel}{AMSa}{"40}
%% \DeclareMathSymbol{\sqsupset} {\mathrel}{AMSa}{"41}
\DeclareMathSymbol{\vartriangleright}{\mathrel}{AMSa}{"42}
\DeclareMathSymbol{\vartriangleleft} {\mathrel}{AMSa}{"43}
\DeclareMathSymbol{\trianglerighteq} {\mathrel}{AMSa}{"44}
\DeclareMathSymbol{\trianglelefteq} {\mathrel}{AMSa}{"45}
\DeclareMathSymbol{\bigstar} {\mathord}{AMSa}{"46}
\DeclareMathSymbol{\between} {\mathrel}{AMSa}{"47}
\DeclareMathSymbol{\blacktriangledown} {\mathord}{AMSa}{"48}
\DeclareMathSymbol{\blacktriangleright} {\mathrel}{AMSa}{"49}
\DeclareMathSymbol{\blacktriangleleft} {\mathrel}{AMSa}{"4A}
\DeclareMathSymbol{\vartriangle} {\mathrel}{AMSa}{"4D}
\DeclareMathSymbol{\blacktriangle} {\mathord}{AMSa}{"4E}
\DeclareMathSymbol{\triangledown} {\mathord}{AMSa}{"4F}
\DeclareMathSymbol{\eqcirc} {\mathrel}{AMSa}{"50}
\DeclareMathSymbol{\lesseqgtr} {\mathrel}{AMSa}{"51}
\DeclareMathSymbol{\gtreqless} {\mathrel}{AMSa}{"52}
\DeclareMathSymbol{\lesseqqgtr} {\mathrel}{AMSa}{"53}
\DeclareMathSymbol{\gtreqqless} {\mathrel}{AMSa}{"54}
\DeclareMathSymbol{\Rrightarrow} {\mathrel}{AMSa}{"56}
\DeclareMathSymbol{\Lleftarrow} {\mathrel}{AMSa}{"57}
\DeclareMathSymbol{\veebar} {\mathbin}{AMSa}{"59}
\DeclareMathSymbol{\barwedge} {\mathbin}{AMSa}{"5A}
\DeclareMathSymbol{\doublebarwedge} {\mathbin}{AMSa}{"5B}
%% In amsfonts.sty
%%\DeclareMathSymbol{\angle} {\mathord}{AMSa}{"5C}
\DeclareMathSymbol{\measuredangle} {\mathord}{AMSa}{"5D}
\DeclareMathSymbol{\sphericalangle} {\mathord}{AMSa}{"5E}
\DeclareMathSymbol{\varpropto} {\mathrel}{AMSa}{"5F}
\DeclareMathSymbol{\smallsmile} {\mathrel}{AMSa}{"60}
\DeclareMathSymbol{\smallfrown} {\mathrel}{AMSa}{"61}
\DeclareMathSymbol{\Subset} {\mathrel}{AMSa}{"62}
\DeclareMathSymbol{\Supset} {\mathrel}{AMSa}{"63}
\DeclareMathSymbol{\Cup} {\mathbin}{AMSa}{"64}
\let\doublecup\Cup
\DeclareMathSymbol{\Cap} {\mathbin}{AMSa}{"65}
\let\doublecap\Cap
\DeclareMathSymbol{\curlywedge} {\mathbin}{AMSa}{"66}
\DeclareMathSymbol{\curlyvee} {\mathbin}{AMSa}{"67}
\DeclareMathSymbol{\leftthreetimes} {\mathbin}{AMSa}{"68}
\DeclareMathSymbol{\rightthreetimes}{\mathbin}{AMSa}{"69}
\DeclareMathSymbol{\subseteqq} {\mathrel}{AMSa}{"6A}
\DeclareMathSymbol{\supseteqq} {\mathrel}{AMSa}{"6B}
\DeclareMathSymbol{\bumpeq} {\mathrel}{AMSa}{"6C}
\DeclareMathSymbol{\Bumpeq} {\mathrel}{AMSa}{"6D}
\DeclareMathSymbol{\lll} {\mathrel}{AMSa}{"6E}
\let\llless\lll
\DeclareMathSymbol{\ggg} {\mathrel}{AMSa}{"6F}
\let\gggtr\ggg
\DeclareMathSymbol{\circledS} {\mathord}{AMSa}{"73}
\DeclareMathSymbol{\pitchfork} {\mathrel}{AMSa}{"74}
\DeclareMathSymbol{\dotplus} {\mathbin}{AMSa}{"75}
\DeclareMathSymbol{\backsim} {\mathrel}{AMSa}{"76}
\DeclareMathSymbol{\backsimeq} {\mathrel}{AMSa}{"77}
\DeclareMathSymbol{\complement} {\mathord}{AMSa}{"7B}
\DeclareMathSymbol{\intercal} {\mathbin}{AMSa}{"7C}
\DeclareMathSymbol{\circledcirc} {\mathbin}{AMSa}{"7D}
\DeclareMathSymbol{\circledast} {\mathbin}{AMSa}{"7E}
\DeclareMathSymbol{\circleddash} {\mathbin}{AMSa}{"7F}
%% Begin AMSb declarations
\DeclareMathSymbol{\lvertneqq} {\mathrel}{AMSb}{"00}
\DeclareMathSymbol{\gvertneqq} {\mathrel}{AMSb}{"01}
\DeclareMathSymbol{\nleq} {\mathrel}{AMSb}{"02}
\DeclareMathSymbol{\ngeq} {\mathrel}{AMSb}{"03}
\DeclareMathSymbol{\nless} {\mathrel}{AMSb}{"04}
\DeclareMathSymbol{\ngtr} {\mathrel}{AMSb}{"05}
\DeclareMathSymbol{\nprec} {\mathrel}{AMSb}{"06}
\DeclareMathSymbol{\nsucc} {\mathrel}{AMSb}{"07}
\DeclareMathSymbol{\lneqq} {\mathrel}{AMSb}{"08}
\DeclareMathSymbol{\gneqq} {\mathrel}{AMSb}{"09}
\DeclareMathSymbol{\nleqslant} {\mathrel}{AMSb}{"0A}
\DeclareMathSymbol{\ngeqslant} {\mathrel}{AMSb}{"0B}
\DeclareMathSymbol{\lneq} {\mathrel}{AMSb}{"0C}
\DeclareMathSymbol{\gneq} {\mathrel}{AMSb}{"0D}
\DeclareMathSymbol{\npreceq} {\mathrel}{AMSb}{"0E}
\DeclareMathSymbol{\nsucceq} {\mathrel}{AMSb}{"0F}
\DeclareMathSymbol{\precnsim} {\mathrel}{AMSb}{"10}
\DeclareMathSymbol{\succnsim} {\mathrel}{AMSb}{"11}
\DeclareMathSymbol{\lnsim} {\mathrel}{AMSb}{"12}
\DeclareMathSymbol{\gnsim} {\mathrel}{AMSb}{"13}
\DeclareMathSymbol{\nleqq} {\mathrel}{AMSb}{"14}
\DeclareMathSymbol{\ngeqq} {\mathrel}{AMSb}{"15}
\DeclareMathSymbol{\precneqq} {\mathrel}{AMSb}{"16}
\DeclareMathSymbol{\succneqq} {\mathrel}{AMSb}{"17}
\DeclareMathSymbol{\precnapprox} {\mathrel}{AMSb}{"18}
\DeclareMathSymbol{\succnapprox} {\mathrel}{AMSb}{"19}
\DeclareMathSymbol{\lnapprox} {\mathrel}{AMSb}{"1A}
\DeclareMathSymbol{\gnapprox} {\mathrel}{AMSb}{"1B}
\DeclareMathSymbol{\nsim} {\mathrel}{AMSb}{"1C}
\DeclareMathSymbol{\ncong} {\mathrel}{AMSb}{"1D}
\DeclareMathSymbol{\diagup} {\mathord}{AMSb}{"1E}
\DeclareMathSymbol{\diagdown} {\mathord}{AMSb}{"1F}
\DeclareMathSymbol{\varsubsetneq} {\mathrel}{AMSb}{"20}
\DeclareMathSymbol{\varsupsetneq} {\mathrel}{AMSb}{"21}
\DeclareMathSymbol{\nsubseteqq} {\mathrel}{AMSb}{"22}
\DeclareMathSymbol{\nsupseteqq} {\mathrel}{AMSb}{"23}
\DeclareMathSymbol{\subsetneqq} {\mathrel}{AMSb}{"24}
\DeclareMathSymbol{\supsetneqq} {\mathrel}{AMSb}{"25}
\DeclareMathSymbol{\varsubsetneqq} {\mathrel}{AMSb}{"26}
\DeclareMathSymbol{\varsupsetneqq} {\mathrel}{AMSb}{"27}
\DeclareMathSymbol{\subsetneq} {\mathrel}{AMSb}{"28}
\DeclareMathSymbol{\supsetneq} {\mathrel}{AMSb}{"29}
\DeclareMathSymbol{\nsubseteq} {\mathrel}{AMSb}{"2A}
\DeclareMathSymbol{\nsupseteq} {\mathrel}{AMSb}{"2B}
\DeclareMathSymbol{\nparallel} {\mathrel}{AMSb}{"2C}
\DeclareMathSymbol{\nmid} {\mathrel}{AMSb}{"2D}
\DeclareMathSymbol{\nshortmid} {\mathrel}{AMSb}{"2E}
\DeclareMathSymbol{\nshortparallel} {\mathrel}{AMSb}{"2F}
\DeclareMathSymbol{\nvdash} {\mathrel}{AMSb}{"30}
\DeclareMathSymbol{\nVdash} {\mathrel}{AMSb}{"31}
\DeclareMathSymbol{\nvDash} {\mathrel}{AMSb}{"32}
\DeclareMathSymbol{\nVDash} {\mathrel}{AMSb}{"33}
\DeclareMathSymbol{\ntrianglerighteq}{\mathrel}{AMSb}{"34}
\DeclareMathSymbol{\ntrianglelefteq}{\mathrel}{AMSb}{"35}
\DeclareMathSymbol{\ntriangleleft} {\mathrel}{AMSb}{"36}
\DeclareMathSymbol{\ntriangleright} {\mathrel}{AMSb}{"37}
\DeclareMathSymbol{\nleftarrow} {\mathrel}{AMSb}{"38}
\DeclareMathSymbol{\nrightarrow} {\mathrel}{AMSb}{"39}
\DeclareMathSymbol{\nLeftarrow} {\mathrel}{AMSb}{"3A}
\DeclareMathSymbol{\nRightarrow} {\mathrel}{AMSb}{"3B}
\DeclareMathSymbol{\nLeftrightarrow}{\mathrel}{AMSb}{"3C}
\DeclareMathSymbol{\nleftrightarrow}{\mathrel}{AMSb}{"3D}
\DeclareMathSymbol{\divideontimes} {\mathbin}{AMSb}{"3E}
\DeclareMathSymbol{\varnothing} {\mathord}{AMSb}{"3F}
\DeclareMathSymbol{\nexists} {\mathord}{AMSb}{"40}
\DeclareMathSymbol{\Finv} {\mathord}{AMSb}{"60}
\DeclareMathSymbol{\Game} {\mathord}{AMSb}{"61}
%% In amsfonts.sty:
%%\DeclareMathSymbol{\mho} {\mathord}{AMSb}{"66}
\DeclareMathSymbol{\eth} {\mathord}{AMSb}{"67}
\DeclareMathSymbol{\eqsim} {\mathrel}{AMSb}{"68}
\DeclareMathSymbol{\beth} {\mathord}{AMSb}{"69}
\DeclareMathSymbol{\gimel} {\mathord}{AMSb}{"6A}
\DeclareMathSymbol{\daleth} {\mathord}{AMSb}{"6B}
\DeclareMathSymbol{\lessdot} {\mathbin}{AMSb}{"6C}
\DeclareMathSymbol{\gtrdot} {\mathbin}{AMSb}{"6D}
\DeclareMathSymbol{\ltimes} {\mathbin}{AMSb}{"6E}
\DeclareMathSymbol{\rtimes} {\mathbin}{AMSb}{"6F}
\DeclareMathSymbol{\shortmid} {\mathrel}{AMSb}{"70}
\DeclareMathSymbol{\shortparallel} {\mathrel}{AMSb}{"71}
\DeclareMathSymbol{\smallsetminus} {\mathbin}{AMSb}{"72}
\DeclareMathSymbol{\thicksim} {\mathrel}{AMSb}{"73}
\DeclareMathSymbol{\thickapprox} {\mathrel}{AMSb}{"74}
\DeclareMathSymbol{\approxeq} {\mathrel}{AMSb}{"75}
\DeclareMathSymbol{\succapprox} {\mathrel}{AMSb}{"76}
\DeclareMathSymbol{\precapprox} {\mathrel}{AMSb}{"77}
\DeclareMathSymbol{\curvearrowleft} {\mathrel}{AMSb}{"78}
\DeclareMathSymbol{\curvearrowright}{\mathrel}{AMSb}{"79}
\DeclareMathSymbol{\digamma} {\mathord}{AMSb}{"7A}
\DeclareMathSymbol{\varkappa} {\mathord}{AMSb}{"7B}
\DeclareMathSymbol{\Bbbk} {\mathord}{AMSb}{"7C}
\DeclareMathSymbol{\hslash} {\mathord}{AMSb}{"7D}
%% In amsfonts.sty:
%%\DeclareMathSymbol{\hbar} {\mathord}{AMSb}{"7E}
\DeclareMathSymbol{\backepsilon} {\mathrel}{AMSb}{"7F}
\endinput
%%
%% End of file `amssymb.sty'.
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