2 %% This is file `amssymb.sty',
3 %% generated with the docstrip utility.
5 %% The original source files were:
9 %%% ====================================================================
11 %%% filename = "amssymb.dtx",
13 %%% date = "2002/01/22",
14 %%% time = "10:06:53 EST",
15 %%% checksum = "51146 363 1168 18275",
16 %%% author = "American Mathematical Society",
17 %%% copyright = "Copyright 2001 American Mathematical Society,
18 %%% all rights reserved. Copying of this file is
19 %%% authorized only if either:
20 %%% (1) you make absolutely no changes to your copy,
21 %%% including name; OR
22 %%% (2) if you do make changes, you first rename it
23 %%% to some other name.",
24 %%% address = "American Mathematical Society,
25 %%% Technical Support,
26 %%% Publications Technical Group,
28 %%% Providence, RI 02940,
30 %%% telephone = "401-455-4080 or (in the USA and Canada)
31 %%% 800-321-4AMS (321-4267)",
32 %%% FAX = "401-331-3842",
33 %%% email = "tech-support@ams.org (Internet)",
34 %%% codetable = "ISO/ASCII",
35 %%% keywords = "latex, amslatex, ams-latex, math symbol,
36 %%% amsfonts, msam, msbm",
37 %%% supported = "yes",
38 %%% abstract = "This file is part of the AMSFonts distribution.
39 %%% It is a \LaTeX{} package that defines symbol
40 %%% names for all the math symbols in the fonts
41 %%% MSAM and MSBM, of the AMSFonts (2.0+) collection.",
42 %%% docstring = "The checksum field above contains a CRC-16
43 %%% checksum as the first value, followed by the
44 %%% equivalent of the standard UNIX wc (word
45 %%% count) utility output of lines, words, and
46 %%% characters. This is produced by Robert
47 %%% Solovay's checksum utility.",
49 %%% ====================================================================
50 \NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
51 [1994/12/01]% LaTeX date must be December 1994 or later
52 \ProvidesPackage{amssymb}[2002/01/22 v2.2d]
53 \DeclareOption{psamsfonts}{\PassOptionsToPackage{psamsfonts}{amsfonts}}
55 \RequirePackage{amsfonts}[1995/01/01]
56 \let\square\relax \let\rightsquigarrow\square \let\lozenge\square
57 \let\vartriangleright\square \let\vartriangleleft\square
58 \let\trianglerighteq\square \let\trianglelefteq\square
59 \begingroup \catcode`\"=12
60 \DeclareMathSymbol{\boxdot} {\mathbin}{AMSa}{"00}
61 \DeclareMathSymbol{\boxplus} {\mathbin}{AMSa}{"01}
62 \DeclareMathSymbol{\boxtimes} {\mathbin}{AMSa}{"02}
63 \DeclareMathSymbol{\square} {\mathord}{AMSa}{"03}
64 \DeclareMathSymbol{\blacksquare} {\mathord}{AMSa}{"04}
65 \DeclareMathSymbol{\centerdot} {\mathbin}{AMSa}{"05}
66 \DeclareMathSymbol{\lozenge} {\mathord}{AMSa}{"06}
67 \DeclareMathSymbol{\blacklozenge} {\mathord}{AMSa}{"07}
68 \DeclareMathSymbol{\circlearrowright} {\mathrel}{AMSa}{"08}
69 \DeclareMathSymbol{\circlearrowleft} {\mathrel}{AMSa}{"09}
71 %%\DeclareMathSymbol{\rightleftharpoons}{\mathrel}{AMSa}{"0A}
72 \DeclareMathSymbol{\leftrightharpoons} {\mathrel}{AMSa}{"0B}
73 \DeclareMathSymbol{\boxminus} {\mathbin}{AMSa}{"0C}
74 \DeclareMathSymbol{\Vdash} {\mathrel}{AMSa}{"0D}
75 \DeclareMathSymbol{\Vvdash} {\mathrel}{AMSa}{"0E}
76 \DeclareMathSymbol{\vDash} {\mathrel}{AMSa}{"0F}
77 \DeclareMathSymbol{\twoheadrightarrow} {\mathrel}{AMSa}{"10}
78 \DeclareMathSymbol{\twoheadleftarrow} {\mathrel}{AMSa}{"11}
79 \DeclareMathSymbol{\leftleftarrows} {\mathrel}{AMSa}{"12}
80 \DeclareMathSymbol{\rightrightarrows} {\mathrel}{AMSa}{"13}
81 \DeclareMathSymbol{\upuparrows} {\mathrel}{AMSa}{"14}
82 \DeclareMathSymbol{\downdownarrows} {\mathrel}{AMSa}{"15}
83 \DeclareMathSymbol{\upharpoonright} {\mathrel}{AMSa}{"16}
84 \global\let\restriction\upharpoonright
85 \DeclareMathSymbol{\downharpoonright} {\mathrel}{AMSa}{"17}
86 \DeclareMathSymbol{\upharpoonleft} {\mathrel}{AMSa}{"18}
87 \DeclareMathSymbol{\downharpoonleft}{\mathrel}{AMSa}{"19}
88 \DeclareMathSymbol{\rightarrowtail} {\mathrel}{AMSa}{"1A}
89 \DeclareMathSymbol{\leftarrowtail} {\mathrel}{AMSa}{"1B}
90 \DeclareMathSymbol{\leftrightarrows}{\mathrel}{AMSa}{"1C}
91 \DeclareMathSymbol{\rightleftarrows}{\mathrel}{AMSa}{"1D}
92 \DeclareMathSymbol{\Lsh} {\mathrel}{AMSa}{"1E}
93 \DeclareMathSymbol{\Rsh} {\mathrel}{AMSa}{"1F}
94 \DeclareMathSymbol{\rightsquigarrow} {\mathrel}{AMSa}{"20}
95 \DeclareMathSymbol{\leftrightsquigarrow}{\mathrel}{AMSa}{"21}
96 \DeclareMathSymbol{\looparrowleft} {\mathrel}{AMSa}{"22}
97 \DeclareMathSymbol{\looparrowright} {\mathrel}{AMSa}{"23}
98 \DeclareMathSymbol{\circeq} {\mathrel}{AMSa}{"24}
99 \DeclareMathSymbol{\succsim} {\mathrel}{AMSa}{"25}
100 \DeclareMathSymbol{\gtrsim} {\mathrel}{AMSa}{"26}
101 \DeclareMathSymbol{\gtrapprox} {\mathrel}{AMSa}{"27}
102 \DeclareMathSymbol{\multimap} {\mathrel}{AMSa}{"28}
103 \DeclareMathSymbol{\therefore} {\mathrel}{AMSa}{"29}
104 \DeclareMathSymbol{\because} {\mathrel}{AMSa}{"2A}
105 \DeclareMathSymbol{\doteqdot} {\mathrel}{AMSa}{"2B}
106 \global\let\Doteq\doteqdot
107 \DeclareMathSymbol{\triangleq} {\mathrel}{AMSa}{"2C}
108 \DeclareMathSymbol{\precsim} {\mathrel}{AMSa}{"2D}
109 \DeclareMathSymbol{\lesssim} {\mathrel}{AMSa}{"2E}
110 \DeclareMathSymbol{\lessapprox} {\mathrel}{AMSa}{"2F}
111 \DeclareMathSymbol{\eqslantless} {\mathrel}{AMSa}{"30}
112 \DeclareMathSymbol{\eqslantgtr} {\mathrel}{AMSa}{"31}
113 \DeclareMathSymbol{\curlyeqprec} {\mathrel}{AMSa}{"32}
114 \DeclareMathSymbol{\curlyeqsucc} {\mathrel}{AMSa}{"33}
115 \DeclareMathSymbol{\preccurlyeq} {\mathrel}{AMSa}{"34}
116 \DeclareMathSymbol{\leqq} {\mathrel}{AMSa}{"35}
117 \DeclareMathSymbol{\leqslant} {\mathrel}{AMSa}{"36}
118 \DeclareMathSymbol{\lessgtr} {\mathrel}{AMSa}{"37}
119 \DeclareMathSymbol{\backprime} {\mathord}{AMSa}{"38}
120 \DeclareMathSymbol{\risingdotseq} {\mathrel}{AMSa}{"3A}
121 \DeclareMathSymbol{\fallingdotseq}{\mathrel}{AMSa}{"3B}
122 \DeclareMathSymbol{\succcurlyeq} {\mathrel}{AMSa}{"3C}
123 \DeclareMathSymbol{\geqq} {\mathrel}{AMSa}{"3D}
124 \DeclareMathSymbol{\geqslant} {\mathrel}{AMSa}{"3E}
125 \DeclareMathSymbol{\gtrless} {\mathrel}{AMSa}{"3F}
127 %% \DeclareMathSymbol{\sqsubset} {\mathrel}{AMSa}{"40}
128 %% \DeclareMathSymbol{\sqsupset} {\mathrel}{AMSa}{"41}
129 \DeclareMathSymbol{\vartriangleright}{\mathrel}{AMSa}{"42}
130 \DeclareMathSymbol{\vartriangleleft} {\mathrel}{AMSa}{"43}
131 \DeclareMathSymbol{\trianglerighteq} {\mathrel}{AMSa}{"44}
132 \DeclareMathSymbol{\trianglelefteq} {\mathrel}{AMSa}{"45}
133 \DeclareMathSymbol{\bigstar} {\mathord}{AMSa}{"46}
134 \DeclareMathSymbol{\between} {\mathrel}{AMSa}{"47}
135 \DeclareMathSymbol{\blacktriangledown} {\mathord}{AMSa}{"48}
136 \DeclareMathSymbol{\blacktriangleright} {\mathrel}{AMSa}{"49}
137 \DeclareMathSymbol{\blacktriangleleft} {\mathrel}{AMSa}{"4A}
138 \DeclareMathSymbol{\vartriangle} {\mathrel}{AMSa}{"4D}
139 \DeclareMathSymbol{\blacktriangle} {\mathord}{AMSa}{"4E}
140 \DeclareMathSymbol{\triangledown} {\mathord}{AMSa}{"4F}
141 \DeclareMathSymbol{\eqcirc} {\mathrel}{AMSa}{"50}
142 \DeclareMathSymbol{\lesseqgtr} {\mathrel}{AMSa}{"51}
143 \DeclareMathSymbol{\gtreqless} {\mathrel}{AMSa}{"52}
144 \DeclareMathSymbol{\lesseqqgtr} {\mathrel}{AMSa}{"53}
145 \DeclareMathSymbol{\gtreqqless} {\mathrel}{AMSa}{"54}
146 \DeclareMathSymbol{\Rrightarrow} {\mathrel}{AMSa}{"56}
147 \DeclareMathSymbol{\Lleftarrow} {\mathrel}{AMSa}{"57}
148 \DeclareMathSymbol{\veebar} {\mathbin}{AMSa}{"59}
149 \DeclareMathSymbol{\barwedge} {\mathbin}{AMSa}{"5A}
150 \DeclareMathSymbol{\doublebarwedge} {\mathbin}{AMSa}{"5B}
152 %%\DeclareMathSymbol{\angle} {\mathord}{AMSa}{"5C}
153 \DeclareMathSymbol{\measuredangle} {\mathord}{AMSa}{"5D}
154 \DeclareMathSymbol{\sphericalangle} {\mathord}{AMSa}{"5E}
155 \DeclareMathSymbol{\varpropto} {\mathrel}{AMSa}{"5F}
156 \DeclareMathSymbol{\smallsmile} {\mathrel}{AMSa}{"60}
157 \DeclareMathSymbol{\smallfrown} {\mathrel}{AMSa}{"61}
158 \DeclareMathSymbol{\Subset} {\mathrel}{AMSa}{"62}
159 \DeclareMathSymbol{\Supset} {\mathrel}{AMSa}{"63}
160 \DeclareMathSymbol{\Cup} {\mathbin}{AMSa}{"64}
161 \global\let\doublecup\Cup
162 \DeclareMathSymbol{\Cap} {\mathbin}{AMSa}{"65}
163 \global\let\doublecap\Cap
164 \DeclareMathSymbol{\curlywedge} {\mathbin}{AMSa}{"66}
165 \DeclareMathSymbol{\curlyvee} {\mathbin}{AMSa}{"67}
166 \DeclareMathSymbol{\leftthreetimes} {\mathbin}{AMSa}{"68}
167 \DeclareMathSymbol{\rightthreetimes}{\mathbin}{AMSa}{"69}
168 \DeclareMathSymbol{\subseteqq} {\mathrel}{AMSa}{"6A}
169 \DeclareMathSymbol{\supseteqq} {\mathrel}{AMSa}{"6B}
170 \DeclareMathSymbol{\bumpeq} {\mathrel}{AMSa}{"6C}
171 \DeclareMathSymbol{\Bumpeq} {\mathrel}{AMSa}{"6D}
172 \DeclareMathSymbol{\lll} {\mathrel}{AMSa}{"6E}
173 \global\let\llless\lll
174 \DeclareMathSymbol{\ggg} {\mathrel}{AMSa}{"6F}
175 \global\let\gggtr\ggg
176 \DeclareMathSymbol{\circledS} {\mathord}{AMSa}{"73}
177 \DeclareMathSymbol{\pitchfork} {\mathrel}{AMSa}{"74}
178 \DeclareMathSymbol{\dotplus} {\mathbin}{AMSa}{"75}
179 \DeclareMathSymbol{\backsim} {\mathrel}{AMSa}{"76}
180 \DeclareMathSymbol{\backsimeq} {\mathrel}{AMSa}{"77}
181 \DeclareMathSymbol{\complement} {\mathord}{AMSa}{"7B}
182 \DeclareMathSymbol{\intercal} {\mathbin}{AMSa}{"7C}
183 \DeclareMathSymbol{\circledcirc} {\mathbin}{AMSa}{"7D}
184 \DeclareMathSymbol{\circledast} {\mathbin}{AMSa}{"7E}
185 \DeclareMathSymbol{\circleddash} {\mathbin}{AMSa}{"7F}
186 %% Begin AMSb declarations
187 \DeclareMathSymbol{\lvertneqq} {\mathrel}{AMSb}{"00}
188 \DeclareMathSymbol{\gvertneqq} {\mathrel}{AMSb}{"01}
189 \DeclareMathSymbol{\nleq} {\mathrel}{AMSb}{"02}
190 \DeclareMathSymbol{\ngeq} {\mathrel}{AMSb}{"03}
191 \DeclareMathSymbol{\nless} {\mathrel}{AMSb}{"04}
192 \DeclareMathSymbol{\ngtr} {\mathrel}{AMSb}{"05}
193 \DeclareMathSymbol{\nprec} {\mathrel}{AMSb}{"06}
194 \DeclareMathSymbol{\nsucc} {\mathrel}{AMSb}{"07}
195 \DeclareMathSymbol{\lneqq} {\mathrel}{AMSb}{"08}
196 \DeclareMathSymbol{\gneqq} {\mathrel}{AMSb}{"09}
197 \DeclareMathSymbol{\nleqslant} {\mathrel}{AMSb}{"0A}
198 \DeclareMathSymbol{\ngeqslant} {\mathrel}{AMSb}{"0B}
199 \DeclareMathSymbol{\lneq} {\mathrel}{AMSb}{"0C}
200 \DeclareMathSymbol{\gneq} {\mathrel}{AMSb}{"0D}
201 \DeclareMathSymbol{\npreceq} {\mathrel}{AMSb}{"0E}
202 \DeclareMathSymbol{\nsucceq} {\mathrel}{AMSb}{"0F}
203 \DeclareMathSymbol{\precnsim} {\mathrel}{AMSb}{"10}
204 \DeclareMathSymbol{\succnsim} {\mathrel}{AMSb}{"11}
205 \DeclareMathSymbol{\lnsim} {\mathrel}{AMSb}{"12}
206 \DeclareMathSymbol{\gnsim} {\mathrel}{AMSb}{"13}
207 \DeclareMathSymbol{\nleqq} {\mathrel}{AMSb}{"14}
208 \DeclareMathSymbol{\ngeqq} {\mathrel}{AMSb}{"15}
209 \DeclareMathSymbol{\precneqq} {\mathrel}{AMSb}{"16}
210 \DeclareMathSymbol{\succneqq} {\mathrel}{AMSb}{"17}
211 \DeclareMathSymbol{\precnapprox} {\mathrel}{AMSb}{"18}
212 \DeclareMathSymbol{\succnapprox} {\mathrel}{AMSb}{"19}
213 \DeclareMathSymbol{\lnapprox} {\mathrel}{AMSb}{"1A}
214 \DeclareMathSymbol{\gnapprox} {\mathrel}{AMSb}{"1B}
215 \DeclareMathSymbol{\nsim} {\mathrel}{AMSb}{"1C}
216 \DeclareMathSymbol{\ncong} {\mathrel}{AMSb}{"1D}
217 \DeclareMathSymbol{\diagup} {\mathord}{AMSb}{"1E}
218 \DeclareMathSymbol{\diagdown} {\mathord}{AMSb}{"1F}
219 \DeclareMathSymbol{\varsubsetneq} {\mathrel}{AMSb}{"20}
220 \DeclareMathSymbol{\varsupsetneq} {\mathrel}{AMSb}{"21}
221 \DeclareMathSymbol{\nsubseteqq} {\mathrel}{AMSb}{"22}
222 \DeclareMathSymbol{\nsupseteqq} {\mathrel}{AMSb}{"23}
223 \DeclareMathSymbol{\subsetneqq} {\mathrel}{AMSb}{"24}
224 \DeclareMathSymbol{\supsetneqq} {\mathrel}{AMSb}{"25}
225 \DeclareMathSymbol{\varsubsetneqq} {\mathrel}{AMSb}{"26}
226 \DeclareMathSymbol{\varsupsetneqq} {\mathrel}{AMSb}{"27}
227 \DeclareMathSymbol{\subsetneq} {\mathrel}{AMSb}{"28}
228 \DeclareMathSymbol{\supsetneq} {\mathrel}{AMSb}{"29}
229 \DeclareMathSymbol{\nsubseteq} {\mathrel}{AMSb}{"2A}
230 \DeclareMathSymbol{\nsupseteq} {\mathrel}{AMSb}{"2B}
231 \DeclareMathSymbol{\nparallel} {\mathrel}{AMSb}{"2C}
232 \DeclareMathSymbol{\nmid} {\mathrel}{AMSb}{"2D}
233 \DeclareMathSymbol{\nshortmid} {\mathrel}{AMSb}{"2E}
234 \DeclareMathSymbol{\nshortparallel} {\mathrel}{AMSb}{"2F}
235 \DeclareMathSymbol{\nvdash} {\mathrel}{AMSb}{"30}
236 \DeclareMathSymbol{\nVdash} {\mathrel}{AMSb}{"31}
237 \DeclareMathSymbol{\nvDash} {\mathrel}{AMSb}{"32}
238 \DeclareMathSymbol{\nVDash} {\mathrel}{AMSb}{"33}
239 \DeclareMathSymbol{\ntrianglerighteq}{\mathrel}{AMSb}{"34}
240 \DeclareMathSymbol{\ntrianglelefteq}{\mathrel}{AMSb}{"35}
241 \DeclareMathSymbol{\ntriangleleft} {\mathrel}{AMSb}{"36}
242 \DeclareMathSymbol{\ntriangleright} {\mathrel}{AMSb}{"37}
243 \DeclareMathSymbol{\nleftarrow} {\mathrel}{AMSb}{"38}
244 \DeclareMathSymbol{\nrightarrow} {\mathrel}{AMSb}{"39}
245 \DeclareMathSymbol{\nLeftarrow} {\mathrel}{AMSb}{"3A}
246 \DeclareMathSymbol{\nRightarrow} {\mathrel}{AMSb}{"3B}
247 \DeclareMathSymbol{\nLeftrightarrow}{\mathrel}{AMSb}{"3C}
248 \DeclareMathSymbol{\nleftrightarrow}{\mathrel}{AMSb}{"3D}
249 \DeclareMathSymbol{\divideontimes} {\mathbin}{AMSb}{"3E}
250 \DeclareMathSymbol{\varnothing} {\mathord}{AMSb}{"3F}
251 \DeclareMathSymbol{\nexists} {\mathord}{AMSb}{"40}
252 \DeclareMathSymbol{\Finv} {\mathord}{AMSb}{"60}
253 \DeclareMathSymbol{\Game} {\mathord}{AMSb}{"61}
255 %%\DeclareMathSymbol{\mho} {\mathord}{AMSb}{"66}
256 \DeclareMathSymbol{\eth} {\mathord}{AMSb}{"67}
257 \DeclareMathSymbol{\eqsim} {\mathrel}{AMSb}{"68}
258 \DeclareMathSymbol{\beth} {\mathord}{AMSb}{"69}
259 \DeclareMathSymbol{\gimel} {\mathord}{AMSb}{"6A}
260 \DeclareMathSymbol{\daleth} {\mathord}{AMSb}{"6B}
261 \DeclareMathSymbol{\lessdot} {\mathbin}{AMSb}{"6C}
262 \DeclareMathSymbol{\gtrdot} {\mathbin}{AMSb}{"6D}
263 \DeclareMathSymbol{\ltimes} {\mathbin}{AMSb}{"6E}
264 \DeclareMathSymbol{\rtimes} {\mathbin}{AMSb}{"6F}
265 \DeclareMathSymbol{\shortmid} {\mathrel}{AMSb}{"70}
266 \DeclareMathSymbol{\shortparallel} {\mathrel}{AMSb}{"71}
267 \DeclareMathSymbol{\smallsetminus} {\mathbin}{AMSb}{"72}
268 \DeclareMathSymbol{\thicksim} {\mathrel}{AMSb}{"73}
269 \DeclareMathSymbol{\thickapprox} {\mathrel}{AMSb}{"74}
270 \DeclareMathSymbol{\approxeq} {\mathrel}{AMSb}{"75}
271 \DeclareMathSymbol{\succapprox} {\mathrel}{AMSb}{"76}
272 \DeclareMathSymbol{\precapprox} {\mathrel}{AMSb}{"77}
273 \DeclareMathSymbol{\curvearrowleft} {\mathrel}{AMSb}{"78}
274 \DeclareMathSymbol{\curvearrowright}{\mathrel}{AMSb}{"79}
275 \DeclareMathSymbol{\digamma} {\mathord}{AMSb}{"7A}
276 \DeclareMathSymbol{\varkappa} {\mathord}{AMSb}{"7B}
277 \DeclareMathSymbol{\Bbbk} {\mathord}{AMSb}{"7C}
278 \DeclareMathSymbol{\hslash} {\mathord}{AMSb}{"7D}
280 %%\DeclareMathSymbol{\hbar} {\mathord}{AMSb}{"7E}
281 \DeclareMathSymbol{\backepsilon} {\mathrel}{AMSb}{"7F}
285 %% End of file `amssymb.sty'.