1\begin{theindex} 2 3 \item \texttt{*}, \hyperpage{57} 4 \subitem for character tables, \hyperpage{1108} 5 \item \texttt{+}, \hyperpage{57} 6 \item \texttt{-}, \hyperpage{57} 7 \item \texttt {-A}, \hyperpage{33} 8 \item \texttt {-B}, \hyperpage{33} 9 \item \texttt {-D}, \hyperpage{34} 10 \item \texttt {-E}, \hyperpage{34} 11 \item \texttt {-K}, \hyperpage{35} 12 \item \texttt {-L}, \hyperpage{35} 13 \item \texttt {-M}, \hyperpage{36} 14 \item \texttt {-O}, \hyperpage{36} 15 \item \texttt{-P}, \hyperpage{37} 16 \item \texttt {-R}, \hyperpage{36} 17 \item \texttt {-T}, \hyperpage{37} 18 \item \texttt{-W}, \hyperpage{37} 19 \item \texttt {-b}, \hyperpage{34} 20 \item \texttt {-e}, \hyperpage{34} 21 \item \texttt {-f}, \hyperpage{34} 22 \item \texttt {-g}, \hyperpage{34} 23 \item \texttt {-g -g}, \hyperpage{35} 24 \item \texttt {-h}, \hyperpage{35} 25 \item \texttt {-infinity}, \hyperpage{241} 26 \item \texttt {-l}, \hyperpage{35} 27 \item \texttt {-m}, \hyperpage{36} 28 \item \texttt {-n}, \hyperpage{36} 29 \item \texttt {-o}, \hyperpage{36} 30 \item \texttt{-p}, \hyperpage{37} 31 \item \texttt {-q}, \hyperpage{36} 32 \item \texttt {-r}, \hyperpage{36} 33 \item \texttt {-s}, \hyperpage{36} 34 \item \texttt {-x}, \hyperpage{37} 35 \item \texttt {-y}, \hyperpage{37} 36 \item \texttt{-z}, \hyperpage{37} 37 \item \texttt{/}, \hyperpage{57} 38 \subitem for character tables, \hyperpage{1108} 39 \item \#, \hyperpage{46} 40 \item \#\%, \hyperpage{78} 41 \item \texttt{\texttt{\symbol{92}}*} 42 \subitem for transformations, \hyperpage{828} 43 \item \texttt{\texttt{\symbol{92}}/} 44 \subitem for a transformation and a permutation, \hyperpage{829} 45 \item \texttt{\texttt{\symbol{92}}{\textless}} 46 \subitem for transformations, \hyperpage{829} 47 \item \texttt{\texttt{\symbol{92}}=} 48 \subitem for transformations, \hyperpage{829} 49 \item \texttt{\texttt{\symbol{92}}\texttt{\symbol{94}}} 50 \subitem for a positive integer and a transformation, 51 \hyperpage{828} 52 \subitem for a transformation and a permutation, \hyperpage{828} 53 \item \texttt {\texttt {\char 92\relax }'}, \hyperpage{378} 54 \item \texttt {\texttt {\char 92\relax }0xYZ}, \hyperpage{378} 55 \item \texttt {\texttt {\char 92\relax }XYZ}, \hyperpage{378} 56 \item \texttt {\texttt {\char 92\relax }\texttt {\char 92\relax }}, 57 \hyperpage{378} 58 \item \texttt {\texttt {\char 92\relax }b}, \hyperpage{378} 59 \item \texttt {\texttt {\char 92\relax }c}, \hyperpage{378} 60 \item \texttt {\texttt {\char 92\relax }r}, \hyperpage{378} 61 \item \texttt{\texttt{\symbol{94}}} 62 \subitem for class functions, \hyperpage{1161} 63 \item \texttt{\texttt{\symbol{94}}}, \hyperpage{57} 64 65 \indexspace 66 67 \item abelian number field, \hyperpage{922} 68 \item abelian number fields 69 \subitem CanonicalBasis, \hyperpage{923} 70 \subitem Galois group, \hyperpage{925} 71 \item \texttt {AbelianGroup}, \hyperpage{762} 72 \item \texttt {AbelianInvariants}, \hyperpage{559} 73 \subitem for a character table, \hyperpage{1111} 74 \item \texttt{AbelianInvariants} 75 \subitem for groups, \hyperpage{559} 76 \item \texttt {AbelianInvariantsMultiplier}, \hyperpage{582} 77 \item \texttt {Abelian}\discretionary {-}{}{}\texttt {Invariants}\discretionary {-}{}{}\texttt {Normal}\discretionary {-}{}{}\texttt {Closure}\discretionary {-}{}{}\texttt {Fp}\discretionary {-}{}{}\texttt {Group}, 78 \hyperpage{723} 79 \item \texttt {Abelian}\discretionary {-}{}{}\texttt {Invariants}\discretionary {-}{}{}\texttt {Normal}\discretionary {-}{}{}\texttt {Closure}\discretionary {-}{}{}\texttt {Fp}\discretionary {-}{}{}\texttt {GroupRrs}, 80 \hyperpage{723} 81 \item \texttt {AbelianInvariantsOfList}, \hyperpage{365} 82 \item \texttt {AbelianInvariantsSubgroupFpGroup}, \hyperpage{723} 83 \item \texttt {AbelianInvariantsSubgroupFpGroupMtc}, \hyperpage{723} 84 \item \texttt {AbelianInvariantsSubgroupFpGroupRrs} 85 \subitem for a group and a coset table, \hyperpage{723} 86 \subitem for two groups, \hyperpage{723} 87 \item \texttt {AbelianNumberField}, \hyperpage{921} 88 \item \texttt {AbelianSubfactorAction}, \hyperpage{618} 89 \item About \textsf{GAP} manual, \hyperpage{23} 90 \item \texttt {AbsInt}, \hyperpage{190} 91 \item absolute value of an integer, \hyperpage{190} 92 \item \texttt {AbsoluteDiameter}, \hyperpage{257} 93 \item \texttt {AbsoluteIrreducibleModules}, \hyperpage{1135} 94 \item \texttt {AbsolutelyIrreducibleModules}, \hyperpage{1135} 95 \item \texttt {AbsoluteValue}, \hyperpage{239} 96 \subitem for floats, \hyperpage{255} 97 \item \texttt {AbsolutIrreducibleModules}, \hyperpage{1135} 98 \item abstract word, \hyperpage{496} 99 \item \texttt {AbstractWordTietzeWord}, \hyperpage{733} 100 \item accessing 101 \subitem list elements, \hyperpage{266} 102 \subitem record elements, \hyperpage{403} 103 \item \texttt {AClosest}\discretionary {-}{}{}\texttt {Vector}\discretionary {-}{}{}\texttt {Combinations}\discretionary {-}{}{}\texttt {Mat}\discretionary {-}{}{}\texttt {F}\discretionary {-}{}{}\texttt {F}\discretionary {-}{}{}\texttt {E}\discretionary {-}{}{}\texttt {VecFFE}, 104 \hyperpage{329} 105 \item \texttt {AClosest}\discretionary {-}{}{}\texttt {Vector}\discretionary {-}{}{}\texttt {Combinations}\discretionary {-}{}{}\texttt {Mat}\discretionary {-}{}{}\texttt {F}\discretionary {-}{}{}\texttt {F}\discretionary {-}{}{}\texttt {E}\discretionary {-}{}{}\texttt {Vec}\discretionary {-}{}{}\texttt {F}\discretionary {-}{}{}\texttt {F}\discretionary {-}{}{}\texttt {E}\discretionary {-}{}{}\texttt {Coords}, 106 \hyperpage{329} 107 \item \texttt {Acos}, \hyperpage{255} 108 \item \texttt {Acosh}, \hyperpage{255} 109 \item \texttt {ActingAlgebra}, \hyperpage{977} 110 \item \texttt {ActingDomain}, \hyperpage{625} 111 \item \texttt {Action} 112 \subitem for a group, an action domain, etc., \hyperpage{616} 113 \subitem for an external set, \hyperpage{616} 114 \item action 115 \subitem by conjugation, \hyperpage{607} 116 \subitem on blocks, \hyperpage{608} 117 \subitem on sets, \hyperpage{608} 118 \item \texttt {ActionHomomorphism} 119 \subitem for a group, an action domain, etc., \hyperpage{616} 120 \subitem for an action image, \hyperpage{616} 121 \subitem for an external set, \hyperpage{616} 122 \item actions, \hyperpage{607} 123 \item \texttt {ActivateProfileColour}, \hyperpage{121} 124 \item \texttt {ActorOfExternalSet}, \hyperpage{628} 125 \item \texttt {Add}, \hyperpage{269} 126 \item add 127 \subitem an element to a set, \hyperpage{297} 128 \item \texttt {AddCoeffs}, \hyperpage{327} 129 \item \texttt {AddDictionary}, \hyperpage{399} 130 \item \texttt {AddGenerator}, \hyperpage{736} 131 \item \texttt {AddGeneratorsExtendSchreierTree}, \hyperpage{651} 132 \item addition, \hyperpage{57} 133 \subitem list and non-list, \hyperpage{280} 134 \subitem matrices, \hyperpage{334} 135 \subitem matrix and scalar, \hyperpage{334} 136 \subitem operation, \hyperpage{440} 137 \subitem rational functions, \hyperpage{1025} 138 \subitem scalar and matrix, \hyperpage{334} 139 \subitem scalar and matrix list, \hyperpage{335} 140 \subitem vector and scalar, \hyperpage{323} 141 \subitem vectors, \hyperpage{323} 142 \item \texttt {AdditiveInverse}, \hyperpage{439} 143 \item \texttt {AdditiveInverseAttr}, \hyperpage{439} 144 \item \texttt {AdditiveInverseImmutable}, \hyperpage{439} 145 \item \texttt {AdditiveInverseMutable}, \hyperpage{439} 146 \item \texttt {AdditiveInverseOp}, \hyperpage{439} 147 \item \texttt {AdditiveInverseSameMutability}, \hyperpage{439} 148 \item \texttt {AdditiveInverseSM}, \hyperpage{439} 149 \item \texttt {AdditiveNeutralElement}, \hyperpage{874} 150 \item \texttt {AddRelator}, \hyperpage{737} 151 \item \texttt {AddRowVector}, \hyperpage{326} 152 \item \texttt {AddRule}, \hyperpage{521} 153 \item \texttt {AddRuleReduced}, \hyperpage{521} 154 \item \texttt {AddSet}, \hyperpage{297} 155 \item \texttt {AdjointAssociativeAlgebra}, \hyperpage{1003} 156 \item \texttt {AdjointBasis}, \hyperpage{962} 157 \item \texttt {AdjointMatrix}, \hyperpage{1002} 158 \item \texttt {AdjointModule}, \hyperpage{979} 159 \item \texttt {AffineAction}, \hyperpage{684} 160 \item \texttt {AffineActionLayer}, \hyperpage{684} 161 \item \texttt {Agemo}, \hyperpage{551} 162 \item \texttt {Algebra}, \hyperpage{949} 163 \item \texttt {AlgebraByStructureConstants}, \hyperpage{951} 164 \item \texttt {AlgebraGeneralMappingByImages}, \hyperpage{969} 165 \item \texttt {AlgebraHomomorphismByImages}, \hyperpage{969} 166 \item \texttt {AlgebraHomomorphismByImagesNC}, \hyperpage{969} 167 \item \texttt {AlgebraicExtension}, \hyperpage{1055} 168 \item \texttt {AlgebraicExtensionNC}, \hyperpage{1055} 169 \item \texttt {AlgebraWithOne}, \hyperpage{950} 170 \item \texttt {Algebra}\discretionary {-}{}{}\texttt {With}\discretionary {-}{}{}\texttt {One}\discretionary {-}{}{}\texttt {General}\discretionary {-}{}{}\texttt {Mapping}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Images}, 171 \hyperpage{970} 172 \item \texttt {AlgebraWithOneHomomorphismByImages}, \hyperpage{970} 173 \item \texttt {Algebra}\discretionary {-}{}{}\texttt {With}\discretionary {-}{}{}\texttt {One}\discretionary {-}{}{}\texttt {Homomorphism}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {ImagesNC}, 174 \hyperpage{971} 175 \item \texttt {AllAutomorphisms}, \hyperpage{601} 176 \item \texttt {AllBlocks}, \hyperpage{624} 177 \item \texttt {AllEndomorphisms}, \hyperpage{601} 178 \item \texttt {AllHomomorphismClasses}, \hyperpage{601} 179 \item \texttt {AllHomomorphisms}, \hyperpage{601} 180 \item \texttt{All\mbox{\texttt{\mdseries\slshape Library}}Groups}, 181 \hyperpage{773} 182 \item \texttt{AllPrimitiveGroups}, \hyperpage{773} 183 \item \texttt {AllSmallNonabelianSimpleGroups}, \hyperpage{556} 184 \item \texttt {AllSubgroups}, \hyperpage{568} 185 \item \texttt{AllTransitiveGroups}, \hyperpage{773} 186 \item \texttt {Alpha}, \hyperpage{1228} 187 \item \texttt {AlternatingGroup} 188 \subitem for a degree, \hyperpage{764} 189 \subitem for a domain, \hyperpage{764} 190 \item \texttt{and}, \hyperpage{261} 191 \subitem for filters, \hyperpage{171}, \hyperpage{261} 192 \item \texttt {ANFAutomorphism}, \hyperpage{927} 193 \item \texttt {Anti}\discretionary {-}{}{}\texttt {Isomorphism}\discretionary {-}{}{}\texttt {Transformation}\discretionary {-}{}{}\texttt {Semigroup}, 194 \hyperpage{843} 195 \item antisymmetric relation, \hyperpage{472} 196 \item \texttt {AntiSymmetricParts}, \hyperpage{1183} 197 \item \texttt {Append}, \hyperpage{270} 198 \item \texttt {AppendTo}, \hyperpage{139} 199 \subitem for streams, \hyperpage{148} 200 \item \texttt {ApplicableMethod}, \hyperpage{105} 201 \item \texttt {ApplicableMethodTypes}, \hyperpage{105} 202 \item \texttt {Apply}, \hyperpage{301} 203 \item \texttt {ApplySimpleReflection}, \hyperpage{998} 204 \item \texttt {Approximate}\discretionary {-}{}{}\texttt {Suborbits}\discretionary {-}{}{}\texttt {Stabilizer}\discretionary {-}{}{}\texttt {Perm}\discretionary {-}{}{}\texttt {Group}, 205 \hyperpage{649} 206 \item \texttt {ARC}\discretionary {-}{}{}\texttt {H{\textunderscore }}\discretionary {-}{}{}\texttt {I}\discretionary {-}{}{}\texttt {S{\textunderscore }}\discretionary {-}{}{}\texttt {M}\discretionary {-}{}{}\texttt {A}\discretionary {-}{}{}\texttt {C{\textunderscore }}\discretionary {-}{}{}\texttt {O}\discretionary {-}{}{}\texttt {S{\textunderscore }X}, 207 \hyperpage{42} 208 \item \texttt {ARC}\discretionary {-}{}{}\texttt {H{\textunderscore }}\discretionary {-}{}{}\texttt {I}\discretionary {-}{}{}\texttt {S{\textunderscore }}\discretionary {-}{}{}\texttt {UNIX}, 209 \hyperpage{42} 210 \item \texttt {ARC}\discretionary {-}{}{}\texttt {H{\textunderscore }}\discretionary {-}{}{}\texttt {I}\discretionary {-}{}{}\texttt {S{\textunderscore }}\discretionary {-}{}{}\texttt {W}\discretionary {-}{}{}\texttt {I}\discretionary {-}{}{}\texttt {N}\discretionary {-}{}{}\texttt {DOWS}, 211 \hyperpage{42} 212 \item \texttt{arg} 213 \subitem special function argument, \hyperpage{66} 214 \subitem special function argument, calling with, \hyperpage{54} 215 \item \texttt {Argument} 216 \subitem for complex floats, \hyperpage{256} 217 \item arithmetic operators 218 \subitem precedence, \hyperpage{58} 219 \item \texttt {ArithmeticElementCreator}, \hyperpage{1312} 220 \item \texttt {Arrangements}, \hyperpage{222} 221 \item arrow notation for functions, \hyperpage{67} 222 \item \texttt {AsAlgebra}, \hyperpage{962} 223 \item \texttt {AsAlgebraWithOne}, \hyperpage{963} 224 \item \texttt {AsBinaryRelationOnPoints} 225 \subitem for a binary relation, \hyperpage{474} 226 \subitem for a permutation, \hyperpage{474} 227 \subitem for a transformation, \hyperpage{474} 228 \item \texttt {AsBlockMatrix}, \hyperpage{358} 229 \item \texttt {AscendingChain}, \hyperpage{564} 230 \item \texttt {AsDivisionRing}, \hyperpage{904} 231 \item \texttt {AsDuplicateFreeList}, \hyperpage{300} 232 \item \texttt {AsField}, \hyperpage{904} 233 \item \texttt {AsGroup}, \hyperpage{527} 234 \item \texttt {AsGroupGeneralMappingByImages}, \hyperpage{591} 235 \item \texttt {Asin}, \hyperpage{255} 236 \item \texttt {Asinh}, \hyperpage{255} 237 \item \texttt {AsInternalFFE}, \hyperpage{915} 238 \item \texttt {AsLeftIdeal}, \hyperpage{882} 239 \item \texttt {AsLeftModule}, \hyperpage{897} 240 \item \texttt {AsList}, \hyperpage{416} 241 \item \texttt {AsMagma}, \hyperpage{489} 242 \item \texttt {AsMonoid}, \hyperpage{793} 243 \item \texttt {AsPartialPerm} 244 \subitem for a permutation, \hyperpage{859} 245 \subitem for a permutation and a positive integer, \hyperpage{859} 246 \subitem for a permutation and a set of positive integers, 247 \hyperpage{859} 248 \subitem for a transformation and a positive integer, 249 \hyperpage{860} 250 \subitem for a transformation and a set of positive integer, 251 \hyperpage{860} 252 \item \texttt {AsPermutation}, \hyperpage{635} 253 \item \texttt {AsPolynomial}, \hyperpage{1028} 254 \item \texttt {AsRightIdeal}, \hyperpage{882} 255 \item \texttt {AsSemigroup}, \hyperpage{790} 256 \item \texttt {Assert}, \hyperpage{110} 257 \item \texttt {AssertionLevel}, \hyperpage{110} 258 \item \texttt {AsSet}, \hyperpage{417} 259 \item \texttt {AssignGeneratorVariables}, \hyperpage{504} 260 \item assignment 261 \subitem to a list, \hyperpage{267} 262 \subitem to a record, \hyperpage{404} 263 \subitem variable, \hyperpage{59} 264 \item \texttt {Assign}\discretionary {-}{}{}\texttt {Nice}\discretionary {-}{}{}\texttt {Monomorphism}\discretionary {-}{}{}\texttt {Automorphism}\discretionary {-}{}{}\texttt {Group}, 265 \hyperpage{600} 266 \item \texttt {AssociatedPartition}, \hyperpage{229} 267 \item \texttt {Associated}\discretionary {-}{}{}\texttt {Rees}\discretionary {-}{}{}\texttt {Matrix}\discretionary {-}{}{}\texttt {Semigroup}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {D}\discretionary {-}{}{}\texttt {Class}, 268 \hyperpage{811} 269 \item \texttt {Associates}, \hyperpage{886} 270 \item associativity, \hyperpage{57} 271 \item \texttt {AssocWordByLetterRep}, \hyperpage{510} 272 \item \texttt {AsSortedList}, \hyperpage{416} 273 \item \texttt {AsSSortedList}, \hyperpage{417} 274 \item \texttt{As\mbox{\texttt{\mdseries\slshape Struct}}}, 275 \hyperpage{431} 276 \item \texttt {AsSubalgebra}, \hyperpage{963} 277 \item \texttt {AsSubalgebraWithOne}, \hyperpage{963} 278 \item \texttt {AsSubgroup}, \hyperpage{529} 279 \item \texttt {AsSubgroupOfWholeGroupByQuotient}, \hyperpage{719} 280 \item \texttt {AsSubmagma}, \hyperpage{489} 281 \item \texttt {AsSubmonoid}, \hyperpage{794} 282 \item \texttt {AsSubsemigroup}, \hyperpage{790} 283 \item \texttt {AsSubspace}, \hyperpage{929} 284 \item \texttt{AsSub\mbox{\texttt{\mdseries\slshape struct}}}, 285 \hyperpage{434} 286 \item \texttt {AsTransformation}, \hyperpage{826} 287 \item \texttt {AsTwoSidedIdeal}, \hyperpage{882} 288 \item \texttt {AsVectorSpace}, \hyperpage{929} 289 \item at exit functions, \hyperpage{93} 290 \item \texttt {Atan}, \hyperpage{255} 291 \item \texttt {Atan2}, \hyperpage{255} 292 \item \texttt {Atanh}, \hyperpage{255} 293 \item \texttt {AtlasIrrationality}, \hyperpage{245} 294 \item atomic irrationalities, \hyperpage{242} 295 \item \texttt {AttributeValueNotSet}, \hyperpage{181} 296 \item \texttt {AugmentationIdeal}, \hyperpage{1017} 297 \item \texttt {AugmentedCosetTableInWholeGroup}, \hyperpage{712} 298 \item \texttt {AugmentedCosetTableMtc}, \hyperpage{712} 299 \item \texttt {AugmentedCosetTableRrs}, \hyperpage{713} 300 \item automatic loading of GAP packages, \hyperpage{1237} 301 \item automorphism group 302 \subitem of number fields, \hyperpage{925} 303 \item \texttt {AutomorphismDomain}, \hyperpage{598} 304 \item \texttt {AutomorphismGroup}, \hyperpage{598} 305 \item \texttt{AutomorphismGroup} 306 \subitem for groups with pcgs, \hyperpage{685} 307 \item \texttt {AutomorphismsOfTable}, \hyperpage{1113} 308 \item autoreadable variables, \hyperpage{1259} 309 310 \indexspace 311 312 \item $b_N$ (irrational value), \hyperpage{242} 313 \item backslash character, \hyperpage{378} 314 \item backspace character, \hyperpage{378} 315 \item Backtrace 316 \subitem GAP3 name for Where, \hyperpage{90} 317 \item \texttt{BANNER}, \hyperpage{1273} 318 \item banner 319 \subitem for a GAP package, \hyperpage{1262} 320 \item \texttt {BaseFixedSpace}, \hyperpage{344} 321 \item \texttt {BaseIntersectionIntMats}, \hyperpage{361} 322 \item \texttt {BaseIntMat}, \hyperpage{361} 323 \item \texttt {BaseMat}, \hyperpage{349} 324 \item \texttt {BaseMatDestructive}, \hyperpage{349} 325 \item \texttt {BaseOfGroup}, \hyperpage{647} 326 \item \texttt {BaseOrthogonalSpaceMat}, \hyperpage{349} 327 \item \texttt {BaseStabChain}, \hyperpage{647} 328 \item \texttt {BaseSteinitzVectors}, \hyperpage{350} 329 \item \texttt {Basic}\discretionary {-}{}{}\texttt {Spin}\discretionary {-}{}{}\texttt {Representation}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Symmetric}\discretionary {-}{}{}\texttt {Group}, 330 \hyperpage{584} 331 \item \texttt {BasicWreathProductOrdering}, \hyperpage{484} 332 \item \texttt {Basis}, \hyperpage{932} 333 \item \texttt {BasisNC}, \hyperpage{932} 334 \item \texttt {BasisNullspaceModN}, \hyperpage{356} 335 \item \texttt {BasisVectors}, \hyperpage{933} 336 \item \texttt {Bell}, \hyperpage{219} 337 \item \texttt {Bernoulli}, \hyperpage{219} 338 \item \texttt {BestQuoInt}, \hyperpage{192} 339 \item \texttt {BestSplittingMatrix}, \hyperpage{1137} 340 \item \texttt {BetaSet}, \hyperpage{230} 341 \item \texttt {BiAlgebraModule}, \hyperpage{975} 342 \item \texttt {BiAlgebraModuleByGenerators}, \hyperpage{974} 343 \item \texttt {BibEntry}, \hyperpage{1246} 344 \item bicoset, \hyperpage{538} 345 \item \texttt {BilinearFormMat}, \hyperpage{996} 346 \item binary relation, \hyperpage{470} 347 \item \texttt {BinaryRelationByElements}, \hyperpage{470} 348 \item \texttt {BinaryRelationOnPoints}, \hyperpage{474} 349 \item \texttt {BinaryRelationOnPointsNC}, \hyperpage{474} 350 \item \texttt {BindConstant}, \hyperpage{52} 351 \item \texttt {BindGlobal}, \hyperpage{52} 352 \item \texttt {Binomial}, \hyperpage{218} 353 \item \texttt {BisectInterval}, \hyperpage{258} 354 \item blank, \hyperpage{46} 355 \item \texttt {BlistList}, \hyperpage{316} 356 \item \texttt {BlockMatrix}, \hyperpage{358} 357 \item \texttt {Blocks} 358 \subitem for a group, an action domain, etc., \hyperpage{623} 359 \subitem for an external set, \hyperpage{623} 360 \item \texttt {BlocksInfo}, \hyperpage{1121} 361 \item \texttt {BlownUpMat}, \hyperpage{352} 362 \item \texttt {BlownUpVector}, \hyperpage{353} 363 \item \texttt {BlowupInterval}, \hyperpage{258} 364 \item \texttt {BlowUpIsomorphism}, \hyperpage{657} 365 \item body, \hyperpage{65} 366 \item \texttt {BombieriNorm}, \hyperpage{1037} 367 \item bound, \hyperpage{49} 368 \item Brauer character, \hyperpage{1167} 369 \item \texttt {BrauerCharacterValue}, \hyperpage{1195} 370 \item \texttt {BrauerTable} 371 \subitem for a character table, and a prime integer, 372 \hyperpage{1101} 373 \subitem for a group, and a prime integer, \hyperpage{1101} 374 \item \texttt {BrauerTableOp}, \hyperpage{1101} 375 \item \texttt {BravaisGroup}, \hyperpage{662} 376 \item \texttt {BravaisSubgroups}, \hyperpage{662} 377 \item \texttt {BravaisSupergroups}, \hyperpage{663} 378 \item Break loop message, \hyperpage{89} 379 \item \texttt{break} statement, \hyperpage{64} 380 \item browsing backwards, \hyperpage{28} 381 \item browsing backwards one chapter, \hyperpage{29} 382 \item browsing forward, \hyperpage{28} 383 \item browsing forward one chapter, \hyperpage{29} 384 \item browsing the next section browsed, \hyperpage{29} 385 \item browsing the previous section browsed, \hyperpage{29} 386 \item \texttt {\texttt {\char 92\relax }*}, \hyperpage{440} 387 \subitem for pcwords, \hyperpage{689} 388 \item \texttt {\texttt {\char 92\relax }+}, \hyperpage{440} 389 \item \texttt {\texttt {\char 92\relax }.}, \hyperpage{408} 390 \item \texttt {\texttt {\char 92\relax }.\texttt {\char 92\relax }:\texttt {\char 92\relax }=}, 391 \hyperpage{409} 392 \item \texttt {\texttt {\char 92\relax }/}, \hyperpage{440} 393 \subitem for a free group and a list of elements, \hyperpage{702} 394 \subitem for a free group and a list of pairs of elements, 395 \hyperpage{702} 396 \subitem for a free semigroup or monoid and a list of pairs of elements, 397 \hyperpage{815} 398 \item \texttt {\texttt {\char 92\relax }{\textless }}, 399 \hyperpage{439} 400 \subitem for associative words, \hyperpage{505} 401 \subitem for nonassociative words, \hyperpage{498} 402 \subitem for pcwords, \hyperpage{689} 403 \subitem for permutations, \hyperpage{631} 404 \subitem for two elements in a f.p. group, \hyperpage{704} 405 \subitem for two strings, \hyperpage{382} 406 \item \texttt {\texttt {\char 92\relax }=}, \hyperpage{439} 407 \subitem for associative words, \hyperpage{504} 408 \subitem for nonassociative words, \hyperpage{498} 409 \subitem for pcwords, \hyperpage{689} 410 \subitem for permutations, \hyperpage{631} 411 \subitem for two elements in a f.p. group, \hyperpage{703} 412 \subitem for two elements in a f.p. semigroup, \hyperpage{816} 413 \subitem for two strings, \hyperpage{381} 414 \item \texttt {\texttt {\char 92\relax }[\texttt {\char 92\relax }]}, 415 \hyperpage{265} 416 \item \texttt {\texttt {\char 92\relax }[\texttt {\char 92\relax }]\texttt {\char 92\relax }:\texttt {\char 92\relax }=}, 417 \hyperpage{265} 418 \item \texttt {\texttt {\char 92\relax }\texttt {\char 94\relax }}, 419 \hyperpage{440} 420 \subitem for a field and a pair of integers, \hyperpage{940} 421 \subitem for a field and an integer, \hyperpage{939} 422 \item \texttt {\texttt {\char 92\relax }in} 423 \subitem element test for lists, \hyperpage{275} 424 \subitem for a collection, \hyperpage{422} 425 \subitem for strictly sorted lists, \hyperpage{296} 426 \item \texttt {\texttt {\char 92\relax }mod}, \hyperpage{440} 427 \subitem for residue class rings, \hyperpage{200} 428 \subitem for two pcgs, \hyperpage{674} 429 \item \texttt {\texttt {\char 92\relax }\texttt {\char 123\relax }\texttt {\char 92\relax }\texttt {\char 125\relax }}, 430 \hyperpage{267} 431 \item \texttt {\texttt {\char 92\relax }\texttt {\char 123\relax }\texttt {\char 92\relax }\texttt {\char 125\relax }\texttt {\char 92\relax }:\texttt {\char 92\relax }=}, 432 \hyperpage{269} 433 \item \texttt {BuildBitfields}, \hyperpage{206} 434 435 \indexspace 436 437 \item $c_N$ (irrational value), \hyperpage{242} 438 \item \texttt {CallFuncList}, \hyperpage{73} 439 \item \texttt {CallFuncListWrap}, \hyperpage{73} 440 \item \texttt {CanComputeIndex}, \hyperpage{587} 441 \item \texttt {CanComputeIsSubset}, \hyperpage{587} 442 \item \texttt {CanComputeSize}, \hyperpage{587} 443 \item \texttt {CanComputeSizeAnySubgroup}, \hyperpage{587} 444 \item candidates 445 \subitem for permutation characters, \hyperpage{1187} 446 \item \texttt {CanEasilyCompareElements}, \hyperpage{440} 447 \item \texttt {CanEasilyCompareElementsFamily}, \hyperpage{440} 448 \item \texttt {CanEasilyComputePcgs}, \hyperpage{665} 449 \item \texttt {Can}\discretionary {-}{}{}\texttt {Easily}\discretionary {-}{}{}\texttt {Compute}\discretionary {-}{}{}\texttt {With}\discretionary {-}{}{}\texttt {Independent}\discretionary {-}{}{}\texttt {Gens}\discretionary {-}{}{}\texttt {Abelian}\discretionary {-}{}{}\texttt {Group}, 450 \hyperpage{587} 451 \item \texttt {CanEasilySortElements}, \hyperpage{440} 452 \item \texttt {CanEasilySortElementsFamily}, \hyperpage{440} 453 \item \texttt {CanEasilyTestMembership}, \hyperpage{586} 454 \item canonical basis 455 \subitem for matrix spaces, \hyperpage{941} 456 \subitem for row spaces, \hyperpage{941} 457 \item \texttt {CanonicalBasis}, \hyperpage{933} 458 \item \texttt {CanonicalGenerators}, \hyperpage{997} 459 \item \texttt {CanonicalPcElement}, \hyperpage{669} 460 \item \texttt {CanonicalPcgs}, \hyperpage{673} 461 \item \texttt {CanonicalPcgsByGeneratorsWithImages}, \hyperpage{675} 462 \item \texttt {Canonical}\discretionary {-}{}{}\texttt {Representative}\discretionary {-}{}{}\texttt {Determinator}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {ExternalSet}, 463 \hyperpage{627} 464 \item \texttt {Canonical}\discretionary {-}{}{}\texttt {Representative}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {ExternalSet}, 465 \hyperpage{627} 466 \item \texttt {CanonicalRightCosetElement}, \hyperpage{537} 467 \item Carmichael's lambda function, \hyperpage{209} 468 \item carriage return character, \hyperpage{378} 469 \item \texttt {CartanMatrix}, \hyperpage{996} 470 \item \texttt {CartanSubalgebra}, \hyperpage{992} 471 \item \texttt {Cartesian} 472 \subitem for a list, \hyperpage{303} 473 \subitem for various objects, \hyperpage{303} 474 \item \texttt {CategoriesOfObject}, \hyperpage{175} 475 \item \texttt {CategoryByName}, \hyperpage{175} 476 \item \texttt {CategoryCollections}, \hyperpage{411} 477 \item \texttt {CategoryFamily}, \hyperpage{176} 478 \item \texttt {Ceil}, \hyperpage{255} 479 \item \texttt {Center}, \hyperpage{493} 480 \item center, \hyperpage{493} 481 \item central character, \hyperpage{1171} 482 \item \texttt {CentralCharacter}, \hyperpage{1171} 483 \item \texttt {CentralIdempotentsOfAlgebra}, \hyperpage{966} 484 \item centraliser, \hyperpage{493} 485 \item \texttt {Centralizer} 486 \subitem for a class of objects in a magma, \hyperpage{493} 487 \subitem for a magma and a submagma, \hyperpage{493} 488 \subitem for a magma and an element, \hyperpage{493} 489 \item \texttt{Centralizer} 490 \subitem for groups with pcgs, \hyperpage{685} 491 \item \texttt {CentralizerInGLnZ}, \hyperpage{662} 492 \item \texttt {CentralizerModulo}, \hyperpage{566} 493 \item \texttt {Centralizer}\discretionary {-}{}{}\texttt {Size}\discretionary {-}{}{}\texttt {Limit}\discretionary {-}{}{}\texttt {Consider}\discretionary {-}{}{}\texttt {Function}, 494 \hyperpage{686} 495 \item \texttt {CentralNormalSeriesByPcgs}, \hyperpage{678} 496 \item \texttt {Centre}, \hyperpage{493} 497 \item \texttt{Centre} 498 \subitem for groups with pcgs, \hyperpage{685} 499 \item centre 500 \subitem of a character, \hyperpage{1170} 501 \item \texttt {CentreOfCharacter}, \hyperpage{1170} 502 \item \texttt {CF} 503 \subitem for (subfield and) conductor, \hyperpage{920} 504 \subitem for (subfield and) generators, \hyperpage{920} 505 \item \texttt {ChangeStabChain}, \hyperpage{650} 506 \item \texttt {Character} 507 \subitem for a character table and a list, \hyperpage{1164} 508 \subitem for a group and a list, \hyperpage{1164} 509 \item character tables, \hyperpage{1100} 510 \subitem access to, \hyperpage{1100} 511 \subitem calculate, \hyperpage{1100} 512 \subitem infix operators, \hyperpage{1108} 513 \subitem of groups, \hyperpage{1100} 514 \item character value 515 \subitem of group element using powering operator, \hyperpage{1161} 516 \item \texttt {CharacterDegrees} 517 \subitem for a character table, \hyperpage{1109} 518 \subitem for a group, \hyperpage{1109} 519 \item \texttt {Characteristic}, \hyperpage{435} 520 \subitem for a class function, \hyperpage{1162} 521 \item characteristic polynomial 522 \subitem for field elements, \hyperpage{907} 523 \item \texttt {CharacteristicPolynomial}, \hyperpage{351} 524 \item \texttt {CharacteristicSubgroups}, \hyperpage{569} 525 \item \texttt {CharacterNames}, \hyperpage{1114} 526 \item \texttt {CharacterParameters}, \hyperpage{1114} 527 \item characters, \hyperpage{1155} 528 \subitem permutation, \hyperpage{1187} 529 \subitem symmetrizations of, \hyperpage{1182} 530 \item \texttt {CharacterTable} 531 \subitem for a group, \hyperpage{1100} 532 \subitem for a string, \hyperpage{1100} 533 \subitem for an ordinary character table, \hyperpage{1100} 534 \item \texttt {CharacterTableDirectProduct}, \hyperpage{1141} 535 \item \texttt {CharacterTableFactorGroup}, \hyperpage{1142} 536 \item \texttt {CharacterTableIsoclinic}, \hyperpage{1142} 537 \subitem for a Brauer table and an ordinary table, \hyperpage{1142} 538 \subitem for a character table and one or two lists, 539 \hyperpage{1142} 540 \item \texttt {CharacterTableOfNormalSubgroup}, \hyperpage{1145} 541 \item \texttt {CharacterTableRegular}, \hyperpage{1102} 542 \item \texttt {CharacterTableWithSortedCharacters}, \hyperpage{1147} 543 \item \texttt {CharacterTableWithSortedClasses}, \hyperpage{1148} 544 \item \texttt {CharacterTableWithStoredGroup}, \hyperpage{1106} 545 \item \texttt {CharacterTableWreathSymmetric}, \hyperpage{1146} 546 \item \texttt {CharacterValueWreathSymmetric}, \hyperpage{1146} 547 \item \texttt {CharInt}, \hyperpage{390} 548 \item \texttt {CharsFamily}, \hyperpage{380} 549 \item \texttt {CharSInt}, \hyperpage{390} 550 \item \texttt {CheckDigitISBN}, \hyperpage{202} 551 \item \texttt {CheckDigitISBN13}, \hyperpage{202} 552 \item \texttt {CheckDigitPostalMoneyOrder}, \hyperpage{202} 553 \item \texttt {CheckDigitTestFunction}, \hyperpage{203} 554 \item \texttt {CheckDigitUPC}, \hyperpage{202} 555 \item \texttt {CheckFixedPoints}, \hyperpage{1213} 556 \item \texttt {CheckForHandlingByNiceBasis}, \hyperpage{948} 557 \item \texttt {CheckPermChar}, \hyperpage{1221} 558 \item \texttt {ChevalleyBasis}, \hyperpage{995} 559 \item \texttt {ChiefNormalSeriesByPcgs}, \hyperpage{679} 560 \item \texttt {ChiefSeries}, \hyperpage{560} 561 \item \texttt {ChiefSeriesThrough}, \hyperpage{560} 562 \item \texttt {ChiefSeriesUnderAction}, \hyperpage{560} 563 \item Chinese remainder, \hyperpage{195} 564 \item \texttt {ChineseRem}, \hyperpage{195} 565 \item \texttt {Chomp}, \hyperpage{387} 566 \item \texttt {Cite}, \hyperpage{1247} 567 \item \texttt {CIUnivPols}, \hyperpage{1025} 568 \item class function, \hyperpage{1157} 569 \item class function objects, \hyperpage{1157} 570 \item class functions, \hyperpage{1208} 571 \subitem as ring elements, \hyperpage{1160} 572 \item class multiplication coefficient, \hyperpage{1126, 1127} 573 \item \texttt {ClassElementLattice}, \hyperpage{570} 574 \item classes 575 \subitem real, \hyperpage{1116} 576 \item \texttt {ClassesSolvableGroup}, \hyperpage{686} 577 \item \texttt {ClassFunction} 578 \subitem for a character table and a list, \hyperpage{1164} 579 \subitem for a group and a list, \hyperpage{1164} 580 \item \texttt {ClassFunctionSameType}, \hyperpage{1165} 581 \item \texttt {ClassMultiplicationCoefficient} 582 \subitem for character tables, \hyperpage{1126} 583 \item \texttt{ClassMultiplicationCoefficient} 584 \subitem for character tables, \hyperpage{1126} 585 \item \texttt {ClassNames}, \hyperpage{1114} 586 \item \texttt {ClassNamesTom}, \hyperpage{1083} 587 \item \texttt {ClassOrbit}, \hyperpage{1116} 588 \item \texttt {ClassParameters}, \hyperpage{1114} 589 \item \texttt {ClassPermutation}, \hyperpage{1149} 590 \item \texttt {ClassPositionsOfAgemo}, \hyperpage{1117} 591 \item \texttt {ClassPositionsOfCenter} 592 \subitem for a character table, \hyperpage{1117} 593 \item \texttt {ClassPositionsOfCentre} 594 \subitem for a character, \hyperpage{1170} 595 \subitem for a character table, \hyperpage{1117} 596 \item \texttt {ClassPositionsOfDerivedSubgroup}, \hyperpage{1118} 597 \item \texttt {Class}\discretionary {-}{}{}\texttt {Positions}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Direct}\discretionary {-}{}{}\texttt {Product}\discretionary {-}{}{}\texttt {Decompositions}, 598 \hyperpage{1118} 599 \item \texttt {Class}\discretionary {-}{}{}\texttt {Positions}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Elementary}\discretionary {-}{}{}\texttt {Abelian}\discretionary {-}{}{}\texttt {Series}, 600 \hyperpage{1118} 601 \item \texttt {ClassPositionsOfFittingSubgroup}, \hyperpage{1118} 602 \item \texttt {ClassPositionsOfKernel}, \hyperpage{1169} 603 \item \texttt {ClassPositionsOfLowerCentralSeries}, \hyperpage{1119} 604 \item \texttt {Class}\discretionary {-}{}{}\texttt {Positions}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Maximal}\discretionary {-}{}{}\texttt {Normal}\discretionary {-}{}{}\texttt {Subgroups}, 605 \hyperpage{1117} 606 \item \texttt {Class}\discretionary {-}{}{}\texttt {Positions}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Minimal}\discretionary {-}{}{}\texttt {Normal}\discretionary {-}{}{}\texttt {Subgroups}, 607 \hyperpage{1117} 608 \item \texttt {ClassPositionsOfNormalClosure}, \hyperpage{1120} 609 \item \texttt {ClassPositionsOfNormalSubgroup}, \hyperpage{1153} 610 \item \texttt {ClassPositionsOfNormalSubgroups}, \hyperpage{1117} 611 \item \texttt {ClassPositionsOfPCore}, \hyperpage{1120} 612 \item \texttt {ClassPositionsOfSolvableRadical}, \hyperpage{1119} 613 \item \texttt {Class}\discretionary {-}{}{}\texttt {Positions}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Supersolvable}\discretionary {-}{}{}\texttt {Residuum}, 614 \hyperpage{1119} 615 \item \texttt {ClassPositionsOfUpperCentralSeries}, \hyperpage{1119} 616 \item \texttt {ClassRoots}, \hyperpage{1116} 617 \item \texttt {ClassStructureCharTable}, \hyperpage{1127} 618 \item \texttt {ClassTypesTom}, \hyperpage{1082} 619 \item \texttt {CleanedTailPcElement}, \hyperpage{669} 620 \item \texttt {ClearAllBlist}, \hyperpage{320} 621 \item \texttt {ClearCacheStats}, \hyperpage{121} 622 \item \texttt {ClearProfile}, \hyperpage{115} 623 \item clone 624 \subitem an object, \hyperpage{165} 625 \item \texttt {CloseMutableBasis}, \hyperpage{938} 626 \item \texttt {CloseStream}, \hyperpage{144} 627 \item \texttt {ClosureGroup}, \hyperpage{531} 628 \item \texttt {ClosureGroupAddElm}, \hyperpage{531} 629 \item \texttt {ClosureGroupCompare}, \hyperpage{531} 630 \item \texttt {ClosureGroupDefault}, \hyperpage{531} 631 \item \texttt {ClosureGroupIntest}, \hyperpage{531} 632 \item \texttt {ClosureLeftModule}, \hyperpage{898} 633 \item \texttt {ClosureNearAdditiveGroup} 634 \subitem for a near-additive group and an element, \hyperpage{875} 635 \subitem for two near-additive groups, \hyperpage{875} 636 \item \texttt {ClosureRing} 637 \subitem for a ring and a ring element, \hyperpage{878} 638 \subitem for two rings, \hyperpage{878} 639 \item \texttt{Closure\mbox{\texttt{\mdseries\slshape Struct}}}, 640 \hyperpage{430} 641 \item \texttt {ClosureSubgroup}, \hyperpage{532} 642 \item \texttt {ClosureSubgroupNC}, \hyperpage{532} 643 \item \texttt {Coboundaries}, \hyperpage{1008} 644 \item \texttt {Cochain}, \hyperpage{1007} 645 \item \texttt {CochainSpace}, \hyperpage{1007} 646 \item \texttt {Cocycles} 647 \subitem for Lie algebra module, \hyperpage{1008} 648 \item cocycles, \hyperpage{578} 649 \item Code annotations, \hyperpage{78} 650 \item \texttt {CodegreeOfPartialPerm}, \hyperpage{852} 651 \item \texttt {CodegreeOfPartialPermCollection}, \hyperpage{852} 652 \item \texttt {CodegreeOfPartialPermSemigroup}, \hyperpage{866} 653 \item \texttt {CodePcGroup}, \hyperpage{699} 654 \item \texttt {CodePcgs}, \hyperpage{698} 655 \item coefficient 656 \subitem binomial, \hyperpage{218} 657 \item \texttt {Coefficients}, \hyperpage{934} 658 \item coefficients 659 \subitem for cyclotomics, \hyperpage{239} 660 \item \texttt {CoefficientsAndMagmaElements}, \hyperpage{1018} 661 \item \texttt {CoefficientsFamily}, \hyperpage{1049} 662 \item \texttt {CoefficientsMultiadic}, \hyperpage{194} 663 \item \texttt {CoefficientsOfLaurentPolynomial}, \hyperpage{1038} 664 \item \texttt {CoefficientsOfUnivariatePolynomial}, \hyperpage{1029} 665 \item \texttt {Coefficients}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Univariate}\discretionary {-}{}{}\texttt {Rational}\discretionary {-}{}{}\texttt {Function}, 666 \hyperpage{1028} 667 \item \texttt {CoefficientsQadic}, \hyperpage{194} 668 \item \texttt {CoefficientsRing}, \hyperpage{1040} 669 \item \texttt {CoeffsCyc}, \hyperpage{239} 670 \item \texttt {CoeffsMod}, \hyperpage{327} 671 \item cohomology, \hyperpage{578} 672 \item \texttt {CoKernelOfAdditiveGeneralMapping}, \hyperpage{465} 673 \item \texttt {CoKernel}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Multiplicative}\discretionary {-}{}{}\texttt {General}\discretionary {-}{}{}\texttt {Mapping}, 674 \hyperpage{463} 675 \item \texttt {CollapsedMat}, \hyperpage{1216} 676 \item \texttt {Collected}, \hyperpage{299} 677 \item \texttt {CollectionsFamily}, \hyperpage{410} 678 \item \texttt {ColorPrompt}, \hyperpage{42} 679 \item \texttt {Columns}, \hyperpage{810} 680 \item \texttt {Combinations}, \hyperpage{221} 681 \item \texttt {CombinatorialCollector}, \hyperpage{691} 682 \item \texttt {Comm}, \hyperpage{441} 683 \item \texttt{Comm} 684 \subitem for words, \hyperpage{505} 685 \item comments, \hyperpage{46} 686 \item \texttt {CommutativeDiagram}, \hyperpage{1212} 687 \item \texttt {CommutatorFactorGroup}, \hyperpage{565} 688 \item \texttt {CommutatorLength}, \hyperpage{546} 689 \subitem for a character table, \hyperpage{1111} 690 \item \texttt {CommutatorSubgroup}, \hyperpage{546} 691 \item \texttt {Compacted}, \hyperpage{299} 692 \item \texttt {CompanionMat}, \hyperpage{353} 693 \item \texttt {CompareVersionNumbers}, \hyperpage{1243} 694 \item comparison 695 \subitem fp semigroup elements, \hyperpage{816} 696 \subitem operation, \hyperpage{439} 697 \subitem rational functions, \hyperpage{1026} 698 \item comparisons 699 \subitem of booleans, \hyperpage{260} 700 \subitem of lists, \hyperpage{276} 701 \item \texttt {CompatibleConjugacyClasses}, \hyperpage{1107} 702 \item \texttt {CompatiblePairs}, \hyperpage{697} 703 \item \texttt {ComplementClassesRepresentatives}, \hyperpage{545} 704 \item \texttt {ComplementClassesRepresentativesEA}, \hyperpage{581} 705 \item \texttt {ComplementIntMat}, \hyperpage{361} 706 \item \texttt {ComplementSystem}, \hyperpage{550} 707 \item \texttt {ComplexConjugate}, \hyperpage{246} 708 \subitem for a class function, \hyperpage{1162} 709 \item \texttt {ComplexificationQuat} 710 \subitem for a matrix, \hyperpage{955} 711 \subitem for a vector, \hyperpage{955} 712 \item \texttt {ComponentPartialPermInt}, \hyperpage{862} 713 \item \texttt {ComponentRepsOfPartialPerm}, \hyperpage{858} 714 \item \texttt {ComponentRepsOfTransformation}, \hyperpage{837} 715 \item \texttt {ComponentsOfPartialPerm}, \hyperpage{857} 716 \item \texttt {ComponentsOfTransformation}, \hyperpage{836} 717 \item \texttt {ComponentTransformationInt}, \hyperpage{830} 718 \item \texttt {CompositionMapping}, \hyperpage{454} 719 \item \texttt{CompositionMapping} 720 \subitem for Frobenius automorphisms, \hyperpage{916} 721 \item \texttt {CompositionMapping2}, \hyperpage{454} 722 \item \texttt {CompositionMapping2General}, \hyperpage{454} 723 \item \texttt {CompositionMaps}, \hyperpage{1209} 724 \item \texttt {CompositionOfStraightLinePrograms}, \hyperpage{515} 725 \item \texttt {CompositionSeries}, \hyperpage{561} 726 \item \texttt{CompositionSeries} 727 \subitem for groups with pcgs, \hyperpage{685} 728 \item \texttt {ComputedBrauerTables}, \hyperpage{1101} 729 \item \texttt {ComputedClassFusions}, \hyperpage{1204} 730 \item \texttt {ComputedIndicators}, \hyperpage{1126} 731 \item \texttt {ComputedIsPSolubleCharacterTables}, \hyperpage{1125} 732 \item \texttt {ComputedIsPSolvableCharacterTables}, \hyperpage{1125} 733 \item \texttt {ComputedPowerMaps}, \hyperpage{1198} 734 \item \texttt {ComputedPrimeBlockss}, \hyperpage{1120} 735 \item \texttt {Concatenation} 736 \subitem for a list of lists, \hyperpage{298} 737 \subitem for several lists, \hyperpage{298} 738 \item concatenation 739 \subitem of lists, \hyperpage{298} 740 \item \texttt {ConcatenationOfVectors} 741 \subitem for IsVectorObj, \hyperpage{373} 742 \subitem for list of IsVectorObj, \hyperpage{373} 743 \item \texttt {Conductor} 744 \subitem for a collection of cyclotomics, \hyperpage{238} 745 \subitem for a cyclotomic, \hyperpage{238} 746 \item \texttt {ConfluentRws}, \hyperpage{520} 747 \item \texttt {Congruences} 748 \subitem for character tables, \hyperpage{1218} 749 \item \texttt {ConjugacyClass}, \hyperpage{541} 750 \item \texttt {ConjugacyClasses} 751 \subitem attribute, \hyperpage{541} 752 \subitem for character tables, \hyperpage{1105} 753 \item \texttt{ConjugacyClasses} 754 \subitem for groups with pcgs, \hyperpage{685} 755 \subitem for linear groups, \hyperpage{772} 756 \item \texttt {ConjugacyClassesByOrbits}, \hyperpage{542} 757 \item \texttt {ConjugacyClassesByRandomSearch}, \hyperpage{542} 758 \item \texttt {ConjugacyClassesMaximalSubgroups}, \hyperpage{567} 759 \item \texttt {ConjugacyClassesPerfectSubgroups}, \hyperpage{573} 760 \item \texttt {ConjugacyClassesSubgroups}, \hyperpage{566} 761 \item \texttt {ConjugacyClassSubgroups}, \hyperpage{566} 762 \item conjugate 763 \subitem matrix, \hyperpage{335} 764 \subitem of a word, \hyperpage{505} 765 \item \texttt {ConjugateDominantWeight}, \hyperpage{999} 766 \item \texttt {ConjugateDominantWeightWithWord}, \hyperpage{999} 767 \item \texttt {ConjugateGroup}, \hyperpage{527} 768 \item \texttt {Conjugates}, \hyperpage{908} 769 \item \texttt {ConjugateSubgroup}, \hyperpage{530} 770 \item \texttt {ConjugateSubgroups}, \hyperpage{530} 771 \item conjugation, \hyperpage{607} 772 \item \texttt {ConjugatorAutomorphism}, \hyperpage{596} 773 \item \texttt {ConjugatorAutomorphismNC}, \hyperpage{596} 774 \item \texttt {ConjugatorIsomorphism}, \hyperpage{596} 775 \item \texttt {ConjugatorOfConjugatorIsomorphism}, \hyperpage{597} 776 \item \texttt {ConsiderKernels}, \hyperpage{1219} 777 \item \texttt {ConsiderSmallerPowerMaps}, \hyperpage{1219} 778 \item \texttt {ConsiderStructureConstants}, \hyperpage{1207} 779 \item \texttt {ConsiderTableAutomorphisms}, \hyperpage{1222} 780 \item \texttt {ConstantTimeAccessList}, \hyperpage{293} 781 \item \texttt {ConstantTransformation}, \hyperpage{826} 782 \item constituent 783 \subitem of a group character, \hyperpage{1168} 784 \item \texttt {ConstituentsCompositionMapping}, \hyperpage{455} 785 \item \texttt {ConstituentsOfCharacter}, \hyperpage{1169} 786 \item \texttt {ConstructingFilter} 787 \subitem for IsVectorObj, \hyperpage{373} 788 \item \texttt {ContainedCharacters}, \hyperpage{1217} 789 \item \texttt {ContainedConjugates}, \hyperpage{572} 790 \item \texttt {ContainedDecomposables}, \hyperpage{1217} 791 \item \texttt {ContainedMaps}, \hyperpage{1211} 792 \item \texttt {ContainedPossibleCharacters}, \hyperpage{1215} 793 \item \texttt {ContainedPossibleVirtualCharacters}, \hyperpage{1215} 794 \item \texttt {ContainedSpecialVectors}, \hyperpage{1215} 795 \item \texttt {ContainedTom}, \hyperpage{1088} 796 \item \texttt {ContainingConjugates}, \hyperpage{572} 797 \item \texttt {ContainingTom}, \hyperpage{1088} 798 \item \texttt{continue} statement, \hyperpage{64} 799 \item \texttt {Continued}\discretionary {-}{}{}\texttt {Fraction}\discretionary {-}{}{}\texttt {Approximation}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Root}, 800 \hyperpage{215} 801 \item \texttt {ContinuedFractionExpansionOfRoot}, \hyperpage{215} 802 \item convert 803 \subitem to a string, \hyperpage{379} 804 \item \texttt {ConvertToBlistRep}, \hyperpage{321} 805 \item \texttt {ConvertToCharacterTable}, \hyperpage{1103} 806 \item \texttt {ConvertToCharacterTableNC}, \hyperpage{1103} 807 \item \texttt {ConvertToMatrixRep} 808 \subitem for a list (and a field), \hyperpage{355} 809 \subitem for a list (and a prime power), \hyperpage{355} 810 \item \texttt {ConvertToMatrixRepNC} 811 \subitem for a list (and a field), \hyperpage{355} 812 \subitem for a list (and a prime power), \hyperpage{355} 813 \item \texttt {ConvertToRangeRep}, \hyperpage{312} 814 \item \texttt {ConvertToStringRep}, \hyperpage{379} 815 \item \texttt {ConvertToTableOfMarks}, \hyperpage{1081} 816 \item \texttt {ConvertToVectorRep} 817 \subitem for a list (and a field), \hyperpage{325} 818 \subitem for a list (and a prime power), \hyperpage{325} 819 \item \texttt {ConvertToVectorRepNC} 820 \subitem for a list (and a field), \hyperpage{325} 821 \subitem for a list (and a prime power), \hyperpage{325} 822 \item \texttt {ConwayPolynomial}, \hyperpage{917} 823 \item coprime, \hyperpage{57} 824 \item Copy, \hyperpage{165} 825 \item copy 826 \subitem an object, \hyperpage{165} 827 \item \texttt {CopyListEntries}, \hyperpage{270} 828 \item \texttt {CopyOptionsDefaults}, \hyperpage{650} 829 \item \texttt {CopyStabChain}, \hyperpage{650} 830 \item \texttt {CopyToStringRep}, \hyperpage{379} 831 \item \texttt {Core}, \hyperpage{544} 832 \item \texttt {CorrespondingGeneratorsByModuloPcgs}, \hyperpage{675} 833 \item \texttt {Cos}, \hyperpage{255} 834 \item coset, \hyperpage{536} 835 \item \texttt {CosetDecomposition}, \hyperpage{538} 836 \item \texttt {CosetLeadersMatFFE}, \hyperpage{329} 837 \item \texttt {CosetTable}, \hyperpage{707} 838 \item \texttt {CosetTableBySubgroup}, \hyperpage{708} 839 \item \texttt {CosetTableDefaultLimit}, \hyperpage{710} 840 \item \texttt {CosetTableDefaultMaxLimit}, \hyperpage{709} 841 \item \texttt {CosetTableFromGensAndRels}, \hyperpage{708} 842 \item \texttt {CosetTableInWholeGroup}, \hyperpage{712} 843 \item \texttt {CosetTableOfFpSemigroup}, \hyperpage{820} 844 \item \texttt {CosetTableStandard}, \hyperpage{711} 845 \item \texttt {Cosh}, \hyperpage{255} 846 \item \texttt {Cot}, \hyperpage{255} 847 \item \texttt {Coth}, \hyperpage{255} 848 \item \texttt {CoverageLineByLine}, \hyperpage{120} 849 \item \texttt {CrcFile}, \hyperpage{140} 850 \item \texttt {CrcString}, \hyperpage{393} 851 \item \texttt {CrystGroupDefaultAction}, \hyperpage{663} 852 \item \texttt {Csc}, \hyperpage{255} 853 \item \texttt {Csch}, \hyperpage{255} 854 \item \texttt {CubeRoot}, \hyperpage{255} 855 \item \texttt {Cyc} 856 \subitem for floats, \hyperpage{253} 857 \item \texttt {Cycle}, \hyperpage{619} 858 \item \texttt {CycleFromList}, \hyperpage{634} 859 \item \texttt {CycleIndex} 860 \subitem for a permutation and an action domain, \hyperpage{620} 861 \subitem for a permutation group and an action domain, 862 \hyperpage{620} 863 \item \texttt {CycleLength}, \hyperpage{619} 864 \item \texttt {CycleLengths}, \hyperpage{620} 865 \item \texttt {Cycles}, \hyperpage{620} 866 \item \texttt {CyclesOfTransformation}, \hyperpage{838} 867 \item \texttt {CycleStructureClass}, \hyperpage{1171} 868 \item \texttt {CycleStructurePerm}, \hyperpage{633} 869 \item \texttt {CycleTransformationInt}, \hyperpage{838} 870 \item \texttt {CyclicExtensionsTom} 871 \subitem for a list of primes, \hyperpage{1088} 872 \subitem for a prime, \hyperpage{1088} 873 \item \texttt {CyclicGroup}, \hyperpage{761} 874 \item cyclotomic field elements, \hyperpage{236} 875 \item cyclotomic fields 876 \subitem CanonicalBasis, \hyperpage{923} 877 \item \texttt {CyclotomicField} 878 \subitem for (subfield and) conductor, \hyperpage{920} 879 \subitem for (subfield and) generators, \hyperpage{920} 880 \item \texttt {CyclotomicPolynomial}, \hyperpage{1035} 881 \item \texttt {Cyclotomics}, \hyperpage{236} 882 \item \texttt{CyclotomicsFamily}, \hyperpage{237} 883 884 \indexspace 885 886 \item $d_N$ (irrational value), \hyperpage{242} 887 \item Darstellungsgruppe 888 \subitem see EpimorphismSchurCover, \hyperpage{581} 889 \item data type 890 \subitem unknown, \hyperpage{1224} 891 \item \texttt {DataType}, \hyperpage{186} 892 \item \texttt {DayDMY}, \hyperpage{393} 893 \item \texttt {DaysInMonth}, \hyperpage{393} 894 \item \texttt {DaysInYear}, \hyperpage{393} 895 \item DEC, \hyperpage{365} 896 \item \texttt {DeclareAttribute}, \hyperpage{179} 897 \item \texttt{DeclareAttribute} 898 \subitem example, \hyperpage{1306} 899 \item \texttt{DeclareAttribute!example}, \hyperpage{1311} 900 \item \texttt{DeclareAutoPackage}, \hyperpage{1273} 901 \item \texttt {DeclareAutoreadableVariables}, \hyperpage{1243} 902 \item \texttt {DeclareCategory}, \hyperpage{175} 903 \item \texttt {DeclareCategoryCollections}, \hyperpage{411} 904 \item \texttt {DeclareConstructor}, \hyperpage{1280} 905 \item \texttt {DeclareFilter}, \hyperpage{186} 906 \item \texttt {DeclareGlobalFunction}, \hyperpage{1300} 907 \item \texttt {DeclareGlobalVariable}, \hyperpage{1300} 908 \item \texttt {DeclareHandlingByNiceBasis}, \hyperpage{947} 909 \item \texttt {DeclareInfoClass}, \hyperpage{108} 910 \item \texttt {DeclareOperation}, \hyperpage{1277} 911 \item \texttt{DeclarePackage}, \hyperpage{1273} 912 \item \texttt{DeclarePackageAutoDocumentation}, \hyperpage{1273} 913 \item \texttt{DeclarePackageDocumentation}, \hyperpage{1273} 914 \item \texttt {DeclareProperty}, \hyperpage{185} 915 \item \texttt {DeclareRepresentation}, \hyperpage{178} 916 \item \texttt{DeclareRepresentation} 917 \subitem belongs to implementation part, \hyperpage{1302} 918 \subitem example, \hyperpage{1307} 919 \item \texttt {DeclareSynonym}, \hyperpage{1301} 920 \item \texttt {DeclareSynonymAttr}, \hyperpage{1301} 921 \item \texttt {DeclareUserPreference}, \hyperpage{40} 922 \item \texttt {DecodeTree}, \hyperpage{747} 923 \item decompose 924 \subitem a group character, \hyperpage{1168} 925 \item \texttt {DecomposedFixedPointVector}, \hyperpage{1089} 926 \item \texttt {DecomposeTensorProduct}, \hyperpage{1009} 927 \item \texttt {Decomposition}, \hyperpage{366} 928 \item decomposition matrix, \hyperpage{365} 929 \item \texttt {DecompositionInt}, \hyperpage{367} 930 \item \texttt {DecompositionMatrix}, \hyperpage{1122} 931 \item \texttt {Decreased}, \hyperpage{1180} 932 \item \texttt {DEFAULTDISPLAYSTRING}, \hyperpage{382} 933 \item \texttt {DefaultField} 934 \subitem for a list of generators, \hyperpage{903} 935 \subitem for cyclotomics, \hyperpage{241} 936 \subitem for finite field elements, \hyperpage{915} 937 \subitem for several generators, \hyperpage{903} 938 \item \texttt {DefaultFieldByGenerators}, \hyperpage{903} 939 \item \texttt {DefaultFieldOfMatrix}, \hyperpage{336} 940 \item \texttt {DefaultFieldOfMatrixGroup}, \hyperpage{656} 941 \item \texttt{DefaultInfoHandler}, \hyperpage{110} 942 \item \texttt {DefaultRing} 943 \subitem for a collection, \hyperpage{877} 944 \subitem for finite field elements, \hyperpage{915} 945 \subitem for ring elements, \hyperpage{877} 946 \item \texttt {DefaultRingByGenerators}, \hyperpage{877} 947 \item \texttt {DefaultStabChainOptions}, \hyperpage{645} 948 \item \texttt {DEFAULTVIEWSTRING}, \hyperpage{383} 949 \item \texttt {DefiningPolynomial}, \hyperpage{905} 950 \item \texttt {DefiningQuotientHomomorphism}, \hyperpage{719} 951 \item \texttt {DegreeFFE} 952 \subitem for a FFE, \hyperpage{913} 953 \subitem for a matrix of FFEs, \hyperpage{913} 954 \subitem for a vector of FFEs, \hyperpage{913} 955 \item \texttt {DegreeIndeterminate}, \hyperpage{1032} 956 \item \texttt {DegreeOfBinaryRelation}, \hyperpage{473} 957 \item \texttt {DegreeOfCharacter}, \hyperpage{1167} 958 \item \texttt {DegreeOfLaurentPolynomial}, \hyperpage{1030} 959 \item \texttt {DegreeOfPartialPerm}, \hyperpage{851} 960 \item \texttt {DegreeOfPartialPermCollection}, \hyperpage{851} 961 \item \texttt {DegreeOfPartialPermSemigroup}, \hyperpage{866} 962 \item \texttt {DegreeOfTransformation}, \hyperpage{830} 963 \item \texttt {DegreeOfTransformationCollection}, \hyperpage{830} 964 \item \texttt {DegreeOfTransformationSemigroup}, \hyperpage{841} 965 \item \texttt {DegreeOverPrimeField}, \hyperpage{905} 966 \item \texttt {Delta}, \hyperpage{1228} 967 \item denominator 968 \subitem of a rational, \hyperpage{235} 969 \item \texttt {DenominatorCyc}, \hyperpage{240} 970 \item \texttt {DenominatorOfModuloPcgs}, \hyperpage{674} 971 \item \texttt {DenominatorOfRationalFunction}, \hyperpage{1027} 972 \item \texttt {DenominatorRat}, \hyperpage{235} 973 \item \texttt {DenseHashTable}, \hyperpage{400} 974 \item \texttt {DenseIntKey}, \hyperpage{400} 975 \item dependencies 976 \subitem for a GAP package, \hyperpage{1257} 977 \item deprecated, \hyperpage{1272} 978 \item \texttt {DepthOfPcElement}, \hyperpage{668} 979 \item \texttt {DepthOfUpperTriangularMatrix}, \hyperpage{351} 980 \item \texttt {Derangements}, \hyperpage{225} 981 \item \texttt {Derivations}, \hyperpage{989} 982 \item \texttt {Derivative}, \hyperpage{1033} 983 \item \texttt {DerivedLength}, \hyperpage{561} 984 \item \texttt {DerivedSeriesOfGroup}, \hyperpage{561} 985 \item \texttt {DerivedSubgroup}, \hyperpage{546} 986 \item \texttt {DerivedSubgroupsTom}, \hyperpage{1087} 987 \item \texttt {DerivedSubgroupsTomPossible}, \hyperpage{1087} 988 \item \texttt {DerivedSubgroupsTomUnique}, \hyperpage{1087} 989 \item \texttt {DerivedSubgroupTom}, \hyperpage{1087} 990 \item \texttt {DescriptionOfRootOfUnity}, \hyperpage{240} 991 \item \texttt {Determinant}, \hyperpage{337} 992 \item determinant 993 \subitem integer matrix, \hyperpage{365} 994 \item determinant character, \hyperpage{1171} 995 \item \texttt {DeterminantIntMat}, \hyperpage{365} 996 \item \texttt {DeterminantMat}, \hyperpage{337} 997 \item \texttt {DeterminantMatDestructive}, \hyperpage{337} 998 \item \texttt {DeterminantMatDivFree}, \hyperpage{337} 999 \item \texttt {DeterminantOfCharacter}, \hyperpage{1171} 1000 \item \texttt {DiagonalizeIntMat}, \hyperpage{364} 1001 \item \texttt {DiagonalizeMat}, \hyperpage{347} 1002 \item \texttt {DiagonalMat}, \hyperpage{339} 1003 \item \texttt {DiagonalOfMat}, \hyperpage{350} 1004 \item \texttt {DiagonalOfMatrix}, \hyperpage{350} 1005 \item \texttt {Diameter}, \hyperpage{257} 1006 \item \texttt {DictionaryByPosition}, \hyperpage{398} 1007 \item \texttt {DicyclicGroup}, \hyperpage{763} 1008 \item \texttt {Difference}, \hyperpage{422} 1009 \item \texttt {DifferenceBlist}, \hyperpage{317} 1010 \item \texttt {DihedralGenerators}, \hyperpage{763} 1011 \item \texttt {DihedralGroup}, \hyperpage{762} 1012 \item \texttt {Dimension}, \hyperpage{900} 1013 \item \texttt {DimensionOfHighestWeightModule}, \hyperpage{1010} 1014 \item \texttt {DimensionOfMatrixGroup}, \hyperpage{656} 1015 \item \texttt {DimensionOfVectors}, \hyperpage{940} 1016 \item \texttt {DimensionsLoewyFactors}, \hyperpage{563} 1017 \item \texttt {DimensionsMat}, \hyperpage{336} 1018 \item \texttt {DirectoriesLibrary}, \hyperpage{135} 1019 \item \texttt {DirectoriesPackageLibrary}, \hyperpage{1242} 1020 \item \texttt {DirectoriesPackagePrograms}, \hyperpage{1243} 1021 \item \texttt {DirectoriesSystemPrograms}, \hyperpage{135} 1022 \item \texttt {Directory}, \hyperpage{134} 1023 \item \texttt {DirectoryContents}, \hyperpage{135} 1024 \item \texttt {DirectoryCurrent}, \hyperpage{135} 1025 \item \texttt {DirectoryDesktop}, \hyperpage{135} 1026 \item \texttt {DirectoryHome}, \hyperpage{136} 1027 \item \texttt {DirectoryTemporary}, \hyperpage{134} 1028 \item \texttt {DirectProduct}, \hyperpage{753} 1029 \item \texttt {DirectProductFamily}, \hyperpage{452} 1030 \item \texttt {DirectProductOp}, \hyperpage{753} 1031 \item \texttt {DirectSum}, \hyperpage{895} 1032 \item \texttt {DirectSumDecomposition} 1033 \subitem for Lie algebras, \hyperpage{966} 1034 \item \texttt {DirectSumOfAlgebraModules} 1035 \subitem for a list of Lie algebra modules, \hyperpage{982} 1036 \subitem for two Lie algebra modules, \hyperpage{982} 1037 \item \texttt {DirectSumOfAlgebras} 1038 \subitem for a list of algebras, \hyperpage{965} 1039 \subitem for two algebras, \hyperpage{965} 1040 \item \texttt {DirectSumOp}, \hyperpage{895} 1041 \item disable automatic loading, \hyperpage{1237} 1042 \item \texttt {DisableAttributeValueStoring}, \hyperpage{182} 1043 \item \texttt {Discriminant}, \hyperpage{1033} 1044 \item \texttt {Display}, \hyperpage{85} 1045 \subitem for a character table, \hyperpage{1128} 1046 \subitem for a ffe, \hyperpage{918} 1047 \subitem for a table of marks, \hyperpage{1078} 1048 \subitem for class functions, \hyperpage{1163} 1049 \item \texttt {DisplayCacheStats}, \hyperpage{121} 1050 \item \texttt {DisplayCompositionSeries}, \hyperpage{561} 1051 \item \texttt {DisplayEggBoxOfDClass}, \hyperpage{802} 1052 \item \texttt {DisplayImfInvariants}, \hyperpage{782} 1053 \item \texttt {DisplayInformationPerfectGroups} 1054 \subitem for a pair [ order, index ], \hyperpage{777} 1055 \subitem for group order (and index), \hyperpage{777} 1056 \item \texttt {DisplayOptions}, \hyperpage{1130} 1057 \item \texttt {DisplayOptionsStack}, \hyperpage{131} 1058 \item \texttt {DisplayPackageLoadingLog}, \hyperpage{1239} 1059 \item \texttt {DisplayProfile}, \hyperpage{115} 1060 \item \texttt {DisplaySemigroup}, \hyperpage{803} 1061 \item \texttt {DisplayString}, \hyperpage{382} 1062 \item \texttt {DistanceOfVectors} 1063 \subitem for IsVectorObj,IsVectorObj, \hyperpage{374} 1064 \item \texttt {DistancePerms}, \hyperpage{631} 1065 \item \texttt {DistancesDistributionMatFFEVecFFE}, \hyperpage{329} 1066 \item \texttt {DistancesDistributionVecFFEsVecFFE}, \hyperpage{329} 1067 \item \texttt {DistanceVecFFE}, \hyperpage{328} 1068 \item division, \hyperpage{57} 1069 \subitem operation, \hyperpage{440} 1070 \item division rings, \hyperpage{902} 1071 \item \texttt {DivisionRingByGenerators}, \hyperpage{904} 1072 \item divisors 1073 \subitem of an integer, \hyperpage{200} 1074 \item \texttt {DivisorsInt}, \hyperpage{200} 1075 \item Dixon-Schneider algorithm, \hyperpage{1135} 1076 \item \texttt {DixonInit}, \hyperpage{1136} 1077 \item \texttt {DixonRecord}, \hyperpage{1136} 1078 \item \texttt {DixonSplit}, \hyperpage{1137} 1079 \item \texttt {DixontinI}, \hyperpage{1137} 1080 \item \texttt {DMYDay}, \hyperpage{393} 1081 \item \texttt {DMYhmsSeconds}, \hyperpage{395} 1082 \item \texttt {DnLattice}, \hyperpage{1181} 1083 \item \texttt {DnLatticeIterative}, \hyperpage{1182} 1084 \item \texttt{do}, \hyperpage{62} 1085 \item document formats 1086 \subitem for help books, \hyperpage{1348} 1087 \item document formats (text, dvi, ps, pdf, HTML), \hyperpage{29} 1088 \item \texttt {Domain}, \hyperpage{435} 1089 \item \texttt {DomainByGenerators}, \hyperpage{435} 1090 \item \texttt {DomainOfPartialPerm}, \hyperpage{852} 1091 \item \texttt {DomainOfPartialPermCollection}, \hyperpage{852} 1092 \item \texttt {DominantCharacter} 1093 \subitem for a root system and a highest weight, \hyperpage{1009} 1094 \subitem for a semisimple Lie algebra and a highest weight, 1095 \hyperpage{1009} 1096 \item \texttt {DominantWeights}, \hyperpage{1009} 1097 \item dot-file, \hyperpage{570} 1098 \item \texttt {DotFileLatticeSubgroups}, \hyperpage{570} 1099 \item \texttt {DoubleCoset}, \hyperpage{539} 1100 \item \texttt {DoubleCosetRepsAndSizes}, \hyperpage{540} 1101 \item \texttt {DoubleCosets}, \hyperpage{540} 1102 \item \texttt {DoubleCosetsNC}, \hyperpage{540} 1103 \item \texttt {DoubleCoverOfAlternatingGroup}, \hyperpage{584} 1104 \item \texttt {DoubleHashArraySize}, \hyperpage{401} 1105 \item doublequote character, \hyperpage{378} 1106 \item doublequotes, \hyperpage{375} 1107 \item \texttt {DownEnv}, \hyperpage{91} 1108 \item duplicate free, \hyperpage{292} 1109 \item \texttt {DuplicateFreeList}, \hyperpage{299} 1110 \item \texttt {DxIncludeIrreducibles}, \hyperpage{1137} 1111 1112 \indexspace 1113 1114 \item \texttt {E}, \hyperpage{236} 1115 \item $e_N$ (irrational value), \hyperpage{242} 1116 \item \texttt {EANormalSeriesByPcgs}, \hyperpage{677} 1117 \item \texttt {Earns} 1118 \subitem for a group, an action domain, etc., \hyperpage{622} 1119 \subitem for an external set, \hyperpage{622} 1120 \item \texttt {EB}, \hyperpage{242} 1121 \item \texttt {EC}, \hyperpage{242} 1122 \item \texttt {ED}, \hyperpage{242} 1123 \item \texttt {Edit}, \hyperpage{100} 1124 \item \texttt {EE}, \hyperpage{242} 1125 \item \texttt {EF}, \hyperpage{242} 1126 \item \texttt {EG}, \hyperpage{242} 1127 \item \texttt {EggBoxOfDClass}, \hyperpage{802} 1128 \item \texttt {EH}, \hyperpage{242} 1129 \item \texttt {EI}, \hyperpage{243} 1130 \item \texttt {Eigenspaces}, \hyperpage{345} 1131 \item \texttt {Eigenvalues}, \hyperpage{345} 1132 \item \texttt {EigenvaluesChar}, \hyperpage{1172} 1133 \item \texttt {Eigenvectors}, \hyperpage{345} 1134 \item \texttt {EJ}, \hyperpage{244} 1135 \item \texttt {EK}, \hyperpage{244} 1136 \item \texttt {EL}, \hyperpage{244} 1137 \item element test 1138 \subitem for lists, \hyperpage{275} 1139 \item \texttt {ElementaryAbelianGroup}, \hyperpage{762} 1140 \item \texttt {ElementaryAbelianSeries} 1141 \subitem for a group, \hyperpage{562} 1142 \subitem for a list, \hyperpage{562} 1143 \item \texttt {ElementaryAbelianSeriesLargeSteps}, \hyperpage{562} 1144 \item \texttt {ElementaryDivisorsMat}, \hyperpage{345} 1145 \item \texttt {ElementaryDivisorsMatDestructive}, \hyperpage{345} 1146 \item \texttt {Elementary}\discretionary {-}{}{}\texttt {Divisors}\discretionary {-}{}{}\texttt {TransformationsMat}, 1147 \hyperpage{346} 1148 \item \texttt {Elementary}\discretionary {-}{}{}\texttt {Divisors}\discretionary {-}{}{}\texttt {Transformations}\discretionary {-}{}{}\texttt {Mat}\discretionary {-}{}{}\texttt {Destructive}, 1149 \hyperpage{346} 1150 \item \texttt {ElementOfFpGroup}, \hyperpage{705} 1151 \item \texttt {ElementOfFpMonoid}, \hyperpage{817} 1152 \item \texttt {ElementOfFpSemigroup}, \hyperpage{817} 1153 \item \texttt {ElementOfMagmaRing}, \hyperpage{1018} 1154 \item \texttt {ElementOrdersPowerMap}, \hyperpage{1200} 1155 \item \texttt {ElementProperty}, \hyperpage{652} 1156 \item \texttt {Elements}, \hyperpage{417} 1157 \item elements 1158 \subitem definition, \hyperpage{160} 1159 \subitem of a list or collection, \hyperpage{417} 1160 \item \texttt {ElementsFamily}, \hyperpage{411} 1161 \item \texttt {ElementsStabChain}, \hyperpage{648} 1162 \item \texttt{elif}, \hyperpage{60} 1163 \item \texttt {EliminatedWord}, \hyperpage{507} 1164 \item \texttt {EliminationOrdering}, \hyperpage{1046} 1165 \item ElmWPObj, \hyperpage{1358} 1166 \item \texttt {ElmWPObj}, \hyperpage{1358} 1167 \item \texttt{else}, \hyperpage{60} 1168 \item \texttt {EM}, \hyperpage{244} 1169 \item \texttt{emacs}, \hyperpage{100} 1170 \item email addresses, \hyperpage{27} 1171 \item \texttt {Embedding} 1172 \subitem for a domain and a positive integer, \hyperpage{455} 1173 \subitem for group products, \hyperpage{759} 1174 \subitem for two domains, \hyperpage{455} 1175 \item \texttt{Embedding} 1176 \subitem example for direct products, \hyperpage{754} 1177 \subitem example for semidirect products, \hyperpage{755} 1178 \subitem example for wreath products, \hyperpage{757} 1179 \subitem for Lie algebras, \hyperpage{987} 1180 \subitem for magma rings, \hyperpage{1018} 1181 \item embeddings 1182 \subitem find all, \hyperpage{602} 1183 \item \texttt {EmptyBinaryRelation} 1184 \subitem for a degree, \hyperpage{471} 1185 \subitem for a domain, \hyperpage{471} 1186 \item \texttt {EmptyMatrix}, \hyperpage{339} 1187 \item \texttt {EmptyPartialPerm}, \hyperpage{850} 1188 \item \texttt {EmptyPlist}, \hyperpage{276} 1189 \item \texttt {EmptySCTable}, \hyperpage{952} 1190 \item \texttt {EmptyStabChain}, \hyperpage{651} 1191 \item \texttt {EmptyString}, \hyperpage{380} 1192 \item \texttt {EnableAttributeValueStoring}, \hyperpage{182} 1193 \item \texttt {End}, \hyperpage{944} 1194 \item \texttt{end}, \hyperpage{65} 1195 \item \texttt {EndlineFunc}, \hyperpage{72} 1196 \item \texttt {EndsWith}, \hyperpage{388} 1197 \item \texttt {Enumerator}, \hyperpage{412} 1198 \item \texttt {EnumeratorByBasis}, \hyperpage{935} 1199 \item \texttt {EnumeratorByFunctions} 1200 \subitem for a domain and a record, \hyperpage{413} 1201 \subitem for a family and a record, \hyperpage{413} 1202 \item \texttt {EnumeratorOfCombinations}, \hyperpage{221} 1203 \item \texttt {EnumeratorOfTuples}, \hyperpage{224} 1204 \item \texttt {EnumeratorSorted}, \hyperpage{412} 1205 \item environment, \hyperpage{65} 1206 \item \texttt {Epicentre}, \hyperpage{582} 1207 \item \texttt {EpimorphismFromFreeGroup}, \hyperpage{532} 1208 \item \texttt {EpimorphismNilpotentQuotient}, \hyperpage{721} 1209 \item \texttt {EpimorphismNonabelianExteriorSquare}, \hyperpage{583} 1210 \item \texttt {EpimorphismPGroup}, \hyperpage{721} 1211 \item \texttt {EpimorphismQuotientSystem}, \hyperpage{720} 1212 \item epimorphisms 1213 \subitem find all, \hyperpage{601} 1214 \item \texttt {EpimorphismSchurCover}, \hyperpage{581} 1215 \item \texttt {EpimorphismSolvableQuotient}, \hyperpage{722} 1216 \item \texttt {EqFloat}, \hyperpage{254} 1217 \item equality 1218 \subitem associative words, \hyperpage{504} 1219 \subitem elements of finitely presented groups, \hyperpage{703} 1220 \subitem for pcwords, \hyperpage{689} 1221 \subitem for transformations, \hyperpage{829} 1222 \subitem nonassociative words, \hyperpage{498} 1223 \subitem of booleans, \hyperpage{260} 1224 \subitem of records, \hyperpage{406} 1225 \subitem operation, \hyperpage{439} 1226 \item equality test, \hyperpage{56} 1227 \subitem for permutations, \hyperpage{631} 1228 \item equivalence class, \hyperpage{477} 1229 \item equivalence relation, \hyperpage{473}, \hyperpage{475} 1230 \item \texttt {EquivalenceClasses} 1231 \subitem attribute, \hyperpage{478} 1232 \item \texttt {EquivalenceClassOfElement}, \hyperpage{478} 1233 \item \texttt {EquivalenceClassOfElementNC}, \hyperpage{478} 1234 \item \texttt {EquivalenceClassRelation}, \hyperpage{477} 1235 \item \texttt {EquivalenceRelationByPairs}, \hyperpage{476} 1236 \item \texttt {EquivalenceRelationByPairsNC}, \hyperpage{476} 1237 \item \texttt {EquivalenceRelationByPartition}, \hyperpage{476} 1238 \item \texttt {EquivalenceRelationByPartitionNC}, \hyperpage{476} 1239 \item \texttt {EquivalenceRelationByProperty}, \hyperpage{476} 1240 \item \texttt {EquivalenceRelationByRelation}, \hyperpage{476} 1241 \item \texttt {EquivalenceRelationPartition}, \hyperpage{477} 1242 \item \texttt {ER}, \hyperpage{243} 1243 \item \texttt {Erf}, \hyperpage{255} 1244 \item \texttt {Error}, \hyperpage{92} 1245 \item \texttt {ErrorCount}, \hyperpage{93} 1246 \item \texttt {ErrorNoReturn}, \hyperpage{93} 1247 \item \texttt{ErrorNoTraceBack}, \hyperpage{88} 1248 \item errors 1249 \subitem syntax, \hyperpage{80} 1250 \item \texttt {ES}, \hyperpage{243} 1251 \item escaped characters, \hyperpage{377} 1252 \item escaping non-special characters, \hyperpage{378} 1253 \item \texttt {ET}, \hyperpage{243} 1254 \item \texttt {EU}, \hyperpage{243} 1255 \item \texttt {EuclideanDegree}, \hyperpage{889} 1256 \item \texttt {EuclideanQuotient}, \hyperpage{889} 1257 \item \texttt {EuclideanRemainder}, \hyperpage{889} 1258 \item Euler's totient function, \hyperpage{209} 1259 \item \texttt {EulerianFunction}, \hyperpage{559} 1260 \item \texttt {EulerianFunctionByTom}, \hyperpage{1089} 1261 \item \texttt {EV}, \hyperpage{243} 1262 \item \texttt {EvalStraightLineProgElm}, \hyperpage{518} 1263 \item \texttt {EvalString}, \hyperpage{392} 1264 \item evaluation, \hyperpage{48} 1265 \subitem strings, \hyperpage{391} 1266 \item \texttt {EW}, \hyperpage{243} 1267 \item \texttt {EX}, \hyperpage{243} 1268 \item \texttt {ExactSizeConsiderFunction}, \hyperpage{576} 1269 \item Excel, \hyperpage{155} 1270 \item \texttt {Exec}, \hyperpage{159} 1271 \item execution, \hyperpage{58} 1272 \item exit, \hyperpage{93} 1273 \item \texttt {Exp}, \hyperpage{255} 1274 \item \texttt {Exp10}, \hyperpage{255} 1275 \item \texttt {Exp2}, \hyperpage{255} 1276 \item Expanded form of monomials, \hyperpage{1050} 1277 \item \texttt {Expm1}, \hyperpage{255} 1278 \item \texttt {Exponent}, \hyperpage{559} 1279 \subitem for a character table, \hyperpage{1111} 1280 \item exponent 1281 \subitem of the prime residue group, \hyperpage{209} 1282 \item exponentiation 1283 \subitem operation, \hyperpage{440} 1284 \item \texttt {ExponentOfPcElement}, \hyperpage{667} 1285 \item \texttt {ExponentsConjugateLayer}, \hyperpage{670} 1286 \item \texttt {ExponentsOfCommutator}, \hyperpage{670} 1287 \item \texttt {ExponentsOfConjugate}, \hyperpage{670} 1288 \item \texttt {ExponentsOfPcElement}, \hyperpage{667} 1289 \item \texttt {ExponentsOfRelativePower}, \hyperpage{670} 1290 \item \texttt {ExponentSumWord}, \hyperpage{506} 1291 \item \texttt {ExponentSyllable}, \hyperpage{508} 1292 \item \texttt {ExtendedPcgs}, \hyperpage{672} 1293 \item \texttt {ExtendRootDirectories}, \hyperpage{1238} 1294 \item \texttt {ExtendStabChain}, \hyperpage{650} 1295 \item \texttt {Extension}, \hyperpage{696} 1296 \item \texttt {ExtensionNC}, \hyperpage{696} 1297 \item \texttt {ExtensionRepresentatives}, \hyperpage{697} 1298 \item \texttt {Extensions}, \hyperpage{696} 1299 \item exterior power, \hyperpage{1183} 1300 \item \texttt {ExteriorCentre}, \hyperpage{582} 1301 \item \texttt {ExteriorPowerOfAlgebraModule}, \hyperpage{1013} 1302 \item external binaries 1303 \subitem for a GAP package, \hyperpage{1260} 1304 \item External representation of polynomials, \hyperpage{1050} 1305 \item \texttt {ExternalOrbit}, \hyperpage{626} 1306 \item \texttt {ExternalOrbits} 1307 \subitem for a group, an action domain, etc., \hyperpage{627} 1308 \subitem for an external set, \hyperpage{627} 1309 \item \texttt {ExternalOrbitsStabilizers} 1310 \subitem for a group, an action domain, etc., \hyperpage{627} 1311 \subitem for an external set, \hyperpage{627} 1312 \item \texttt {ExternalSet}, \hyperpage{625} 1313 \item \texttt{ExternalSet} 1314 \subitem computing orbits, \hyperpage{1353} 1315 \item \texttt {ExternalSubset}, \hyperpage{626} 1316 \item \texttt {Extract}, \hyperpage{1177} 1317 \item \texttt {ExtractSubVector} 1318 \subitem for IsVectorObj,IsList, \hyperpage{373} 1319 \item \texttt {ExtraspecialGroup}, \hyperpage{764} 1320 \item \texttt {ExtRepDenominatorRatFun}, \hyperpage{1051} 1321 \item \texttt {ExtRepNumeratorRatFun}, \hyperpage{1051} 1322 \item \texttt {ExtRepOfObj}, \hyperpage{1297} 1323 \subitem for a cyclotomic, \hyperpage{240} 1324 \item \texttt {ExtRepPolynomialRatFun}, \hyperpage{1051} 1325 \item \texttt {EY}, \hyperpage{243} 1326 1327 \indexspace 1328 1329 \item $f_N$ (irrational value), \hyperpage{242} 1330 \item \texttt {FactorCosetAction}, \hyperpage{618} 1331 \subitem for fp groups, \hyperpage{708} 1332 \item \texttt {FactorFreeMonoidByRelations}, \hyperpage{815} 1333 \item \texttt {FactorFreeSemigroupByRelations}, \hyperpage{815} 1334 \item \texttt {FactorGroup}, \hyperpage{564} 1335 \item \texttt {FactorGroupFpGroupByRels}, \hyperpage{702} 1336 \item \texttt {FactorGroupNC}, \hyperpage{564} 1337 \item \texttt {FactorGroupNormalSubgroupClasses}, \hyperpage{1153} 1338 \item \texttt {FactorGroupTom}, \hyperpage{1090} 1339 \item \texttt {Factorial}, \hyperpage{218} 1340 \item \texttt {Factorization}, \hyperpage{533} 1341 \item factorization, \hyperpage{532} 1342 \item \texttt {Factors}, \hyperpage{888} 1343 \subitem for polynomials over abelian number fields, 1344 \hyperpage{922} 1345 \subitem of polynomial, \hyperpage{1035} 1346 \item \texttt {FactorsInt}, \hyperpage{197} 1347 \subitem using Pollard's Rho, \hyperpage{197} 1348 \item \texttt {FactorsOfDirectProduct}, \hyperpage{1142} 1349 \item \texttt {FactorsSquarefree}, \hyperpage{1036} 1350 \item \texttt {fail}, \hyperpage{259} 1351 \item \texttt {FaithfulModule} 1352 \subitem for Lie algebras, \hyperpage{980} 1353 \item \texttt {FamiliesOfGeneralMappingsAndRanges}, \hyperpage{469} 1354 \item \texttt {FamiliesOfRows}, \hyperpage{1152} 1355 \item \texttt {FamilyForOrdering}, \hyperpage{481} 1356 \item \texttt {FamilyObj}, \hyperpage{170} 1357 \item \texttt {FamilyPcgs}, \hyperpage{688} 1358 \item \texttt {FamilyRange}, \hyperpage{468} 1359 \item \texttt {FamilySource}, \hyperpage{469} 1360 \item features 1361 \subitem under UNIX, \hyperpage{33} 1362 \item \texttt{fi}, \hyperpage{60} 1363 \item \texttt {Fibonacci}, \hyperpage{231} 1364 \item \texttt {Field} 1365 \subitem for (a field and) a list of generators, \hyperpage{903} 1366 \subitem for several generators, \hyperpage{903} 1367 \item field homomorphisms 1368 \subitem Frobenius, \hyperpage{916} 1369 \item \texttt {FieldByGenerators}, \hyperpage{904} 1370 \item \texttt {FieldExtension}, \hyperpage{906} 1371 \item \texttt {FieldOfMatrixGroup}, \hyperpage{656} 1372 \item \texttt {FieldOverItselfByGenerators}, \hyperpage{905} 1373 \item fields, \hyperpage{902} 1374 \item \texttt {FileDescriptorOfStream}, \hyperpage{144} 1375 \item \texttt {Filename} 1376 \subitem for a directory and a string, \hyperpage{136} 1377 \subitem for a list of directories and a string, \hyperpage{136} 1378 \item \texttt {FilenameFunc}, \hyperpage{71} 1379 \item \texttt {FilterByName}, \hyperpage{172} 1380 \item \texttt {Filtered}, \hyperpage{305} 1381 \item \texttt {FiltersObj}, \hyperpage{173} 1382 \item \texttt {FiltersType}, \hyperpage{173} 1383 \item \texttt {FindSl2}, \hyperpage{1004} 1384 \item finiteness test 1385 \subitem for a list or collection, \hyperpage{418} 1386 \item \texttt {First}, \hyperpage{306} 1387 \item \texttt {FittingSubgroup}, \hyperpage{547} 1388 \item \texttt {FixedPointsOfPartialPerm} 1389 \subitem for a partial perm, \hyperpage{853} 1390 \subitem for a partial perm coll, \hyperpage{853} 1391 \item \texttt {Flat}, \hyperpage{300} 1392 \item \texttt {FlatKernelOfTransformation}, \hyperpage{834} 1393 \item \texttt {FlipBlist}, \hyperpage{319} 1394 \item \texttt {FLOAT} 1395 \subitem constants, \hyperpage{253} 1396 \item \texttt {Float}, \hyperpage{252} 1397 \item \texttt {Floor}, \hyperpage{255} 1398 \item flush character, \hyperpage{378} 1399 \item \texttt {FlushCaches}, \hyperpage{1300} 1400 \item FOA triples, \hyperpage{1351} 1401 \item \texttt{for} loop, \hyperpage{62} 1402 \item \texttt {ForAll}, \hyperpage{306} 1403 \item \texttt {ForAny}, \hyperpage{306} 1404 \item \texttt {FOR}\discretionary {-}{}{}\texttt {C}\discretionary {-}{}{}\texttt {E{\textunderscore }}\discretionary {-}{}{}\texttt {Q}\discretionary {-}{}{}\texttt {U}\discretionary {-}{}{}\texttt {I}\discretionary {-}{}{}\texttt {T{\textunderscore }GAP}, 1405 \hyperpage{93} 1406 \item \texttt {FpElmComparisonMethod}, \hyperpage{704} 1407 \item \texttt {FpGroupCocycle}, \hyperpage{585} 1408 \item \texttt {FpGroupPresentation}, \hyperpage{727} 1409 \item \texttt {FpGrpMonSmgOfFpGrpMonSmgElement}, \hyperpage{815} 1410 \item \texttt {FpLieAlgebraByCartanMatrix}, \hyperpage{1005} 1411 \item \texttt {Frac}, \hyperpage{255} 1412 \item Frame, \hyperpage{1183} 1413 \item \texttt {FrattiniSubgroup}, \hyperpage{547} 1414 \item \texttt{FrattiniSubgroup} 1415 \subitem for groups with pcgs, \hyperpage{685} 1416 \item \texttt {FreeAbelianGroup}, \hyperpage{762} 1417 \item \texttt {FreeAlgebra} 1418 \subitem for ring and several names, \hyperpage{950} 1419 \subitem for ring, rank (and name), \hyperpage{950} 1420 \item \texttt {FreeAlgebraWithOne} 1421 \subitem for ring and several names, \hyperpage{950} 1422 \subitem for ring, rank (and name), \hyperpage{950} 1423 \item \texttt {FreeAssociativeAlgebra} 1424 \subitem for ring and several names, \hyperpage{951} 1425 \subitem for ring, rank (and name), \hyperpage{951} 1426 \item \texttt {FreeAssociativeAlgebraWithOne} 1427 \subitem for ring and several names, \hyperpage{951} 1428 \subitem for ring, rank (and name), \hyperpage{951} 1429 \item \texttt {FreeGeneratorsOfFpGroup}, \hyperpage{704} 1430 \item \texttt {FreeGeneratorsOfFpMonoid}, \hyperpage{817} 1431 \item \texttt {FreeGeneratorsOfFpSemigroup}, \hyperpage{817} 1432 \item \texttt {FreeGeneratorsOfWholeGroup}, \hyperpage{704} 1433 \item \texttt {FreeGroup} 1434 \subitem for a list of names, \hyperpage{503} 1435 \subitem for given rank, \hyperpage{503} 1436 \subitem for infinitely many generators, \hyperpage{503} 1437 \subitem for various names, \hyperpage{503} 1438 \item \texttt {FreeGroupOfFpGroup}, \hyperpage{704} 1439 \item \texttt {FreeLeftModule}, \hyperpage{899} 1440 \item \texttt {FreeLieAlgebra} 1441 \subitem for ring and several names, \hyperpage{989} 1442 \subitem for ring, rank (and name), \hyperpage{989} 1443 \item \texttt {FreeMagma} 1444 \subitem for a list of names, \hyperpage{500} 1445 \subitem for given rank, \hyperpage{500} 1446 \subitem for infinitely many generators, \hyperpage{500} 1447 \subitem for various names, \hyperpage{500} 1448 \item \texttt {FreeMagmaRing}, \hyperpage{1016} 1449 \item \texttt {FreeMagmaWithOne} 1450 \subitem for a list of names, \hyperpage{500} 1451 \subitem for given rank, \hyperpage{500} 1452 \subitem for infinitely many generators, \hyperpage{500} 1453 \subitem for various names, \hyperpage{500} 1454 \item \texttt {FreeMonoid} 1455 \subitem for a list of names, \hyperpage{794} 1456 \subitem for given rank, \hyperpage{794} 1457 \subitem for infinitely many generators, \hyperpage{794} 1458 \subitem for various names, \hyperpage{794} 1459 \item \texttt {FreeMonoidOfFpMonoid}, \hyperpage{817} 1460 \item \texttt {FreeMonoidOfRewritingSystem}, \hyperpage{820} 1461 \item \texttt {FreeProduct} 1462 \subitem for a list, \hyperpage{759} 1463 \subitem for several groups, \hyperpage{759} 1464 \item \texttt {FreeSemigroup} 1465 \subitem for a list of names, \hyperpage{791} 1466 \subitem for given rank, \hyperpage{791} 1467 \subitem for infinitely many generators, \hyperpage{791} 1468 \subitem for various names, \hyperpage{791} 1469 \item \texttt {FreeSemigroupOfFpSemigroup}, \hyperpage{817} 1470 \item \texttt {FreeSemigroupOfRewritingSystem}, \hyperpage{820} 1471 \item \texttt {FrExp}, \hyperpage{255} 1472 \item Frobenius automorphism, \hyperpage{916} 1473 \item Frobenius Normal Form, \hyperpage{352} 1474 \item \texttt {FrobeniusAutomorphism}, \hyperpage{916} 1475 \item \texttt {FrobeniusCharacterValue}, \hyperpage{1195} 1476 \item \texttt {FullMatrixAlgebra}, \hyperpage{955} 1477 \item \texttt {FullMatrixAlgebraCentralizer}, \hyperpage{965} 1478 \item \texttt {FullMatrixLieAlgebra}, \hyperpage{989} 1479 \item \texttt {FullMatrixModule}, \hyperpage{901} 1480 \item \texttt {FullMatrixSpace}, \hyperpage{940} 1481 \item \texttt {FullRowModule}, \hyperpage{901} 1482 \item \texttt {FullRowSpace}, \hyperpage{939} 1483 \item \texttt {FullTransformationMonoid}, \hyperpage{842} 1484 \item \texttt {FullTransformationSemigroup}, \hyperpage{842} 1485 \item \texttt {FunctionAction}, \hyperpage{625} 1486 \item \texttt {FunctionField} 1487 \subitem for an integral ring and a list of indeterminate numbers, 1488 \hyperpage{1042} 1489 \subitem for an integral ring and a list of indeterminates, 1490 \hyperpage{1042} 1491 \subitem for an integral ring and a list of names (and an exclusion list), 1492 \hyperpage{1042} 1493 \subitem for an integral ring and a rank (and an exclusion list), 1494 \hyperpage{1042} 1495 \item \texttt{FunctionOperation}, \hyperpage{1272} 1496 \item functions 1497 \subitem as in mathematics, \hyperpage{451} 1498 \subitem as in programming language, \hyperpage{70} 1499 \subitem definition by arrow notation, \hyperpage{67} 1500 \subitem definition of, \hyperpage{65} 1501 \subitem recursive, \hyperpage{65} 1502 \subitem with a variable number of arguments, \hyperpage{66} 1503 \subitem with a variable number of arguments, calling, 1504 \hyperpage{54} 1505 \item \texttt {FunctionsFamily}, \hyperpage{77} 1506 \item \texttt {FusionCharTableTom}, \hyperpage{1094} 1507 \item \texttt {FusionConjugacyClasses} 1508 \subitem for a homomorphism, \hyperpage{1203} 1509 \subitem for two character tables, \hyperpage{1203} 1510 \subitem for two groups, \hyperpage{1203} 1511 \item \texttt {FusionConjugacyClassesOp} 1512 \subitem for a homomorphism, \hyperpage{1203} 1513 \subitem for two character tables, \hyperpage{1203} 1514 \item fusions, \hyperpage{1202} 1515 \item \texttt {FusionsAllowedByRestrictions}, \hyperpage{1222} 1516 \item \texttt {FusionsTom}, \hyperpage{1083} 1517 1518 \indexspace 1519 1520 \item $G$-sets, \hyperpage{624} 1521 \subitem computing orbits, \hyperpage{1353} 1522 \item $g_N$ (irrational value), \hyperpage{242} 1523 \item \texttt{gac}, \hyperpage{1244} 1524 \item \texttt {GaloisCyc} 1525 \subitem for a class function, \hyperpage{1162} 1526 \subitem for a cyclotomic, \hyperpage{245} 1527 \subitem for a list of cyclotomics, \hyperpage{245} 1528 \item \texttt {GaloisField} 1529 \subitem for characteristic and degree, \hyperpage{915} 1530 \subitem for characteristic and polynomial, \hyperpage{915} 1531 \subitem for field size, \hyperpage{915} 1532 \subitem for subfield and degree, \hyperpage{915} 1533 \subitem for subfield and polynomial, \hyperpage{915} 1534 \item \texttt {GaloisGroup} 1535 \subitem for abelian number fields, \hyperpage{926} 1536 \subitem of field, \hyperpage{907} 1537 \subitem of rational class of a group, \hyperpage{543} 1538 \item \texttt {GaloisMat}, \hyperpage{247} 1539 \item \texttt {GaloisStabilizer}, \hyperpage{923} 1540 \item \texttt {GaloisType}, \hyperpage{1037} 1541 \item \texttt {Gamma}, \hyperpage{256} 1542 \item \texttt {GammaL}, \hyperpage{770} 1543 \item \texttt{gap.ini}, \hyperpage{38} 1544 \item GAPDoc format 1545 \subitem for writing package documentation, \hyperpage{1250} 1546 \item \texttt{GAPDocManualLab}, \hyperpage{1268} 1547 \item \texttt {GAPInfo}, \hyperpage{42} 1548 \item \texttt{GAPInfo.Architecture}, \hyperpage{1243} 1549 \item \texttt{GAPInfo.CommandLineOptions}, \hyperpage{33} 1550 \item \texttt{GAPInfo.Keywords}, \hyperpage{47} 1551 \item \texttt {GAPInfo.ProfileThreshold}, \hyperpage{115} 1552 \item \texttt{GAPInfo.RootPaths}, \hyperpage{133} 1553 \item \texttt{GAPInfo.UserGapRoot}, \hyperpage{133} 1554 \item \texttt{GAPInfo.Version}, \hyperpage{121} 1555 \item \texttt {GapInputPcGroup}, \hyperpage{694} 1556 \item \texttt {GapInputSCTable}, \hyperpage{953} 1557 \item \texttt {GAPKB{\textunderscore }REW}, \hyperpage{819} 1558 \item \texttt{GAPTCENUM}, \hyperpage{708} 1559 \item \texttt {GAP{\textunderscore }}\discretionary {-}{}{}\texttt {E}\discretionary {-}{}{}\texttt {X}\discretionary {-}{}{}\texttt {I}\discretionary {-}{}{}\texttt {T{\textunderscore }}\discretionary {-}{}{}\texttt {CODE}, 1560 \hyperpage{93} 1561 \item \texttt{GASMAN}, \hyperpage{128} 1562 \item \texttt {GasmanLimits}, \hyperpage{129} 1563 \item \texttt {GasmanMessageStatus}, \hyperpage{129} 1564 \item \texttt {GasmanStatistics}, \hyperpage{128} 1565 \item Gaussian algorithm, \hyperpage{342} 1566 \item \texttt {GaussianIntegers}, \hyperpage{927} 1567 \item \texttt {GaussianRationals}, \hyperpage{921} 1568 \item \texttt {Gcd} 1569 \subitem for (a ring and) a list of elements, \hyperpage{890} 1570 \subitem for (a ring and) several elements, \hyperpage{890} 1571 \item \texttt {Gcdex}, \hyperpage{193} 1572 \item \texttt {GcdInt}, \hyperpage{193} 1573 \item \texttt {GcdOp}, \hyperpage{890} 1574 \item \texttt {GcdRepresentation} 1575 \subitem for (a ring and) a list of elements, \hyperpage{890} 1576 \subitem for (a ring and) several elements, \hyperpage{890} 1577 \item \texttt {GcdRepresentationOp}, \hyperpage{891} 1578 \item \texttt {GeneralisedEigenspaces}, \hyperpage{345} 1579 \item \texttt {GeneralisedEigenvalues}, \hyperpage{344} 1580 \item \texttt {GeneralisedQuaternionGenerators}, \hyperpage{763} 1581 \item generalized characters, \hyperpage{1155} 1582 \item generalized conjugation technique, \hyperpage{1361} 1583 \item \texttt {GeneralizedEigenspaces}, \hyperpage{345} 1584 \item \texttt {GeneralizedEigenvalues}, \hyperpage{344} 1585 \item \texttt {GeneralLinearGroup} 1586 \subitem for dimension and a ring, \hyperpage{766} 1587 \subitem for dimension and field size, \hyperpage{766} 1588 \item \texttt {GeneralMappingByElements}, \hyperpage{453} 1589 \item \texttt {GeneralMappingsFamily}, \hyperpage{469} 1590 \item \texttt {GeneralOrthogonalGroup}, \hyperpage{768} 1591 \item \texttt {GeneralSemilinearGroup}, \hyperpage{770} 1592 \item \texttt {GeneralUnitaryGroup}, \hyperpage{767} 1593 \item generator 1594 \subitem of the prime residue group, \hyperpage{211} 1595 \item \texttt {GeneratorsOfAdditiveGroup}, \hyperpage{874} 1596 \item \texttt {GeneratorsOfAdditiveMagma}, \hyperpage{874} 1597 \item \texttt {GeneratorsOfAdditiveMagmaWithZero}, \hyperpage{874} 1598 \item \texttt {GeneratorsOfAlgebra}, \hyperpage{961} 1599 \item \texttt {GeneratorsOfAlgebraModule}, \hyperpage{976} 1600 \item \texttt {GeneratorsOfAlgebraWithOne}, \hyperpage{961} 1601 \item \texttt {GeneratorsOfDivisionRing}, \hyperpage{904} 1602 \item \texttt {GeneratorsOfDomain}, \hyperpage{434} 1603 \item \texttt {Generators}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Equivalence}\discretionary {-}{}{}\texttt {Relation}\discretionary {-}{}{}\texttt {Partition}, 1604 \hyperpage{477} 1605 \item \texttt {GeneratorsOfField}, \hyperpage{904} 1606 \item \texttt {GeneratorsOfGroup}, \hyperpage{526} 1607 \item \texttt {GeneratorsOfIdeal}, \hyperpage{881} 1608 \item \texttt {GeneratorsOfInverseMonoid}, \hyperpage{796} 1609 \item \texttt {GeneratorsOfInverseSemigroup}, \hyperpage{796} 1610 \item \texttt {GeneratorsOfLeftIdeal}, \hyperpage{881} 1611 \item \texttt {GeneratorsOfLeftModule}, \hyperpage{896} 1612 \item \texttt {Generators}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Left}\discretionary {-}{}{}\texttt {Operator}\discretionary {-}{}{}\texttt {Additive}\discretionary {-}{}{}\texttt {Group}, 1613 \hyperpage{896} 1614 \item \texttt {GeneratorsOfLeftVectorSpace}, \hyperpage{930} 1615 \item \texttt {GeneratorsOfMagma}, \hyperpage{492} 1616 \item \texttt {GeneratorsOfMagmaWithInverses}, \hyperpage{493} 1617 \item \texttt {GeneratorsOfMagmaWithOne}, \hyperpage{492} 1618 \item \texttt {GeneratorsOfMonoid}, \hyperpage{794} 1619 \item \texttt {GeneratorsOfNearAdditiveGroup}, \hyperpage{874} 1620 \item \texttt {GeneratorsOfNearAdditiveMagma}, \hyperpage{874} 1621 \item \texttt {Generators}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Near}\discretionary {-}{}{}\texttt {Additive}\discretionary {-}{}{}\texttt {Magma}\discretionary {-}{}{}\texttt {With}\discretionary {-}{}{}\texttt {Zero}, 1622 \hyperpage{874} 1623 \item \texttt {GeneratorsOfPresentation}, \hyperpage{727} 1624 \item \texttt {GeneratorsOfRightIdeal}, \hyperpage{882} 1625 \item \texttt {GeneratorsOfRightModule}, \hyperpage{897} 1626 \item \texttt {Generators}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Right}\discretionary {-}{}{}\texttt {Operator}\discretionary {-}{}{}\texttt {Additive}\discretionary {-}{}{}\texttt {Group}, 1627 \hyperpage{897} 1628 \item \texttt {GeneratorsOfRing}, \hyperpage{878} 1629 \item \texttt {GeneratorsOfRingWithOne}, \hyperpage{883} 1630 \item \texttt {GeneratorsOfRws}, \hyperpage{521} 1631 \item \texttt {GeneratorsOfSemigroup}, \hyperpage{791} 1632 \item \texttt{GeneratorsOf\mbox{\texttt{\mdseries\slshape Struct}}}, 1633 \hyperpage{430} 1634 \item \texttt {GeneratorsOfTwoSidedIdeal}, \hyperpage{881} 1635 \item \texttt {GeneratorsOfVectorSpace}, \hyperpage{930} 1636 \item \texttt {GeneratorsPrimeResidues}, \hyperpage{209} 1637 \item \texttt {GeneratorsSmallest}, \hyperpage{577} 1638 \item \texttt {GeneratorsSubgroupsTom}, \hyperpage{1091} 1639 \item \texttt {GeneratorSyllable}, \hyperpage{508} 1640 \item \texttt {GetCyclotomicsLimit}, \hyperpage{249} 1641 \item \texttt {GetFusionMap}, \hyperpage{1204} 1642 \item \texttt {GetRecursionDepth}, \hyperpage{127} 1643 \item getting help, \hyperpage{28} 1644 \item \texttt {GetWithDefault}, \hyperpage{271} 1645 \item \texttt {GF} 1646 \subitem for characteristic and degree, \hyperpage{915} 1647 \subitem for characteristic and polynomial, \hyperpage{915} 1648 \subitem for field size, \hyperpage{915} 1649 \subitem for subfield and degree, \hyperpage{915} 1650 \subitem for subfield and polynomial, \hyperpage{915} 1651 \item \texttt {GL} 1652 \subitem for dimension and a ring, \hyperpage{766} 1653 \subitem for dimension and field size, \hyperpage{766} 1654 \item \texttt {GlobalMersenneTwister}, \hyperpage{205} 1655 \item \texttt {GlobalRandomSource}, \hyperpage{205} 1656 \item \texttt {GModuleByMats} 1657 \subitem for empty list, the dimension, and a field, 1658 \hyperpage{1062} 1659 \subitem for generators and a field, \hyperpage{1062} 1660 \item \texttt {GO}, \hyperpage{768} 1661 \item \texttt {GQuotients}, \hyperpage{601} 1662 \item \texttt {Grading}, \hyperpage{967} 1663 \item graphviz, \hyperpage{570} 1664 \item \texttt {GreensDClasses}, \hyperpage{802} 1665 \item \texttt {GreensDClassOfElement}, \hyperpage{802} 1666 \item \texttt {GreensDRelation}, \hyperpage{801} 1667 \item \texttt {GreensHClasses}, \hyperpage{802} 1668 \item \texttt {GreensHClassOfElement}, \hyperpage{802} 1669 \item \texttt {GreensHRelation}, \hyperpage{801} 1670 \item \texttt {GreensJClasses}, \hyperpage{802} 1671 \item \texttt {GreensJClassOfElement}, \hyperpage{802} 1672 \item \texttt {GreensJRelation}, \hyperpage{801} 1673 \item \texttt {GreensLClasses}, \hyperpage{802} 1674 \item \texttt {GreensLClassOfElement}, \hyperpage{802} 1675 \item \texttt {GreensLRelation}, \hyperpage{801} 1676 \item \texttt {GreensRClasses}, \hyperpage{802} 1677 \item \texttt {GreensRClassOfElement}, \hyperpage{802} 1678 \item \texttt {GreensRRelation}, \hyperpage{801} 1679 \item \texttt {GroebnerBasis} 1680 \subitem for a list and a monomial ordering, \hyperpage{1047} 1681 \subitem for an ideal and a monomial ordering, \hyperpage{1047} 1682 \item \texttt {GroebnerBasisNC}, \hyperpage{1047} 1683 \item \texttt {Group} 1684 \subitem for a list of generators (and an identity element), 1685 \hyperpage{526} 1686 \subitem for several generators, \hyperpage{526} 1687 \item group actions, \hyperpage{606, 607} 1688 \subitem operations syntax, \hyperpage{606} 1689 \item group algebra, \hyperpage{1015} 1690 \item group characters, \hyperpage{1155} 1691 \item group operations, \hyperpage{607}, \hyperpage{1272} 1692 \item group ring, \hyperpage{1015} 1693 \item \texttt {GroupByGenerators}, \hyperpage{526} 1694 \subitem with explicitly specified identity element, 1695 \hyperpage{526} 1696 \item \texttt {GroupByRws}, \hyperpage{692} 1697 \item \texttt {GroupByRwsNC}, \hyperpage{692} 1698 \item \texttt {GroupGeneralMappingByImages}, \hyperpage{590} 1699 \subitem from group to itself, \hyperpage{590} 1700 \item \texttt {GroupGeneralMappingByImagesNC}, \hyperpage{590} 1701 \subitem from group to itself, \hyperpage{590} 1702 \item \texttt {GroupHClassOfGreensDClass}, \hyperpage{803} 1703 \item \texttt {GroupHomomorphismByFunction} 1704 \subitem by function (and inverse function) between two domains, 1705 \hyperpage{591} 1706 \subitem by function and function that computes one preimage, 1707 \hyperpage{591} 1708 \item \texttt {GroupHomomorphismByImages}, \hyperpage{589} 1709 \item \texttt {GroupHomomorphismByImagesNC}, \hyperpage{590} 1710 \item \texttt {GroupOfPcgs}, \hyperpage{667} 1711 \item \texttt {GroupRing}, \hyperpage{1016} 1712 \item \texttt {GroupStabChain}, \hyperpage{648} 1713 \item \texttt {GroupWithGenerators}, \hyperpage{526} 1714 \item \texttt {GrowthFunctionOfGroup}, \hyperpage{533} 1715 \subitem with word length limit, \hyperpage{533} 1716 \item \texttt {GU}, \hyperpage{767} 1717 1718 \indexspace 1719 1720 \item $h_N$ (irrational value), \hyperpage{242} 1721 \item \texttt {HallSubgroup}, \hyperpage{550} 1722 \item \texttt {HallSystem}, \hyperpage{551} 1723 \item \texttt{HallSystem} 1724 \subitem for groups with pcgs, \hyperpage{685} 1725 \item \texttt {HasAbelianFactorGroup}, \hyperpage{565} 1726 \item \texttt {HasElementaryAbelianFactorGroup}, \hyperpage{565} 1727 \item \texttt {HasIndeterminateName}, \hyperpage{1024} 1728 \item \texttt {HasParent}, \hyperpage{433} 1729 \item \texttt {HasseDiagramBinaryRelation}, \hyperpage{475} 1730 \item \texttt {HeadPcElementByNumber}, \hyperpage{669} 1731 \item \texttt {HEL}\discretionary {-}{}{}\texttt {P{\textunderscore }}\discretionary {-}{}{}\texttt {A}\discretionary {-}{}{}\texttt {D}\discretionary {-}{}{}\texttt {D{\textunderscore }}\discretionary {-}{}{}\texttt {BOOK}, 1732 \hyperpage{1347} 1733 \item \texttt {HEL}\discretionary {-}{}{}\texttt {P{\textunderscore }}\discretionary {-}{}{}\texttt {R}\discretionary {-}{}{}\texttt {E}\discretionary {-}{}{}\texttt {M}\discretionary {-}{}{}\texttt {O}\discretionary {-}{}{}\texttt {V}\discretionary {-}{}{}\texttt {E{\textunderscore }}\discretionary {-}{}{}\texttt {BOOK}, 1734 \hyperpage{1348} 1735 \item \texttt {HEL}\discretionary {-}{}{}\texttt {P{\textunderscore }}\discretionary {-}{}{}\texttt {V}\discretionary {-}{}{}\texttt {I}\discretionary {-}{}{}\texttt {E}\discretionary {-}{}{}\texttt {W}\discretionary {-}{}{}\texttt {E}\discretionary {-}{}{}\texttt {R{\textunderscore }}\discretionary {-}{}{}\texttt {INFO}, 1736 \hyperpage{1350} 1737 \item \texttt {HenselBound}, \hyperpage{1038} 1738 \item Hermite normal form, \hyperpage{1273} 1739 \item \texttt {HermiteNormalFormIntegerMat}, \hyperpage{363} 1740 \item \texttt {Hermite}\discretionary {-}{}{}\texttt {Normal}\discretionary {-}{}{}\texttt {Form}\discretionary {-}{}{}\texttt {Integer}\discretionary {-}{}{}\texttt {Mat}\discretionary {-}{}{}\texttt {Transform}, 1741 \hyperpage{363} 1742 \item \texttt {HeuristicCancelPolynomialsExtRep}, \hyperpage{1054} 1743 \item hexadecimal character codes, \hyperpage{378} 1744 \item \texttt {HexStringInt}, \hyperpage{384} 1745 \item \texttt {HighestWeightModule}, \hyperpage{1012} 1746 \item \texttt {HMSMSec}, \hyperpage{394} 1747 \item \texttt {Hom}, \hyperpage{944} 1748 \item home directory 1749 \subitem for a GAP package, \hyperpage{1248} 1750 \item \texttt {HomeEnumerator}, \hyperpage{625} 1751 \item \texttt {HomomorphismQuotientSemigroup}, \hyperpage{800} 1752 \item homomorphisms 1753 \subitem find all, \hyperpage{600} 1754 \subitem Frobenius, field, \hyperpage{916} 1755 \item \texttt {Hypothenuse}, \hyperpage{255} 1756 1757 \indexspace 1758 1759 \item $i_N$ (irrational value), \hyperpage{243} 1760 \item \texttt {Ideal}, \hyperpage{879} 1761 \item \texttt {IdealByGenerators}, \hyperpage{881} 1762 \item \texttt {IdealDecompositionsOfPolynomial}, \hyperpage{1057} 1763 \item \texttt {IdealNC}, \hyperpage{880} 1764 \item \texttt {Ideals}, \hyperpage{894} 1765 \item \texttt {Idempotent}, \hyperpage{824} 1766 \item \texttt {Idempotents}, \hyperpage{493} 1767 \item \texttt {IdempotentsTom}, \hyperpage{1084} 1768 \item \texttt {IdempotentsTomInfo}, \hyperpage{1084} 1769 \item \texttt {IdentificationOfConjugacyClasses}, \hyperpage{1106} 1770 \item \texttt {Identifier} 1771 \subitem for character tables, \hyperpage{1115} 1772 \subitem for tables of marks, \hyperpage{1084} 1773 \item \texttt {Identity}, \hyperpage{436} 1774 \item \texttt {IdentityBinaryRelation} 1775 \subitem for a degree, \hyperpage{470} 1776 \subitem for a domain, \hyperpage{470} 1777 \item \texttt {IdentityFromSCTable}, \hyperpage{954} 1778 \item \texttt {IdentityMapping}, \hyperpage{455} 1779 \item \texttt {IdentityMat}, \hyperpage{338} 1780 \item \texttt {IdentityTransformation}, \hyperpage{826} 1781 \item \texttt {IdFunc}, \hyperpage{76} 1782 \item \texttt{if} statement, \hyperpage{60} 1783 \item \texttt {Image} 1784 \subitem set of images of a collection under a mapping, 1785 \hyperpage{458} 1786 \subitem set of images of the source of a general mapping, 1787 \hyperpage{458} 1788 \subitem unique image of an element under a mapping, 1789 \hyperpage{458} 1790 \item \texttt{Image} 1791 \subitem for Frobenius automorphisms, \hyperpage{917} 1792 \item image 1793 \subitem vector under matrix, \hyperpage{335} 1794 \item \texttt {ImageElm}, \hyperpage{458} 1795 \item \texttt {ImageListOfPartialPerm}, \hyperpage{853} 1796 \item \texttt {ImageListOfTransformation}, \hyperpage{831} 1797 \item \texttt {ImageOfPartialPermCollection}, \hyperpage{852} 1798 \item \texttt {Images} 1799 \subitem set of images of a collection under a mapping, 1800 \hyperpage{459} 1801 \subitem set of images of an element under a mapping, 1802 \hyperpage{459} 1803 \subitem set of images of the source of a general mapping, 1804 \hyperpage{459} 1805 \item \texttt {ImagesElm}, \hyperpage{458} 1806 \item \texttt {ImageSetOfPartialPerm}, \hyperpage{853} 1807 \item \texttt {ImageSetOfTransformation}, \hyperpage{831} 1808 \item \texttt {ImagesRepresentative}, \hyperpage{458} 1809 \item \texttt {ImagesSet}, \hyperpage{458} 1810 \item \texttt {ImagesSmallestGenerators}, \hyperpage{594} 1811 \item \texttt {ImagesSource}, \hyperpage{457} 1812 \item \texttt {ImaginaryPart}, \hyperpage{246} 1813 \item \texttt {ImfInvariants}, \hyperpage{784} 1814 \item \texttt {ImfMatrixGroup}, \hyperpage{785} 1815 \item \texttt {ImfNumberQClasses}, \hyperpage{781} 1816 \item \texttt {ImfNumberQQClasses}, \hyperpage{781} 1817 \item \texttt {ImfNumberZClasses}, \hyperpage{781} 1818 \item immediate integer, \hyperpage{188} 1819 \item \texttt {Immutable}, \hyperpage{164} 1820 \item \texttt {ImmutableBasis}, \hyperpage{937} 1821 \item \texttt {ImmutableMatrix}, \hyperpage{355} 1822 \item \texttt {ImmutableVector}, \hyperpage{326} 1823 \item \texttt{\texttt{\symbol{92}}in} 1824 \subitem operation for testing membership, \hyperpage{422} 1825 \item \texttt{in} 1826 \subitem for lists, \hyperpage{275} 1827 \subitem operation for, \hyperpage{422} 1828 \item \texttt {IncreaseInterval}, \hyperpage{258} 1829 \item \texttt {IndependentGeneratorExponents}, \hyperpage{578} 1830 \item \texttt {IndependentGeneratorsOfAbelianGroup}, \hyperpage{578} 1831 \item \texttt {Indeterminate} 1832 \subitem for a family and a number, \hyperpage{1023} 1833 \subitem for a ring (and a name, and an exclusion list), 1834 \hyperpage{1023} 1835 \subitem for a ring (and a number), \hyperpage{1023} 1836 \item \texttt {IndeterminateName}, \hyperpage{1024} 1837 \item \texttt {Indeterminateness}, \hyperpage{1215} 1838 \item \texttt {Indeterminate}\discretionary {-}{}{}\texttt {Number}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Laurent}\discretionary {-}{}{}\texttt {Polynomial}, 1839 \hyperpage{1039} 1840 \item \texttt {Indeterminate}\discretionary {-}{}{}\texttt {Number}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Univariate}\discretionary {-}{}{}\texttt {Rational}\discretionary {-}{}{}\texttt {Function}, 1841 \hyperpage{1024} 1842 \item \texttt {Indeterminate}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Univariate}\discretionary {-}{}{}\texttt {Rational}\discretionary {-}{}{}\texttt {Function}, 1843 \hyperpage{1024} 1844 \item \texttt {IndeterminatesOfFunctionField}, \hyperpage{1040} 1845 \item \texttt {IndeterminatesOfPolynomialRing}, \hyperpage{1040} 1846 \item \texttt {Index} 1847 \subitem for a group and its subgroup, \hyperpage{528} 1848 \subitem for two character tables, \hyperpage{1124} 1849 \item \texttt {IndexInWholeGroup}, \hyperpage{528} 1850 \item \texttt {IndexNC} 1851 \subitem for a group and its subgroup, \hyperpage{528} 1852 \item \texttt {IndexPeriodOfPartialPerm}, \hyperpage{856} 1853 \item \texttt {IndexPeriodOfTransformation}, \hyperpage{836} 1854 \item \texttt {Indicator}, \hyperpage{1125} 1855 \item \texttt {IndicatorOp}, \hyperpage{1125} 1856 \item \texttt {IndicesCentralNormalSteps}, \hyperpage{677} 1857 \item \texttt {IndicesChiefNormalSteps}, \hyperpage{679} 1858 \item \texttt {IndicesEANormalSteps}, \hyperpage{676} 1859 \item \texttt {IndicesEANormalStepsBounded}, \hyperpage{676} 1860 \item \texttt {IndicesInvolutaryGenerators}, \hyperpage{710} 1861 \item \texttt {IndicesNormalSteps}, \hyperpage{680} 1862 \item \texttt {IndicesOfAdjointBasis}, \hyperpage{962} 1863 \item \texttt {IndicesPCentralNormalStepsPGroup}, \hyperpage{678} 1864 \item \texttt {IndicesStabChain}, \hyperpage{648} 1865 \item \texttt {Indirected}, \hyperpage{1210} 1866 \item \texttt {InducedAutomorphism}, \hyperpage{599} 1867 \item \texttt {InducedClassFunction} 1868 \subitem for a given monomorphism, \hyperpage{1174} 1869 \subitem for a supergroup, \hyperpage{1174} 1870 \subitem for the character table of a supergroup, \hyperpage{1174} 1871 \item \texttt {InducedClassFunctions}, \hyperpage{1174} 1872 \item \texttt {InducedClassFunctionsByFusionMap}, \hyperpage{1174} 1873 \item \texttt {InducedCyclic}, \hyperpage{1175} 1874 \item \texttt {InducedPcgs}, \hyperpage{671} 1875 \item \texttt {InducedPcgsByGenerators}, \hyperpage{672} 1876 \item \texttt {InducedPcgsByGeneratorsNC}, \hyperpage{672} 1877 \item \texttt {InducedPcgsByPcSequence}, \hyperpage{671} 1878 \item \texttt {Induced}\discretionary {-}{}{}\texttt {Pcgs}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Pc}\discretionary {-}{}{}\texttt {Sequence}\discretionary {-}{}{}\texttt {And}\discretionary {-}{}{}\texttt {Generators}, 1879 \hyperpage{672} 1880 \item \texttt {InducedPcgsByPcSequenceNC}, \hyperpage{671} 1881 \item \texttt {InducedPcgsWrtFamilyPcgs}, \hyperpage{688} 1882 \item \texttt {InducedPcgsWrtSpecialPcgs}, \hyperpage{683} 1883 \item \texttt {Inequalities}, \hyperpage{1194} 1884 \item inequality 1885 \subitem of booleans, \hyperpage{260} 1886 \subitem of records, \hyperpage{406} 1887 \item inequality test, \hyperpage{56} 1888 \item \texttt {InertiaSubgroup}, \hyperpage{1170} 1889 \item \texttt {Inf}, \hyperpage{257} 1890 \item \texttt {infinity}, \hyperpage{241} 1891 \item inflated class functions, \hyperpage{1173} 1892 \item \texttt {Info}, \hyperpage{108} 1893 \item \texttt {InfoAlgebra}, \hyperpage{949} 1894 \item \texttt {InfoAttributes}, \hyperpage{182} 1895 \item \texttt {InfoBckt}, \hyperpage{653} 1896 \item \texttt {InfoCharacterTable}, \hyperpage{1104} 1897 \item \texttt{InfoClass} 1898 \subitem for a GAP package, \hyperpage{1262} 1899 \item \texttt {InfoCoh}, \hyperpage{581} 1900 \item \texttt {InfoComplement}, \hyperpage{546} 1901 \item \texttt {InfoCoset}, \hyperpage{540} 1902 \item \texttt {InfoFpGroup}, \hyperpage{702} 1903 \item \texttt {InfoGroebner}, \hyperpage{1048} 1904 \item \texttt {InfoGroup}, \hyperpage{528} 1905 \item \texttt {InfoLattice}, \hyperpage{573} 1906 \item \texttt {InfoLevel}, \hyperpage{108} 1907 \item \texttt {InfoMatrix}, \hyperpage{332} 1908 \item \texttt {InfoMonomial}, \hyperpage{1228} 1909 \item \texttt {InfoNumtheor}, \hyperpage{208} 1910 \item \texttt {InfoObsolete}, \hyperpage{1274} 1911 \item \texttt {InfoOptions}, \hyperpage{131} 1912 \item \texttt {InfoOutput}, \hyperpage{109} 1913 \item \texttt {InfoPackageLoading}, \hyperpage{1239} 1914 \item \texttt {InfoPcSubgroup}, \hyperpage{576} 1915 \item \texttt {InfoPoly}, \hyperpage{1032} 1916 \item \texttt {InfoText}, \hyperpage{167} 1917 \subitem for character tables, \hyperpage{1115} 1918 \item \texttt{InfoText} 1919 \subitem (for Conway polynomials), \hyperpage{917} 1920 \item \texttt {InfoTom}, \hyperpage{1080} 1921 \item \texttt {InfoWarning}, \hyperpage{110} 1922 \item \texttt {Init}, \hyperpage{204} 1923 \item \texttt{init.g} 1924 \subitem for a GAP package, \hyperpage{1250} 1925 \item \texttt {InitFusion}, \hyperpage{1221} 1926 \item \texttt {InitPowerMap}, \hyperpage{1218} 1927 \item \texttt {InjectionZeroMagma}, \hyperpage{489} 1928 \item inner product 1929 \subitem of group characters, \hyperpage{1168} 1930 \item \texttt {InnerAutomorphism}, \hyperpage{596} 1931 \item \texttt {InnerAutomorphismNC}, \hyperpage{596} 1932 \item \texttt {InnerAutomorphismsAutomorphismGroup}, \hyperpage{599} 1933 \item \texttt {InParentFOA}, \hyperpage{1353} 1934 \item \texttt {InputFromUser}, \hyperpage{151} 1935 \item \texttt {InputLogTo} 1936 \subitem for a filename, \hyperpage{140} 1937 \subitem for streams, \hyperpage{148} 1938 \subitem stop logging input, \hyperpage{140} 1939 \item \texttt {InputOutputLocalProcess}, \hyperpage{153} 1940 \item \texttt {InputTextFile}, \hyperpage{150} 1941 \item \texttt {InputTextNone}, \hyperpage{154} 1942 \item \texttt {InputTextString}, \hyperpage{152} 1943 \item \texttt {InputTextUser}, \hyperpage{151} 1944 \item \texttt {InsertTrivialStabilizer}, \hyperpage{651} 1945 \item \texttt {InstallAtExit}, \hyperpage{94} 1946 \item \texttt {InstallCharReadHookFunc}, \hyperpage{155} 1947 \item \texttt {InstalledPackageVersion}, \hyperpage{1242} 1948 \item \texttt {InstallFactorMaintenance}, \hyperpage{444} 1949 \item \texttt {InstallFlushableValue}, \hyperpage{1300} 1950 \item \texttt {InstallFlushableValueFromFunction}, \hyperpage{1300} 1951 \item \texttt {InstallGlobalFunction}, \hyperpage{1300} 1952 \item \texttt {InstallHandlingByNiceBasis}, \hyperpage{947} 1953 \item \texttt {InstallImmediateMethod}, \hyperpage{1283} 1954 \item \texttt {InstallIsomorphismMaintenance}, \hyperpage{444} 1955 \item \texttt {InstallMethod}, \hyperpage{1280} 1956 \item \texttt {InstallMethodWithRandomSource}, \hyperpage{1281} 1957 \item \texttt {InstallOtherMethod}, \hyperpage{1281} 1958 \item \texttt {InstallOtherMethodWithRandomSource}, \hyperpage{1281} 1959 \item \texttt{InstallReadlineMacro}, \hyperpage{98} 1960 \item \texttt {InstallSubsetMaintenance}, \hyperpage{443} 1961 \item \texttt {InstallTrueMethod}, \hyperpage{1284} 1962 \item \texttt {InstallValue}, \hyperpage{1300} 1963 \item \texttt {Int}, \hyperpage{189} 1964 \subitem for a cyclotomic, \hyperpage{238} 1965 \subitem for a FFE, \hyperpage{913} 1966 \subitem for strings, \hyperpage{391} 1967 \item \texttt {IntChar}, \hyperpage{390} 1968 \item integer part of a quotient, \hyperpage{192} 1969 \item \texttt {Integers} 1970 \subitem global variable, \hyperpage{188} 1971 \item \texttt {IntegralizedMat}, \hyperpage{367} 1972 \item \texttt {IntegratedStraightLineProgram}, \hyperpage{515} 1973 \item \texttt {IntermediateGroup}, \hyperpage{564} 1974 \item \texttt {IntermediateResultOfSLP}, \hyperpage{516} 1975 \item \texttt {Intermediate}\discretionary {-}{}{}\texttt {Result}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {S}\discretionary {-}{}{}\texttt {L}\discretionary {-}{}{}\texttt {P}\discretionary {-}{}{}\texttt {Without}\discretionary {-}{}{}\texttt {Overwrite}, 1976 \hyperpage{516} 1977 \item \texttt {Intermediate}\discretionary {-}{}{}\texttt {Results}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {S}\discretionary {-}{}{}\texttt {L}\discretionary {-}{}{}\texttt {P}\discretionary {-}{}{}\texttt {Without}\discretionary {-}{}{}\texttt {Overwrite}, 1978 \hyperpage{516} 1979 \item \texttt {IntermediateSubgroups}, \hyperpage{564} 1980 \item \texttt {InterpolatedPolynomial}, \hyperpage{892} 1981 \item \texttt {IntersectBlist}, \hyperpage{318} 1982 \item \texttt {Intersection} 1983 \subitem for a list, \hyperpage{420} 1984 \subitem for various collections, \hyperpage{420} 1985 \item \texttt{Intersection} 1986 \subitem for groups with pcgs, \hyperpage{685} 1987 \item intersection 1988 \subitem of collections, \hyperpage{420} 1989 \subitem of sets, \hyperpage{298} 1990 \item \texttt {Intersection2}, \hyperpage{420} 1991 \item \texttt {IntersectionBlist} 1992 \subitem for a list, \hyperpage{317} 1993 \subitem for various boolean lists, \hyperpage{317} 1994 \item \texttt {IntersectionsTom}, \hyperpage{1089} 1995 \item \texttt {IntersectSet}, \hyperpage{298} 1996 \item \texttt {IntFFE}, \hyperpage{913} 1997 \item \texttt {IntFFESymm} 1998 \subitem for a FFE, \hyperpage{914} 1999 \subitem for a vector of FFEs, \hyperpage{914} 2000 \item \texttt {IntHexString}, \hyperpage{391} 2001 \item INTOBJ{\textunderscore}MAX, \hyperpage{188} 2002 \item INTOBJ{\textunderscore}MIN, \hyperpage{188} 2003 \item \texttt {IntScalarProducts}, \hyperpage{1215} 2004 \item \texttt {IntVecFFE}, \hyperpage{914} 2005 \item \texttt {InvariantBilinearForm}, \hyperpage{659} 2006 \item \texttt {InvariantElementaryAbelianSeries}, \hyperpage{562} 2007 \item \texttt {InvariantLattice}, \hyperpage{661} 2008 \item \texttt {InvariantQuadraticForm}, \hyperpage{659} 2009 \item \texttt {InvariantSesquilinearForm}, \hyperpage{659} 2010 \item \texttt {Invariant}\discretionary {-}{}{}\texttt {Subgroups}\discretionary {-}{}{}\texttt {Elementary}\discretionary {-}{}{}\texttt {Abelian}\discretionary {-}{}{}\texttt {Group}, 2011 \hyperpage{574} 2012 \item Inverse 2013 \subitem group homomorphism, \hyperpage{592} 2014 \item \texttt {Inverse}, \hyperpage{438} 2015 \subitem for a pcword, \hyperpage{689} 2016 \subitem for a transformation, \hyperpage{835} 2017 \item inverse 2018 \subitem matrix, \hyperpage{335} 2019 \subitem of class function, \hyperpage{1160} 2020 \item \texttt {InverseAttr}, \hyperpage{438} 2021 \item \texttt {InverseClasses}, \hyperpage{1116} 2022 \item \texttt {InverseGeneralMapping}, \hyperpage{453} 2023 \item \texttt {InverseImmutable}, \hyperpage{438} 2024 \item \texttt {InverseMap}, \hyperpage{1209} 2025 \item \texttt {InverseMatMod}, \hyperpage{356} 2026 \item \texttt {InverseMonoid}, \hyperpage{795} 2027 \item \texttt {InverseMutable}, \hyperpage{438} 2028 \item \texttt {InverseOfTransformation}, \hyperpage{835} 2029 \item \texttt {InverseOp}, \hyperpage{438} 2030 \item \texttt {InverseRepresentative}, \hyperpage{649} 2031 \item \texttt {InverseSameMutability}, \hyperpage{438} 2032 \item \texttt {InverseSemigroup}, \hyperpage{795} 2033 \item \texttt {InverseSM}, \hyperpage{438} 2034 \item \texttt {InversesOfSemigroupElement}, \hyperpage{797} 2035 \item \texttt{InvocationReadlineMacro}, \hyperpage{98} 2036 \item \texttt {Irr} 2037 \subitem for a character table, \hyperpage{1109} 2038 \subitem for a group, \hyperpage{1109} 2039 \item irrationalities, \hyperpage{236} 2040 \item \texttt {IrrBaumClausen}, \hyperpage{1133} 2041 \item \texttt {IrrConlon}, \hyperpage{1132} 2042 \item \texttt {IrrDixonSchneider}, \hyperpage{1132} 2043 \item irreducible character, \hyperpage{1167} 2044 \item irreducible characters 2045 \subitem computation, \hyperpage{1136} 2046 \item \texttt {IrreducibleDifferences}, \hyperpage{1176} 2047 \item \texttt {IrreducibleModules}, \hyperpage{1135} 2048 \item \texttt{IrreducibleModules} 2049 \subitem for groups with pcgs, \hyperpage{685} 2050 \item \texttt {IrreducibleRepresentations}, \hyperpage{1133} 2051 \item \texttt {IrreducibleRepresentationsDixon}, \hyperpage{1134} 2052 \item \texttt {Is16BitsFamily}, \hyperpage{510} 2053 \item \texttt {Is32BitsFamily}, \hyperpage{510} 2054 \item \texttt {IsAbelian}, \hyperpage{494} 2055 \subitem for a character table, \hyperpage{1111} 2056 \item \texttt {IsAbelianNumberField}, \hyperpage{922} 2057 \item \texttt {IsAbelianNumberFieldPolynomialRing}, \hyperpage{1041} 2058 \item \texttt {IsAbelianTom}, \hyperpage{1086} 2059 \item \texttt {IsAdditiveElement}, \hyperpage{445} 2060 \item \texttt {IsAdditiveElementWithInverse}, \hyperpage{446} 2061 \item \texttt {IsAdditiveElementWithZero}, \hyperpage{445} 2062 \item \texttt {IsAdditiveGroup}, \hyperpage{871} 2063 \item \texttt {IsAdditiveGroupGeneralMapping}, \hyperpage{464} 2064 \item \texttt {IsAdditiveGroupHomomorphism}, \hyperpage{464} 2065 \item \texttt {IsAdditivelyCommutative}, \hyperpage{874} 2066 \item \texttt {IsAdditivelyCommutativeElement}, \hyperpage{449} 2067 \item \texttt {IsAdditively}\discretionary {-}{}{}\texttt {Commutative}\discretionary {-}{}{}\texttt {Element}\discretionary {-}{}{}\texttt {Coll}\discretionary {-}{}{}\texttt {Coll}, 2068 \hyperpage{449} 2069 \item \texttt {IsAdditively}\discretionary {-}{}{}\texttt {Commutative}\discretionary {-}{}{}\texttt {Element}\discretionary {-}{}{}\texttt {Collection}, 2070 \hyperpage{449} 2071 \item \texttt {IsAdditively}\discretionary {-}{}{}\texttt {Commutative}\discretionary {-}{}{}\texttt {Element}\discretionary {-}{}{}\texttt {Family}, 2072 \hyperpage{449} 2073 \item \texttt {IsAdditiveMagma}, \hyperpage{871} 2074 \item \texttt {IsAdditiveMagmaWithInverses}, \hyperpage{871} 2075 \item \texttt {IsAdditiveMagmaWithZero}, \hyperpage{871} 2076 \item \texttt {IsAlgebra}, \hyperpage{959} 2077 \item \texttt {IsAlgebraGeneralMapping}, \hyperpage{466} 2078 \item \texttt {IsAlgebraHomomorphism}, \hyperpage{466} 2079 \item \texttt {IsAlgebraicElement}, \hyperpage{1057} 2080 \item \texttt {IsAlgebraicExtension}, \hyperpage{1056} 2081 \item \texttt {IsAlgebraModuleElement}, \hyperpage{976} 2082 \item \texttt {IsAlgebraModuleElementCollection}, \hyperpage{976} 2083 \item \texttt {IsAlgebraModuleElementFamily}, \hyperpage{976} 2084 \item \texttt {IsAlgebraWithOne}, \hyperpage{959} 2085 \item \texttt {IsAlgebraWithOneGeneralMapping}, \hyperpage{466} 2086 \item \texttt {IsAlgebraWithOneHomomorphism}, \hyperpage{466} 2087 \item \texttt {IsAlmostSimple} 2088 \subitem for a character table, \hyperpage{1111} 2089 \item \texttt {IsAlmostSimpleGroup}, \hyperpage{553} 2090 \item \texttt {IsAlphaChar}, \hyperpage{381} 2091 \item \texttt {IsAlternatingGroup}, \hyperpage{639} 2092 \item \texttt {IsAnticommutative}, \hyperpage{885} 2093 \item \texttt {IsAntisymmetricBinaryRelation}, \hyperpage{472} 2094 \item \texttt {IsAssociated}, \hyperpage{886} 2095 \item \texttt {IsAssociative}, \hyperpage{494} 2096 \item \texttt {IsAssociativeElement}, \hyperpage{448} 2097 \item \texttt {IsAssociativeElementCollColl}, \hyperpage{448} 2098 \item \texttt {IsAssociativeElementCollection}, \hyperpage{448} 2099 \item \texttt {IsAssocWord}, \hyperpage{503} 2100 \item \texttt {IsAssocWordWithInverse}, \hyperpage{503} 2101 \item \texttt {IsAssocWordWithOne}, \hyperpage{503} 2102 \item \texttt {IsAttribute}, \hyperpage{178} 2103 \item \texttt {IsAttributeStoringRep}, \hyperpage{180} 2104 \item \texttt {IsAutomorphismGroup}, \hyperpage{598} 2105 \item \texttt {IsBasicWreathLessThanOrEqual}, \hyperpage{505} 2106 \item \texttt {IsBasicWreathProductOrdering}, \hyperpage{484} 2107 \item \texttt {IsBasis}, \hyperpage{932} 2108 \item \texttt {IsBasisByNiceBasis}, \hyperpage{947} 2109 \item \texttt {IsBasisOfAlgebraModuleElementSpace}, \hyperpage{977} 2110 \item \texttt {IsBergerCondition} 2111 \subitem for a character, \hyperpage{1228} 2112 \subitem for a group, \hyperpage{1228} 2113 \item \texttt {IsBiCoset}, \hyperpage{538} 2114 \item \texttt {IsBijective}, \hyperpage{457} 2115 \item \texttt {IsBinaryRelation}, \hyperpage{470} 2116 \item \texttt{IsBinaryRelation} 2117 \subitem same as IsEndoGeneralMapping, \hyperpage{470} 2118 \item \texttt {IsBLetterAssocWordRep}, \hyperpage{509} 2119 \item \texttt {IsBLetterWordsFamily}, \hyperpage{509} 2120 \item \texttt {IsBlist}, \hyperpage{315} 2121 \item \texttt {IsBlistRep}, \hyperpage{321} 2122 \item IsBlockMatrixRep, \hyperpage{358} 2123 \item \texttt {IsBool}, \hyperpage{259} 2124 \item \texttt {IsBound} 2125 \subitem for a global variable, \hyperpage{50} 2126 \subitem for a list index, \hyperpage{271} 2127 \subitem for a record component, \hyperpage{407} 2128 \item \texttt {IsBound\texttt {\char 92\relax }.}, \hyperpage{408} 2129 \item \texttt {IsBound\texttt {\char 92\relax }[\texttt {\char 92\relax }]}, 2130 \hyperpage{265} 2131 \item \texttt {IsBoundElmWPObj}, \hyperpage{1358} 2132 \item \texttt {IsBoundGlobal}, \hyperpage{52} 2133 \item \texttt {IsBrauerTable}, \hyperpage{1103} 2134 \item \texttt {IsBravaisGroup}, \hyperpage{662} 2135 \item \texttt {IsBuilt}\discretionary {-}{}{}\texttt {From}\discretionary {-}{}{}\texttt {Additive}\discretionary {-}{}{}\texttt {Magma}\discretionary {-}{}{}\texttt {With}\discretionary {-}{}{}\texttt {Inverses}, 2136 \hyperpage{522} 2137 \item \texttt {IsBuiltFromGroup}, \hyperpage{522} 2138 \item \texttt {IsBuiltFromMagma}, \hyperpage{522} 2139 \item \texttt {IsBuiltFromMagmaWithInverses}, \hyperpage{522} 2140 \item \texttt {IsBuiltFromMagmaWithOne}, \hyperpage{522} 2141 \item \texttt {IsBuiltFromSemigroup}, \hyperpage{522} 2142 \item \texttt {IsCanonicalBasis}, \hyperpage{935} 2143 \item \texttt {IsCanonicalBasisFullMatrixModule}, \hyperpage{941} 2144 \item \texttt {IsCanonicalBasisFullRowModule}, \hyperpage{941} 2145 \item \texttt {IsCanonicalNiceMonomorphism}, \hyperpage{596} 2146 \item \texttt {IsCanonicalPcgs}, \hyperpage{673} 2147 \item \texttt {IsCategory}, \hyperpage{175} 2148 \item \texttt {IsCentral}, \hyperpage{494} 2149 \item \texttt {IsCentralFactor}, \hyperpage{583} 2150 \item \texttt {IsChar}, \hyperpage{375} 2151 \item \texttt {IsCharacter}, \hyperpage{1167} 2152 \item \texttt {IsCharacteristicSubgroup}, \hyperpage{530} 2153 \item \texttt {IsCharacterTable}, \hyperpage{1103} 2154 \item \texttt {IsCharacterTableInProgress}, \hyperpage{1103} 2155 \item \texttt {IsCharCollection}, \hyperpage{375} 2156 \item \texttt {IsCheapConwayPolynomial}, \hyperpage{918} 2157 \item \texttt {IsClassFunction}, \hyperpage{1157} 2158 \item \texttt {IsClassFusionOfNormalSubgroup}, \hyperpage{1125} 2159 \item \texttt {IsClosedStream}, \hyperpage{142} 2160 \item \texttt {IsCochain}, \hyperpage{1007} 2161 \item \texttt {IsCochainCollection}, \hyperpage{1007} 2162 \item \texttt {IsCollection}, \hyperpage{410} 2163 \item \texttt {IsCollectionFamily}, \hyperpage{411} 2164 \item \texttt {IsCommutative}, \hyperpage{494} 2165 \item \texttt {IsCommutativeElement}, \hyperpage{449} 2166 \item \texttt {IsCommutativeElementCollColl}, \hyperpage{449} 2167 \item \texttt {IsCommutativeElementCollection}, \hyperpage{449} 2168 \item \texttt {IsComponentObjectRep}, \hyperpage{176} 2169 \item \texttt {IsCompositionMappingRep}, \hyperpage{454} 2170 \item \texttt {IsConfluent} 2171 \subitem for a rewriting system, \hyperpage{520} 2172 \subitem for an algebra with canonical rewriting system, 2173 \hyperpage{520} 2174 \subitem for pc groups, \hyperpage{692} 2175 \item \texttt {IsConjugacy}\discretionary {-}{}{}\texttt {Class}\discretionary {-}{}{}\texttt {Subgroups}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {StabilizerRep}, 2176 \hyperpage{566} 2177 \item \texttt {IsConjugacyClassSubgroupsRep}, \hyperpage{566} 2178 \item \texttt {IsConjugate} 2179 \subitem for a group and two elements, \hyperpage{543} 2180 \subitem for a group and two groups, \hyperpage{543} 2181 \item \texttt {IsConjugatorAutomorphism}, \hyperpage{597} 2182 \item \texttt {IsConjugatorIsomorphism}, \hyperpage{597} 2183 \item \texttt {IsConstantRationalFunction}, \hyperpage{1029} 2184 \item \texttt {IsConstantTimeAccessGeneralMapping}, \hyperpage{467} 2185 \item \texttt {IsConstantTimeAccessList}, \hyperpage{265} 2186 \item \texttt {IsContainedInSpan}, \hyperpage{938} 2187 \item \texttt {IsCopyable}, \hyperpage{163} 2188 \item \texttt {IsCyc}, \hyperpage{237} 2189 \item \texttt {IsCyclic}, \hyperpage{552} 2190 \subitem for a character table, \hyperpage{1111} 2191 \item \texttt {IsCyclicTom}, \hyperpage{1086} 2192 \item \texttt {IsCyclotomic}, \hyperpage{237} 2193 \item \texttt {IsCyclotomicField}, \hyperpage{922} 2194 \item \texttt {IsCyclotomicMatrixGroup}, \hyperpage{661} 2195 \item \texttt {IsDataObjectRep}, \hyperpage{176} 2196 \item \texttt {IsDenseList}, \hyperpage{264} 2197 \item \texttt {IsDiagonalMat}, \hyperpage{338} 2198 \item \texttt {IsDiagonalMatrix}, \hyperpage{338} 2199 \item \texttt {IsDictionary}, \hyperpage{399} 2200 \item \texttt {IsDigitChar}, \hyperpage{381} 2201 \item \texttt {IsDihedralGroup}, \hyperpage{763} 2202 \item \texttt {IsDirectory}, \hyperpage{134} 2203 \item \texttt {IsDirectoryPath}, \hyperpage{138} 2204 \item \texttt {IsDirectProductElement}, \hyperpage{451} 2205 \item \texttt {IsDisjoint}, \hyperpage{257} 2206 \item \texttt {IsDistributive}, \hyperpage{885} 2207 \item \texttt {IsDivisionRing}, \hyperpage{902} 2208 \item \texttt {IsDomain}, \hyperpage{434} 2209 \item \texttt {IsDoneIterator}, \hyperpage{425} 2210 \item \texttt {IsDoubleCoset} 2211 \subitem operation, \hyperpage{540} 2212 \item \texttt {IsDuplicateFree}, \hyperpage{292} 2213 \item \texttt {IsDuplicateFreeList}, \hyperpage{292} 2214 \item \texttt {IsDxLargeGroup}, \hyperpage{1138} 2215 \item \texttt {IsElementaryAbelian}, \hyperpage{552} 2216 \subitem for a character table, \hyperpage{1111} 2217 \item \texttt {IsElementOfFpMonoid}, \hyperpage{814} 2218 \item \texttt {IsElementOfFpSemigroup}, \hyperpage{814} 2219 \item \texttt {IsElementOfFreeMagmaRing}, \hyperpage{1018} 2220 \item \texttt {IsElementOfFreeMagmaRingCollection}, \hyperpage{1018} 2221 \item \texttt {IsElementOfFreeMagmaRingFamily}, \hyperpage{1018} 2222 \item \texttt {IsElementOfMagmaRingModuloRelations}, 2223 \hyperpage{1019} 2224 \item \texttt {IsElement}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Magma}\discretionary {-}{}{}\texttt {Ring}\discretionary {-}{}{}\texttt {Modulo}\discretionary {-}{}{}\texttt {Relations}\discretionary {-}{}{}\texttt {Collection}, 2225 \hyperpage{1019} 2226 \item \texttt {IsElement}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Magma}\discretionary {-}{}{}\texttt {Ring}\discretionary {-}{}{}\texttt {Modulo}\discretionary {-}{}{}\texttt {Relations}\discretionary {-}{}{}\texttt {Family}, 2227 \hyperpage{1019} 2228 \item \texttt {IsElement}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Magma}\discretionary {-}{}{}\texttt {Ring}\discretionary {-}{}{}\texttt {Modulo}\discretionary {-}{}{}\texttt {Span}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Zero}\discretionary {-}{}{}\texttt {Family}, 2229 \hyperpage{1020} 2230 \item \texttt {IsEmpty}, \hyperpage{418} 2231 \item \texttt {IsEmptyMatrix} 2232 \subitem for matrices, \hyperpage{337} 2233 \item \texttt {IsEmptyString}, \hyperpage{380} 2234 \item \texttt {IsEndOfStream}, \hyperpage{146} 2235 \item \texttt {IsEndoGeneralMapping}, \hyperpage{467} 2236 \item \texttt{IsEndoGeneralMapping} 2237 \subitem same as IsBinaryRelation, \hyperpage{470} 2238 \item \texttt {IsEqualSet}, \hyperpage{296} 2239 \item \texttt {IsEquivalenceClass}, \hyperpage{477} 2240 \item \texttt {IsEquivalenceRelation}, \hyperpage{473} 2241 \item \texttt {IsEuclideanRing}, \hyperpage{888} 2242 \item \texttt {IsEvenInt}, \hyperpage{190} 2243 \item \texttt {IsExecutableFile}, \hyperpage{138} 2244 \item \texttt {IsExistingFile}, \hyperpage{137} 2245 \item \texttt {IsExtAElement}, \hyperpage{445} 2246 \item \texttt {IsExternalOrbit}, \hyperpage{626} 2247 \item \texttt {IsExternalSet}, \hyperpage{625} 2248 \item \texttt {IsExternalSubset}, \hyperpage{626} 2249 \item \texttt {IsExtLElement}, \hyperpage{446} 2250 \item \texttt {IsExtRElement}, \hyperpage{446} 2251 \item \texttt {IsFamilyPcgs}, \hyperpage{688} 2252 \item \texttt {IsFFE}, \hyperpage{910} 2253 \item \texttt {IsFFECollColl}, \hyperpage{910} 2254 \item \texttt {IsFFECollCollColl}, \hyperpage{910} 2255 \item \texttt {IsFFECollection}, \hyperpage{910} 2256 \item \texttt {IsFFEMatrixGroup}, \hyperpage{656} 2257 \item \texttt {IsField}, \hyperpage{902} 2258 \item \texttt{IsFieldControlledByGaloisGroup}, \hyperpage{906} 2259 \item \texttt {IsFieldHomomorphism}, \hyperpage{466} 2260 \item \texttt {IsFinite}, \hyperpage{418} 2261 \subitem for a character table, \hyperpage{1111} 2262 \subitem for floats, \hyperpage{254} 2263 \item \texttt {IsFiniteDimensional}, \hyperpage{900} 2264 \subitem for matrix algebras, \hyperpage{960} 2265 \item \texttt {IsFiniteFieldPolynomialRing}, \hyperpage{1041} 2266 \item \texttt {IsFinitelyGeneratedGroup}, \hyperpage{557} 2267 \item \texttt {IsFiniteOrderElement}, \hyperpage{449} 2268 \item \texttt {IsFiniteOrderElementCollColl}, \hyperpage{449} 2269 \item \texttt {IsFiniteOrderElementCollection}, \hyperpage{449} 2270 \item \texttt {IsFiniteOrdersPcgs}, \hyperpage{666} 2271 \item \texttt {IsFixedStabilizer}, \hyperpage{651} 2272 \item \texttt {IsFLMLOR}, \hyperpage{958} 2273 \item \texttt {IsFLMLORWithOne}, \hyperpage{959} 2274 \item \texttt {IsFpGroup}, \hyperpage{701} 2275 \item \texttt {IsFpMonoid}, \hyperpage{814} 2276 \item \texttt {IsFpSemigroup}, \hyperpage{814} 2277 \item \texttt {IsFreeGroup}, \hyperpage{503} 2278 \item \texttt {IsFreeLeftModule}, \hyperpage{899} 2279 \item \texttt {IsFreeMagmaRing}, \hyperpage{1016} 2280 \item \texttt {IsFreeMagmaRingWithOne}, \hyperpage{1017} 2281 \item \texttt {IsFromFpGroupGeneralMappingByImages}, \hyperpage{605} 2282 \item \texttt {IsFromFpGroupHomomorphismByImages}, \hyperpage{605} 2283 \item \texttt {IsFrom}\discretionary {-}{}{}\texttt {Fp}\discretionary {-}{}{}\texttt {Group}\discretionary {-}{}{}\texttt {Std}\discretionary {-}{}{}\texttt {Gens}\discretionary {-}{}{}\texttt {General}\discretionary {-}{}{}\texttt {Mapping}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Images}, 2284 \hyperpage{605} 2285 \item \texttt {IsFrom}\discretionary {-}{}{}\texttt {Fp}\discretionary {-}{}{}\texttt {Group}\discretionary {-}{}{}\texttt {Std}\discretionary {-}{}{}\texttt {Gens}\discretionary {-}{}{}\texttt {Homomorphism}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Images}, 2286 \hyperpage{605} 2287 \item \texttt {IsFullHomModule}, \hyperpage{945} 2288 \item \texttt {IsFullMatrixModule}, \hyperpage{901} 2289 \item \texttt {IsFullRowModule}, \hyperpage{901} 2290 \item \texttt {IsFull}\discretionary {-}{}{}\texttt {Subgroup}\discretionary {-}{}{}\texttt {G}\discretionary {-}{}{}\texttt {Lor}\discretionary {-}{}{}\texttt {S}\discretionary {-}{}{}\texttt {L}\discretionary {-}{}{}\texttt {Respecting}\discretionary {-}{}{}\texttt {Bilinear}\discretionary {-}{}{}\texttt {Form}, 2291 \hyperpage{659} 2292 \item \texttt {IsFull}\discretionary {-}{}{}\texttt {Subgroup}\discretionary {-}{}{}\texttt {G}\discretionary {-}{}{}\texttt {Lor}\discretionary {-}{}{}\texttt {S}\discretionary {-}{}{}\texttt {L}\discretionary {-}{}{}\texttt {Respecting}\discretionary {-}{}{}\texttt {Quadratic}\discretionary {-}{}{}\texttt {Form}, 2293 \hyperpage{660} 2294 \item \texttt {IsFull}\discretionary {-}{}{}\texttt {Subgroup}\discretionary {-}{}{}\texttt {G}\discretionary {-}{}{}\texttt {Lor}\discretionary {-}{}{}\texttt {S}\discretionary {-}{}{}\texttt {L}\discretionary {-}{}{}\texttt {Respecting}\discretionary {-}{}{}\texttt {Sesquilinear}\discretionary {-}{}{}\texttt {Form}, 2295 \hyperpage{659} 2296 \item \texttt {IsFullTransformationMonoid}, \hyperpage{842} 2297 \item \texttt {IsFullTransformationSemigroup}, \hyperpage{842} 2298 \item \texttt {IsFunction}, \hyperpage{77} 2299 \item \texttt {IsFunctionField}, \hyperpage{1042} 2300 \item \texttt {IsGAPRandomSource}, \hyperpage{205} 2301 \item \texttt {IsGaussianIntegers}, \hyperpage{927} 2302 \item \texttt {IsGaussianRationals}, \hyperpage{921} 2303 \item \texttt {IsGaussianSpace}, \hyperpage{939} 2304 \item \texttt {IsGaussInt}, \hyperpage{240} 2305 \item \texttt {IsGaussRat}, \hyperpage{240} 2306 \item \texttt {IsGeneralisedQuaternionGroup}, \hyperpage{763} 2307 \item \texttt {IsGeneralizedDomain}, \hyperpage{434} 2308 \item \texttt {IsGeneralizedRowVector}, \hyperpage{278} 2309 \item \texttt {IsGeneralLinearGroup}, \hyperpage{658} 2310 \item \texttt {IsGeneralMapping}, \hyperpage{467} 2311 \item \texttt {IsGeneralMappingFamily}, \hyperpage{468} 2312 \item \texttt {IsGeneratorsOfSemigroup}, \hyperpage{791} 2313 \item \texttt{IsGeneratorsOf\mbox{\texttt{\mdseries\slshape Struct}}}, 2314 \hyperpage{430} 2315 \item \texttt {IsGL}, \hyperpage{658} 2316 \item \texttt {IsGlobalRandomSource}, \hyperpage{205} 2317 \item \texttt {IsGreensClass}, \hyperpage{801} 2318 \item \texttt {IsGreensDClass}, \hyperpage{801} 2319 \item \texttt {IsGreensDRelation}, \hyperpage{801} 2320 \item \texttt {IsGreensHClass}, \hyperpage{801} 2321 \item \texttt {IsGreensHRelation}, \hyperpage{801} 2322 \item \texttt {IsGreensJClass}, \hyperpage{801} 2323 \item \texttt {IsGreensJRelation}, \hyperpage{801} 2324 \item \texttt {IsGreensLClass}, \hyperpage{801} 2325 \item \texttt {IsGreensLessThanOrEqual}, \hyperpage{802} 2326 \item \texttt {IsGreensLRelation}, \hyperpage{801} 2327 \item \texttt {IsGreensRClass}, \hyperpage{801} 2328 \item \texttt {IsGreensRelation}, \hyperpage{801} 2329 \item \texttt {IsGreensRRelation}, \hyperpage{801} 2330 \item \texttt {IsGroup}, \hyperpage{527} 2331 \item \texttt {IsGroupGeneralMapping}, \hyperpage{463} 2332 \item \texttt {IsGroup}\discretionary {-}{}{}\texttt {General}\discretionary {-}{}{}\texttt {Mapping}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {As}\discretionary {-}{}{}\texttt {Group}\discretionary {-}{}{}\texttt {General}\discretionary {-}{}{}\texttt {Mapping}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Images}, 2333 \hyperpage{604} 2334 \item \texttt {IsGroupGeneralMappingByImages}, \hyperpage{604} 2335 \item \texttt {IsGroupGeneralMappingByPcgs}, \hyperpage{605} 2336 \item \texttt {IsGroupHClass}, \hyperpage{803} 2337 \item \texttt {IsGroupHomomorphism}, \hyperpage{463} 2338 \item \texttt {IsGroupOfAutomorphisms}, \hyperpage{598} 2339 \item \texttt {IsGroupRing}, \hyperpage{1017} 2340 \item \texttt {IsHandledByNiceBasis}, \hyperpage{947} 2341 \item \texttt {IsHandledByNiceMonomorphism}, \hyperpage{595} 2342 \item \texttt {IsHasseDiagram}, \hyperpage{472} 2343 \item \texttt {IsHomogeneousList}, \hyperpage{264} 2344 \item \texttt {IsIdempotent}, \hyperpage{438} 2345 \item \texttt {IsIdenticalObj}, \hyperpage{161} 2346 \item \texttt {IsIncomparableUnder}, \hyperpage{480} 2347 \item \texttt {IsInducedFromNormalSubgroup}, \hyperpage{1231} 2348 \item \texttt {IsInducedPcgs}, \hyperpage{671} 2349 \item \texttt {IsInducedPcgsWrtSpecialPcgs}, \hyperpage{683} 2350 \item \texttt {IsInfBitsFamily}, \hyperpage{510} 2351 \item \texttt {IsInfiniteAbelianizationGroup}, \hyperpage{725} 2352 \item \texttt{IsInfiniteAbelianizationGroup} 2353 \subitem for groups, \hyperpage{725} 2354 \item \texttt {IsInfinity}, \hyperpage{241} 2355 \item \texttt {IsInjective}, \hyperpage{456} 2356 \item \texttt {IsInjectiveListTrans}, \hyperpage{829} 2357 \item \texttt {IsInnerAutomorphism}, \hyperpage{597} 2358 \item \texttt {IsInputOutputStream}, \hyperpage{153} 2359 \item \texttt {IsInputStream}, \hyperpage{143} 2360 \item \texttt {IsInputTextNone}, \hyperpage{143} 2361 \item \texttt {IsInputTextStream}, \hyperpage{143} 2362 \item \texttt {IsInt}, \hyperpage{189} 2363 \item \texttt {IsIntegerMatrixGroup}, \hyperpage{661} 2364 \item \texttt {IsIntegers}, \hyperpage{189} 2365 \item \texttt {IsIntegralBasis}, \hyperpage{936} 2366 \item \texttt {IsIntegralCyclotomic}, \hyperpage{237} 2367 \item \texttt {IsIntegralRing}, \hyperpage{884} 2368 \item \texttt {IsInternallyConsistent}, \hyperpage{167} 2369 \subitem for character tables, \hyperpage{1124} 2370 \subitem for tables of marks, \hyperpage{1086} 2371 \item \texttt {IsInternalRep}, \hyperpage{176} 2372 \item \texttt {IsInverseMonoid}, \hyperpage{799} 2373 \item \texttt {IsInverseSemigroup}, \hyperpage{799} 2374 \item \texttt {IsInverseSubsemigroup}, \hyperpage{797} 2375 \item \texttt {IsIrreducibleCharacter}, \hyperpage{1167} 2376 \item \texttt {IsIrreducibleRingElement}, \hyperpage{887} 2377 \item \texttt {IsIterator}, \hyperpage{425} 2378 \item \texttt {IsJacobianElement}, \hyperpage{449} 2379 \item \texttt {IsJacobianElementCollColl}, \hyperpage{449} 2380 \item \texttt {IsJacobianElementCollection}, \hyperpage{449} 2381 \item \texttt {IsJacobianRing}, \hyperpage{885} 2382 \item \texttt {IsLaurentPolynomial}, \hyperpage{1029} 2383 \item \texttt {IsLaurentPolynomialDefaultRep}, \hyperpage{1052} 2384 \item \texttt {IsLDistributive}, \hyperpage{884} 2385 \item \texttt {IsLeftAlgebraModuleElement}, \hyperpage{976} 2386 \item \texttt {IsLeft}\discretionary {-}{}{}\texttt {Algebra}\discretionary {-}{}{}\texttt {Module}\discretionary {-}{}{}\texttt {Element}\discretionary {-}{}{}\texttt {Collection}, 2387 \hyperpage{976} 2388 \item \texttt {IsLeftIdeal}, \hyperpage{880} 2389 \item \texttt {IsLeftIdealInParent}, \hyperpage{880} 2390 \item \texttt {IsLeftModule}, \hyperpage{896} 2391 \item \texttt {IsLeftModuleGeneralMapping}, \hyperpage{465} 2392 \item \texttt {IsLeftModuleHomomorphism}, \hyperpage{465} 2393 \item \texttt {IsLeftOperatorAdditiveGroup}, \hyperpage{896} 2394 \item \texttt {IsLeftSemigroupIdeal}, \hyperpage{799} 2395 \item \texttt {IsLeftVectorSpace}, \hyperpage{928} 2396 \item \texttt {IsLessThanOrEqualUnder}, \hyperpage{481} 2397 \item \texttt {IsLessThanUnder}, \hyperpage{481} 2398 \item \texttt {IsLetterAssocWordRep}, \hyperpage{509} 2399 \item \texttt {IsLetterWordsFamily}, \hyperpage{509} 2400 \item \texttt {IsLexicographicallyLess}, \hyperpage{301} 2401 \item \texttt {IsLexOrderedFFE}, \hyperpage{912} 2402 \item \texttt {IsLieAbelian}, \hyperpage{993} 2403 \item \texttt {IsLieAlgebra}, \hyperpage{959} 2404 \item \texttt {IsLieMatrix}, \hyperpage{333} 2405 \item \texttt {IsLieNilpotent}, \hyperpage{994} 2406 \item \texttt {IsLieObject}, \hyperpage{986} 2407 \item \texttt {IsLieObjectCollection}, \hyperpage{986} 2408 \item \texttt {IsLieSolvable}, \hyperpage{994} 2409 \item \texttt {IsLinearMapping}, \hyperpage{465} 2410 \item \texttt {IsLinearMappingsModule}, \hyperpage{945} 2411 \item \texttt {IsLineByLineProfileActive}, \hyperpage{121} 2412 \item \texttt {IsList}, \hyperpage{263} 2413 \item \texttt {IsListDefault}, \hyperpage{279} 2414 \item \texttt {IsListOrCollection}, \hyperpage{412} 2415 \item \texttt {IsLogOrderedFFE}, \hyperpage{912} 2416 \item \texttt {IsLookupDictionary}, \hyperpage{399} 2417 \item \texttt {IsLowerAlphaChar}, \hyperpage{381} 2418 \item \texttt {IsLowerTriangularMat}, \hyperpage{338} 2419 \item \texttt {IsLowerTriangularMatrix}, \hyperpage{338} 2420 \item \texttt {IsMagma}, \hyperpage{486} 2421 \item \texttt {IsMagmaHomomorphism}, \hyperpage{462} 2422 \item \texttt {IsMagmaRingModuloRelations}, \hyperpage{1020} 2423 \item \texttt {IsMagmaRingModuloSpanOfZero}, \hyperpage{1020} 2424 \item \texttt {IsMagmaRingObjDefaultRep}, \hyperpage{1017} 2425 \item \texttt {IsMagmaWithInverses}, \hyperpage{487} 2426 \item \texttt {IsMagmaWithInversesIfNonzero}, \hyperpage{486} 2427 \item \texttt {IsMagmaWithOne}, \hyperpage{486} 2428 \item \texttt {IsMagmaWithZeroAdjoined}, \hyperpage{489} 2429 \item \texttt {IsMapping}, \hyperpage{456} 2430 \item \texttt {IsMatchingSublist}, \hyperpage{291} 2431 \item \texttt {IsMatrix}, \hyperpage{332} 2432 \item \texttt {IsMatrixGroup}, \hyperpage{655} 2433 \item \texttt {IsMatrixModule}, \hyperpage{901} 2434 \item \texttt {IsMatrixSpace}, \hyperpage{939} 2435 \item \texttt {IsMersenneTwister}, \hyperpage{205} 2436 \item \texttt {IsMinimalNonmonomial}, \hyperpage{1235} 2437 \item \texttt {IsModuloPcgs}, \hyperpage{674} 2438 \item \texttt {IsMonoid}, \hyperpage{793} 2439 \item \texttt {IsMonomial} 2440 \subitem for a character table, \hyperpage{1111} 2441 \item \texttt{IsMonomial} 2442 \subitem for positive integers, \hyperpage{1232} 2443 \item \texttt {IsMonomialGroup}, \hyperpage{553} 2444 \item \texttt {IsMonomialMatrix}, \hyperpage{337} 2445 \item \texttt {IsMonomialNumber}, \hyperpage{1232} 2446 \item \texttt {IsMonomialOrdering}, \hyperpage{1043} 2447 \item \texttt {IsMultiplicativeElement}, \hyperpage{446} 2448 \item \texttt {IsMultiplicativeElementWithInverse}, \hyperpage{447} 2449 \item \texttt {IsMultiplicativeElementWithOne}, \hyperpage{446} 2450 \item \texttt {IsMultiplicativeElementWithZero}, \hyperpage{446} 2451 \item \texttt {IsMultiplicative}\discretionary {-}{}{}\texttt {Generalized}\discretionary {-}{}{}\texttt {Row}\discretionary {-}{}{}\texttt {Vector}, 2452 \hyperpage{278} 2453 \item \texttt {IsMultiplicativeZero}, \hyperpage{494} 2454 \item \texttt {IsMutable}, \hyperpage{163} 2455 \item \texttt {IsMutableBasis}, \hyperpage{937} 2456 \item \texttt {IsNaN}, \hyperpage{254} 2457 \item \texttt {IsNaturalAlternatingGroup}, \hyperpage{639} 2458 \item \texttt {IsNaturalGL}, \hyperpage{658} 2459 \item \texttt {IsNaturalGLnZ}, \hyperpage{661} 2460 \item \texttt {IsNaturalSL}, \hyperpage{658} 2461 \item \texttt {IsNaturalSLnZ}, \hyperpage{661} 2462 \item \texttt {IsNaturalSymmetricGroup}, \hyperpage{639} 2463 \item \texttt {IsNearAdditiveElement}, \hyperpage{445} 2464 \item \texttt {IsNearAdditiveElementWithInverse}, \hyperpage{445} 2465 \item \texttt {IsNearAdditiveElementWithZero}, \hyperpage{445} 2466 \item \texttt {IsNearAdditiveGroup}, \hyperpage{870} 2467 \item \texttt {IsNearAdditiveMagma}, \hyperpage{870} 2468 \item \texttt {IsNearAdditiveMagmaWithInverses}, \hyperpage{870} 2469 \item \texttt {IsNearAdditiveMagmaWithZero}, \hyperpage{870} 2470 \item \texttt {IsNearlyCharacterTable}, \hyperpage{1103} 2471 \item \texttt {IsNearRingElement}, \hyperpage{447} 2472 \item \texttt {IsNearRingElementWithInverse}, \hyperpage{448} 2473 \item \texttt {IsNearRingElementWithOne}, \hyperpage{447} 2474 \item \texttt {IsNegInfinity}, \hyperpage{241} 2475 \item \texttt {IsNegRat}, \hyperpage{234} 2476 \item \texttt {IsNilpotent} 2477 \subitem for a character table, \hyperpage{1111} 2478 \item \texttt{IsNilpotent} 2479 \subitem for groups with pcgs, \hyperpage{685} 2480 \item \texttt {IsNilpotentElement}, \hyperpage{1003} 2481 \item \texttt {IsNilpotentGroup}, \hyperpage{552} 2482 \item \texttt {IsNilpotentTom}, \hyperpage{1086} 2483 \item \texttt {IsNInfinity}, \hyperpage{254} 2484 \item \texttt {IsNonabelianSimpleGroup}, \hyperpage{553} 2485 \item \texttt {IsNonassocWord}, \hyperpage{497} 2486 \item \texttt {IsNonassocWordCollection}, \hyperpage{498} 2487 \item \texttt {IsNonassocWordWithOne}, \hyperpage{497} 2488 \item \texttt {IsNonassocWordWithOneCollection}, \hyperpage{498} 2489 \item \texttt {IsNonnegativeIntegers}, \hyperpage{189} 2490 \item \texttt {IsNonSPGeneralMapping}, \hyperpage{468} 2491 \item \texttt {IsNonTrivial}, \hyperpage{418} 2492 \item \texttt {IsNormal}, \hyperpage{529} 2493 \item \texttt {IsNormalBasis}, \hyperpage{936} 2494 \item \texttt {IsNotIdenticalObj}, \hyperpage{162} 2495 \item \texttt {IsNumberField}, \hyperpage{922} 2496 \item \texttt {IsObject}, \hyperpage{160} 2497 \item \texttt {IsOddInt}, \hyperpage{190} 2498 \item isomorphic 2499 \subitem pc group, \hyperpage{692, 693} 2500 \item \texttt {IsomorphicSubgroups}, \hyperpage{602} 2501 \item \texttt {IsomorphismFpAlgebra}, \hyperpage{972} 2502 \item \texttt {IsomorphismFpGroup}, \hyperpage{714} 2503 \item \texttt{IsomorphismFpGroup} 2504 \subitem for subgroups of fp groups, \hyperpage{717} 2505 \item \texttt {IsomorphismFpGroupByGenerators}, \hyperpage{715} 2506 \item \texttt {IsomorphismFpGroupByGeneratorsNC}, \hyperpage{715} 2507 \item \texttt {IsomorphismFpGroupByPcgs}, \hyperpage{690} 2508 \item \texttt {IsomorphismFpMonoid}, \hyperpage{816} 2509 \item \texttt {IsomorphismFpSemigroup}, \hyperpage{816} 2510 \item \texttt {IsomorphismGroups}, \hyperpage{600} 2511 \item \texttt {IsomorphismMatrixAlgebra}, \hyperpage{972} 2512 \item \texttt {IsomorphismPartialPermMonoid}, \hyperpage{868} 2513 \item \texttt {IsomorphismPartialPermSemigroup}, \hyperpage{868} 2514 \item \texttt {IsomorphismPcGroup}, \hyperpage{693} 2515 \item \texttt {IsomorphismPermGroup}, \hyperpage{637} 2516 \subitem for Imf matrix groups, \hyperpage{787} 2517 \item \texttt {IsomorphismPermGroupImfGroup}, \hyperpage{788} 2518 \item \texttt {IsomorphismReesMatrixSemigroup}, \hyperpage{806} 2519 \item \texttt {IsomorphismReesZeroMatrixSemigroup}, \hyperpage{806} 2520 \item \texttt {IsomorphismRefinedPcGroup}, \hyperpage{692} 2521 \item \texttt{Isomorphism\mbox{\texttt{\mdseries\slshape Rep}}\mbox{\texttt{\mdseries\slshape Struct}}}, 2522 \hyperpage{431} 2523 \item isomorphisms 2524 \subitem find all, \hyperpage{600} 2525 \item \texttt {IsomorphismSCAlgebra} 2526 \subitem for an algebra, \hyperpage{973} 2527 \subitem w.r.t. a given basis, \hyperpage{973} 2528 \item \texttt {IsomorphismSimplifiedFpGroup}, \hyperpage{718} 2529 \item \texttt {IsomorphismSpecialPcGroup}, \hyperpage{694} 2530 \item \texttt {IsomorphismTransformationMonoid}, \hyperpage{842} 2531 \item \texttt {IsomorphismTransformationSemigroup}, \hyperpage{842} 2532 \item \texttt {Isomorphism}\discretionary {-}{}{}\texttt {Type}\discretionary {-}{}{}\texttt {Info}\discretionary {-}{}{}\texttt {Finite}\discretionary {-}{}{}\texttt {Simple}\discretionary {-}{}{}\texttt {Group} 2533 \subitem for a character table, \hyperpage{1111} 2534 \subitem for a group, \hyperpage{554} 2535 \subitem for a group order, \hyperpage{554} 2536 \item \texttt {IsOne}, \hyperpage{438} 2537 \item \texttt {IsOperation}, \hyperpage{1276} 2538 \item \texttt {IsOrdering}, \hyperpage{479} 2539 \item \texttt {IsOrderingOnFamilyOfAssocWords}, \hyperpage{482} 2540 \item \texttt {IsOrdinaryMatrix}, \hyperpage{333} 2541 \item \texttt {IsOrdinaryTable}, \hyperpage{1103} 2542 \item \texttt {IsOutputStream}, \hyperpage{143} 2543 \item \texttt {IsOutputTextNone}, \hyperpage{143} 2544 \item \texttt {IsOutputTextStream}, \hyperpage{143} 2545 \item \texttt {IsPackageLoaded}, \hyperpage{1241} 2546 \item \texttt {IsPackageMarkedForLoading}, \hyperpage{1241} 2547 \item \texttt{IsPackageMarkedForLoading}, \hyperpage{1259} 2548 \item \texttt {IsPadicExtensionNumber}, \hyperpage{1061} 2549 \item \texttt {IsPadicExtensionNumberFamily}, \hyperpage{1061} 2550 \item \texttt {IsParentPcgsFamilyPcgs}, \hyperpage{688} 2551 \item \texttt {IsPartialOrderBinaryRelation}, \hyperpage{472} 2552 \item \texttt {IsPartialPerm}, \hyperpage{847} 2553 \item \texttt {IsPartialPermCollection}, \hyperpage{847} 2554 \item \texttt {IsPartialPermMonoid}, \hyperpage{866} 2555 \item \texttt {IsPartialPermSemigroup}, \hyperpage{866} 2556 \item \texttt {IsPcGroup}, \hyperpage{689} 2557 \item \texttt {IsPcGroupGeneralMappingByImages}, \hyperpage{605} 2558 \item \texttt {IsPcGroupHomomorphismByImages}, \hyperpage{605} 2559 \item \texttt {IsPcgs}, \hyperpage{665} 2560 \item \texttt {IsPcgsCentralSeries}, \hyperpage{677} 2561 \item \texttt {IsPcgsChiefSeries}, \hyperpage{679} 2562 \item \texttt {IsPcgsElementaryAbelianSeries}, \hyperpage{676} 2563 \item \texttt {IsPcgsPCentralSeriesPGroup}, \hyperpage{678} 2564 \item \texttt {IsPerfect} 2565 \subitem for a character table, \hyperpage{1111} 2566 \item \texttt {IsPerfectGroup}, \hyperpage{552} 2567 \item \texttt {IsPerfectTom}, \hyperpage{1086} 2568 \item \texttt {IsPerm}, \hyperpage{630} 2569 \item \texttt {IsPermCollColl}, \hyperpage{630} 2570 \item \texttt {IsPermCollection}, \hyperpage{630} 2571 \item \texttt {IsPermGroup}, \hyperpage{636} 2572 \item \texttt {IsPermGroupGeneralMapping}, \hyperpage{604} 2573 \item \texttt {IsPermGroupGeneralMappingByImages}, \hyperpage{604} 2574 \item \texttt {IsPermGroupHomomorphism}, \hyperpage{604} 2575 \item \texttt {IsPermGroupHomomorphismByImages}, \hyperpage{604} 2576 \item \texttt {IsPGroup}, \hyperpage{557} 2577 \item \texttt {IsPInfinity}, \hyperpage{254} 2578 \item \texttt {IsPlistRep}, \hyperpage{313} 2579 \item \texttt {IsPNilpotent}, \hyperpage{558} 2580 \item \texttt {IsPolycyclicGroup}, \hyperpage{553} 2581 \item \texttt {IsPolynomial}, \hyperpage{1028} 2582 \item \texttt {IsPolynomialDefaultRep}, \hyperpage{1051} 2583 \item \texttt {IsPolynomialFunction}, \hyperpage{1027} 2584 \item \texttt {IsPolynomialFunctionsFamily}, \hyperpage{1049} 2585 \item \texttt {IsPolynomialRing}, \hyperpage{1041} 2586 \item \texttt {IsPosInt}, \hyperpage{189} 2587 \item \texttt {IsPositionalObjectRep}, \hyperpage{176} 2588 \item \texttt {IsPositiveIntegers}, \hyperpage{189} 2589 \item \texttt {IsPosRat}, \hyperpage{234} 2590 \item \texttt {IsPowerfulPGroup}, \hyperpage{557} 2591 \item \texttt {IsPreimages}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {As}\discretionary {-}{}{}\texttt {Group}\discretionary {-}{}{}\texttt {General}\discretionary {-}{}{}\texttt {Mapping}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Images}, 2592 \hyperpage{604} 2593 \item \texttt {IsPreOrderBinaryRelation}, \hyperpage{472} 2594 \item \texttt {IsPrime}, \hyperpage{887} 2595 \item \texttt {IsPrimeField}, \hyperpage{905} 2596 \item \texttt {IsPrimeInt}, \hyperpage{196} 2597 \item \texttt {IsPrimeOrdersPcgs}, \hyperpage{666} 2598 \item \texttt {IsPrimePowerInt}, \hyperpage{197} 2599 \item \texttt {IsPrimitive} 2600 \subitem for a group, an action domain, etc., \hyperpage{622} 2601 \subitem for a permutation group, \hyperpage{622} 2602 \subitem for an external set, \hyperpage{622} 2603 \item \texttt {IsPrimitiveCharacter}, \hyperpage{1230} 2604 \item \texttt {IsPrimitivePolynomial}, \hyperpage{1029} 2605 \item \texttt {IsPrimitiveRootMod}, \hyperpage{211} 2606 \item \texttt {IsProbablyPrimeInt}, \hyperpage{196} 2607 \item \texttt {IsProperty}, \hyperpage{184} 2608 \item \texttt {IsPseudoCanonicalBasisFullHomModule}, \hyperpage{945} 2609 \item \texttt {IsPSolubleCharacterTable}, \hyperpage{1125} 2610 \item \texttt {IsPSolubleCharacterTableOp}, \hyperpage{1125} 2611 \item \texttt {IsPSolvable}, \hyperpage{558} 2612 \item \texttt {IsPSolvableCharacterTable}, \hyperpage{1125} 2613 \item \texttt {IsPSolvableCharacterTableOp}, \hyperpage{1125} 2614 \item \texttt {IsPurePadicNumber}, \hyperpage{1059} 2615 \item \texttt {IsPurePadicNumberFamily}, \hyperpage{1059} 2616 \item \texttt {IsQuasiPrimitive}, \hyperpage{1230} 2617 \item \texttt {IsQuaternion}, \hyperpage{960} 2618 \item \texttt {IsQuaternionCollColl}, \hyperpage{960} 2619 \item \texttt {IsQuaternionCollection}, \hyperpage{960} 2620 \item \texttt {IsQuaternionGroup}, \hyperpage{763} 2621 \item \texttt {IsQuickPositionList}, \hyperpage{313} 2622 \item \texttt {IsQuotientSemigroup}, \hyperpage{800} 2623 \item \texttt {IsRandomSource}, \hyperpage{203} 2624 \item \texttt {IsRange}, \hyperpage{311} 2625 \item \texttt {IsRangeRep}, \hyperpage{312} 2626 \item \texttt {IsRat}, \hyperpage{234} 2627 \item \texttt {IsRationalFunction}, \hyperpage{1027} 2628 \item \texttt {IsRationalFunctionDefaultRep}, \hyperpage{1051} 2629 \item \texttt {IsRationalFunctionsFamily}, \hyperpage{1049} 2630 \item \texttt {IsRationalMatrixGroup}, \hyperpage{661} 2631 \item \texttt {IsRationals}, \hyperpage{233} 2632 \item \texttt {IsRationalsPolynomialRing}, \hyperpage{1041} 2633 \item \texttt {IsRDistributive}, \hyperpage{885} 2634 \item \texttt {IsReadableFile}, \hyperpage{137} 2635 \item \texttt {IsReadOnlyGlobal}, \hyperpage{51} 2636 \item \texttt {IsRecord}, \hyperpage{402} 2637 \item \texttt {IsRecordCollColl}, \hyperpage{402} 2638 \item \texttt {IsRecordCollection}, \hyperpage{402} 2639 \item \texttt {IsRectangularTable}, \hyperpage{265} 2640 \item \texttt {IsReduced}, \hyperpage{520} 2641 \item \texttt {IsReductionOrdering}, \hyperpage{482} 2642 \item \texttt {IsReesCongruence}, \hyperpage{800} 2643 \item \texttt {IsReesCongruenceSemigroup}, \hyperpage{798} 2644 \item \texttt {IsReesMatrixSemigroup}, \hyperpage{808} 2645 \item \texttt {IsReesMatrixSemigroupElement}, \hyperpage{807} 2646 \item \texttt {IsReesMatrixSubsemigroup}, \hyperpage{808} 2647 \item \texttt {IsReesZeroMatrixSemigroup}, \hyperpage{808} 2648 \item \texttt {IsReesZeroMatrixSemigroupElement}, \hyperpage{807} 2649 \item \texttt {IsReesZeroMatrixSubsemigroup}, \hyperpage{808} 2650 \item \texttt {IsReflexiveBinaryRelation}, \hyperpage{471} 2651 \item \texttt {IsRegular} 2652 \subitem for a group, an action domain, etc., \hyperpage{622} 2653 \subitem for a permutation group, \hyperpage{622} 2654 \subitem for an external set, \hyperpage{622} 2655 \item \texttt {IsRegularDClass}, \hyperpage{803} 2656 \item \texttt {IsRegularSemigroup}, \hyperpage{797} 2657 \item \texttt {IsRegularSemigroupElement}, \hyperpage{797} 2658 \item \texttt {IsRelativelySM} 2659 \subitem for a character, \hyperpage{1234} 2660 \subitem for a group, \hyperpage{1234} 2661 \item \texttt {IsRepresentation}, \hyperpage{177} 2662 \item \texttt {IsRestrictedJacobianElement}, \hyperpage{449} 2663 \item \texttt {IsRestrictedJacobianElementCollColl}, \hyperpage{449} 2664 \item \texttt {IsRestricted}\discretionary {-}{}{}\texttt {Jacobian}\discretionary {-}{}{}\texttt {Element}\discretionary {-}{}{}\texttt {Collection}, 2665 \hyperpage{449} 2666 \item \texttt {IsRestrictedLieAlgebra}, \hyperpage{1000} 2667 \item \texttt {IsRestrictedLieObject}, \hyperpage{986} 2668 \item \texttt {IsRestrictedLieObjectCollection}, \hyperpage{986} 2669 \item \texttt {IsRewritingSystem}, \hyperpage{519} 2670 \item \texttt {IsRightAlgebraModuleElement}, \hyperpage{976} 2671 \item \texttt {IsRight}\discretionary {-}{}{}\texttt {Algebra}\discretionary {-}{}{}\texttt {Module}\discretionary {-}{}{}\texttt {Element}\discretionary {-}{}{}\texttt {Collection}, 2672 \hyperpage{976} 2673 \item \texttt {IsRightCoset}, \hyperpage{538} 2674 \item \texttt {IsRightIdeal}, \hyperpage{880} 2675 \item \texttt {IsRightIdealInParent}, \hyperpage{880} 2676 \item \texttt {IsRightModule}, \hyperpage{897} 2677 \item \texttt {IsRightOperatorAdditiveGroup}, \hyperpage{897} 2678 \item \texttt {IsRightSemigroupIdeal}, \hyperpage{799} 2679 \item \texttt {IsRing}, \hyperpage{876} 2680 \item \texttt {IsRingElement}, \hyperpage{447} 2681 \item \texttt {IsRingElementWithInverse}, \hyperpage{448} 2682 \item \texttt {IsRingElementWithOne}, \hyperpage{448} 2683 \item \texttt {IsRingGeneralMapping}, \hyperpage{466} 2684 \item \texttt {IsRingHomomorphism}, \hyperpage{466} 2685 \item \texttt {IsRingWithOne}, \hyperpage{882} 2686 \item \texttt {IsRingWithOneGeneralMapping}, \hyperpage{466} 2687 \item \texttt {IsRingWithOneHomomorphism}, \hyperpage{466} 2688 \item \texttt {IsRootSystem}, \hyperpage{995} 2689 \item \texttt {IsRootSystemFromLieAlgebra}, \hyperpage{995} 2690 \item \texttt {IsRowModule}, \hyperpage{900} 2691 \item \texttt {IsRowSpace}, \hyperpage{939} 2692 \item \texttt {IsRowVector}, \hyperpage{322} 2693 \item \texttt {IsScalar}, \hyperpage{448} 2694 \item \texttt {IsSemiEchelonized}, \hyperpage{940} 2695 \item \texttt {IsSemigroup}, \hyperpage{789} 2696 \item \texttt {IsSemigroupCongruence}, \hyperpage{800} 2697 \item \texttt {IsSemigroupIdeal}, \hyperpage{799} 2698 \item \texttt {IsSemiRegular} 2699 \subitem for a group, an action domain, etc., \hyperpage{621} 2700 \subitem for a permutation group, \hyperpage{621} 2701 \subitem for an external set, \hyperpage{621} 2702 \item \texttt {IsSet}, \hyperpage{292} 2703 \item \texttt {IsShortLexLessThanOrEqual}, \hyperpage{505} 2704 \item \texttt {IsShortLexOrdering}, \hyperpage{483} 2705 \item \texttt {IsSimple} 2706 \subitem for a character table, \hyperpage{1111} 2707 \item \texttt {IsSimpleAlgebra}, \hyperpage{960} 2708 \item \texttt {IsSimpleGroup}, \hyperpage{553} 2709 \item \texttt {IsSimpleSemigroup}, \hyperpage{798} 2710 \item \texttt {IsSingleValued}, \hyperpage{456} 2711 \item \texttt {IsSL}, \hyperpage{658} 2712 \item \texttt {IsSolvable} 2713 \subitem for a character table, \hyperpage{1111} 2714 \item \texttt {IsSolvableGroup}, \hyperpage{552} 2715 \item \texttt {IsSolvableTom}, \hyperpage{1086} 2716 \item \texttt {IsSortedList}, \hyperpage{292} 2717 \item \texttt {IsSpecialLinearGroup}, \hyperpage{658} 2718 \item \texttt {IsSpecialPcgs}, \hyperpage{682} 2719 \item \texttt {IsSPGeneralMapping}, \hyperpage{468} 2720 \item \texttt {IsSporadicSimple} 2721 \subitem for a character table, \hyperpage{1111} 2722 \item \texttt {IsSSortedList}, \hyperpage{292} 2723 \item \texttt {IsStandardIterator}, \hyperpage{424} 2724 \item \texttt {IsStraightLineProgElm}, \hyperpage{517} 2725 \item \texttt {IsStraightLineProgram}, \hyperpage{512} 2726 \item \texttt {IsStream}, \hyperpage{142} 2727 \item \texttt {IsString}, \hyperpage{375} 2728 \item \texttt {IsStringRep}, \hyperpage{379} 2729 \item \texttt{Is\mbox{\texttt{\mdseries\slshape Struct}}}, 2730 \hyperpage{432} 2731 \item \texttt {IsSubgroup}, \hyperpage{529} 2732 \item \texttt {IsSubgroupFpGroup}, \hyperpage{701} 2733 \item \texttt {IsSubgroupOfWholeGroupByQuotientRep}, \hyperpage{719} 2734 \item \texttt {IsSubgroupSL}, \hyperpage{658} 2735 \item \texttt {IsSubmonoidFpMonoid}, \hyperpage{814} 2736 \item \texttt {IsSubnormal}, \hyperpage{530} 2737 \item \texttt {IsSubnormallyMonomial} 2738 \subitem for a character, \hyperpage{1234} 2739 \subitem for a group, \hyperpage{1233} 2740 \item \texttt {IsSubsemigroup}, \hyperpage{790} 2741 \item \texttt {IsSubsemigroupFpSemigroup}, \hyperpage{814} 2742 \item \texttt {IsSubset}, \hyperpage{420} 2743 \subitem for interval floats, \hyperpage{258} 2744 \item \texttt {IsSubsetBlist}, \hyperpage{317} 2745 \item \texttt {IsSubsetLocallyFiniteGroup}, \hyperpage{557} 2746 \item \texttt {IsSubsetSet}, \hyperpage{296} 2747 \item \texttt {IsSubspacesVectorSpace}, \hyperpage{931} 2748 \item \texttt{IsSub\mbox{\texttt{\mdseries\slshape struct}}}, 2749 \hyperpage{434} 2750 \item \texttt {IsSupersolvable} 2751 \subitem for a character table, \hyperpage{1111} 2752 \item \texttt{IsSupersolvable} 2753 \subitem for groups with pcgs, \hyperpage{685} 2754 \item \texttt {IsSupersolvableGroup}, \hyperpage{553} 2755 \item \texttt {IsSurjective}, \hyperpage{456} 2756 \item \texttt {IsSyllableAssocWordRep}, \hyperpage{510} 2757 \item \texttt {IsSyllableWordsFamily}, \hyperpage{510} 2758 \item \texttt {IsSymmetricBinaryRelation}, \hyperpage{471} 2759 \item \texttt {IsSymmetricGroup}, \hyperpage{639} 2760 \item \texttt {IsSymmetricInverseMonoid}, \hyperpage{867} 2761 \item \texttt {IsSymmetricInverseSemigroup}, \hyperpage{867} 2762 \item \texttt {IsTable}, \hyperpage{264} 2763 \item \texttt {IsTableOfMarks}, \hyperpage{1080} 2764 \item \texttt {IsTableOfMarksWithGens}, \hyperpage{1092} 2765 \item \texttt {IsToPcGroupGeneralMappingByImages}, \hyperpage{605} 2766 \item \texttt {IsToPcGroupHomomorphismByImages}, \hyperpage{605} 2767 \item \texttt {IsToPermGroupGeneralMappingByImages}, \hyperpage{604} 2768 \item \texttt {IsToPermGroupHomomorphismByImages}, \hyperpage{604} 2769 \item \texttt {IsTotal}, \hyperpage{456} 2770 \item \texttt {IsTotalOrdering}, \hyperpage{480} 2771 \item \texttt {IsTransformation}, \hyperpage{822} 2772 \item \texttt {IsTransformationCollection}, \hyperpage{822} 2773 \item \texttt {IsTransformationMonoid}, \hyperpage{841} 2774 \item \texttt {IsTransformationSemigroup}, \hyperpage{841} 2775 \item \texttt {IsTransitive} 2776 \subitem for a character, \hyperpage{1171} 2777 \subitem for a group, an action domain, etc., \hyperpage{620} 2778 \subitem for a permutation group, \hyperpage{620} 2779 \subitem for an external set, \hyperpage{621} 2780 \item \texttt {IsTransitiveBinaryRelation}, \hyperpage{472} 2781 \item \texttt {IsTranslationInvariantOrdering}, \hyperpage{482} 2782 \item \texttt {IsTrivial}, \hyperpage{418} 2783 \item \texttt {IsTwoSidedIdeal}, \hyperpage{880} 2784 \item \texttt {IsTwoSidedIdealInParent}, \hyperpage{880} 2785 \item \texttt {IsUEALatticeElement}, \hyperpage{1011} 2786 \item \texttt {IsUEALatticeElementCollection}, \hyperpage{1011} 2787 \item \texttt {IsUEALatticeElementFamily}, \hyperpage{1011} 2788 \item \texttt {IsUniqueFactorizationRing}, \hyperpage{884} 2789 \item \texttt {IsUnit}, \hyperpage{886} 2790 \item \texttt {IsUnivariatePolynomial}, \hyperpage{1029} 2791 \item \texttt {IsUnivariatePolynomialRing}, \hyperpage{1042} 2792 \item \texttt {IsUnivariateRationalFunction}, \hyperpage{1028} 2793 \item \texttt {IsUnknown}, \hyperpage{1225} 2794 \item \texttt {IsUpperAlphaChar}, \hyperpage{381} 2795 \item \texttt {IsUpperTriangularMat}, \hyperpage{338} 2796 \item \texttt {IsUpperTriangularMatrix}, \hyperpage{338} 2797 \item \texttt {IsValidIdentifier}, \hyperpage{48} 2798 \item \texttt {IsVector}, \hyperpage{447} 2799 \item \texttt {IsVectorSpace}, \hyperpage{928} 2800 \item \texttt {IsVirtualCharacter}, \hyperpage{1167} 2801 \item \texttt {IsWeightLexOrdering}, \hyperpage{484} 2802 \item \texttt {IsWeightRepElement}, \hyperpage{1012} 2803 \item \texttt {IsWeightRepElementCollection}, \hyperpage{1012} 2804 \item \texttt {IsWeightRepElementFamily}, \hyperpage{1012} 2805 \item \texttt {IsWellFoundedOrdering}, \hyperpage{480} 2806 \item \texttt {IsWeylGroup}, \hyperpage{997} 2807 \item \texttt {IsWholeFamily}, \hyperpage{418} 2808 \item \texttt {IsWLetterAssocWordRep}, \hyperpage{509} 2809 \item \texttt {IsWLetterWordsFamily}, \hyperpage{509} 2810 \item \texttt {IsWord}, \hyperpage{496} 2811 \item \texttt {IsWordCollection}, \hyperpage{497} 2812 \item \texttt {IsWordWithInverse}, \hyperpage{496} 2813 \item \texttt {IsWordWithOne}, \hyperpage{496} 2814 \item \texttt {IsWreathProductOrdering}, \hyperpage{485} 2815 \item \texttt {IsWritableFile}, \hyperpage{138} 2816 \item \texttt {IsXInfinity}, \hyperpage{254} 2817 \item \texttt {IsZero}, \hyperpage{438} 2818 \item \texttt {IsZeroGroup}, \hyperpage{798} 2819 \item \texttt {IsZeroSimpleSemigroup}, \hyperpage{798} 2820 \item \texttt {IsZeroSquaredElement}, \hyperpage{450} 2821 \item \texttt {IsZeroSquaredElementCollColl}, \hyperpage{450} 2822 \item \texttt {IsZeroSquaredElementCollection}, \hyperpage{450} 2823 \item \texttt {IsZeroSquaredRing}, \hyperpage{885} 2824 \item \texttt {IsZmodnZObj}, \hyperpage{201} 2825 \item \texttt {IsZmodnZObjNonprime}, \hyperpage{201} 2826 \item \texttt {IsZmodpZObj}, \hyperpage{201} 2827 \item \texttt {IsZmodpZObjLarge}, \hyperpage{202} 2828 \item \texttt {IsZmodpZObjSmall}, \hyperpage{201} 2829 \item \texttt {Iterated}, \hyperpage{308} 2830 \item \texttt {Iterator}, \hyperpage{424} 2831 \item iterator 2832 \subitem for low index subgroups, \hyperpage{713} 2833 \item \texttt {IteratorByBasis}, \hyperpage{935} 2834 \item \texttt {IteratorByFunctions}, \hyperpage{426} 2835 \item \texttt {IteratorList}, \hyperpage{426} 2836 \item \texttt {IteratorOfCartesianProduct} 2837 \subitem for a list of lists, \hyperpage{304} 2838 \subitem for several lists, \hyperpage{304} 2839 \item \texttt {IteratorOfCombinations}, \hyperpage{221} 2840 \item \texttt {IteratorOfPartitions}, \hyperpage{227} 2841 \item \texttt {IteratorOfTuples}, \hyperpage{224} 2842 \item \texttt {IteratorSorted}, \hyperpage{425} 2843 \item \texttt {IteratorStabChain}, \hyperpage{649} 2844 2845 \indexspace 2846 2847 \item $j_N$ (irrational value), \hyperpage{244} 2848 \item \texttt {Jacobi}, \hyperpage{211} 2849 \item \texttt {JenningsLieAlgebra}, \hyperpage{1001} 2850 \item \texttt {JenningsSeries}, \hyperpage{563} 2851 \item \texttt {JoinEquivalenceRelations}, \hyperpage{477} 2852 \item \texttt {JoinOfIdempotentPartialPermsNC}, \hyperpage{849} 2853 \item \texttt {JoinOfPartialPerms}, \hyperpage{849} 2854 \item \texttt {JoinStringsWithSeparator}, \hyperpage{387} 2855 \item \texttt {JordanDecomposition}, \hyperpage{352} 2856 2857 \indexspace 2858 2859 \item $k_N$ (irrational value), \hyperpage{244} 2860 \item \texttt {KappaPerp}, \hyperpage{1003} 2861 \item \texttt {KB{\textunderscore }REW}, \hyperpage{819} 2862 \item kernel 2863 \subitem group homomorphism, \hyperpage{592} 2864 \subitem of a matrix, \hyperpage{343} 2865 \item \texttt {KernelOfAdditiveGeneralMapping}, \hyperpage{465} 2866 \item \texttt {KernelOfCharacter}, \hyperpage{1169} 2867 \item \texttt {Kernel}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Multiplicative}\discretionary {-}{}{}\texttt {General}\discretionary {-}{}{}\texttt {Mapping}, 2868 \hyperpage{463} 2869 \item \texttt {KernelOfTransformation}, \hyperpage{835} 2870 \item \texttt {KeyDependentOperation}, \hyperpage{1351} 2871 \item \texttt {KillingMatrix}, \hyperpage{1003} 2872 \item \texttt {KnownAttributesOfObject}, \hyperpage{178} 2873 \item \texttt {KnownPropertiesOfObject}, \hyperpage{184} 2874 \item \texttt {KnownTruePropertiesOfObject}, \hyperpage{184} 2875 \item \texttt {KnowsDictionary}, \hyperpage{399} 2876 \item \texttt {KnowsHowToDecompose}, \hyperpage{587} 2877 \item \texttt {KnuthBendixRewritingSystem} 2878 \subitem for a monoid and a reduction ordering, \hyperpage{819} 2879 \subitem for a semigroup and a reduction ordering, \hyperpage{819} 2880 \item Krasner-Kaloujnine theorem, \hyperpage{758} 2881 \item \texttt {KroneckerProduct}, \hyperpage{340} 2882 \item \texttt {KuKGenerators}, \hyperpage{758} 2883 2884 \indexspace 2885 2886 \item $l_N$ (irrational value), \hyperpage{244} 2887 \item \texttt {Lambda}, \hyperpage{209} 2888 \item larger or equal, \hyperpage{56} 2889 \item larger test, \hyperpage{56} 2890 \item \texttt {Larger}\discretionary {-}{}{}\texttt {Quotient}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Subgroup}\discretionary {-}{}{}\texttt {Abelianization}, 2891 \hyperpage{722} 2892 \item \texttt {LargestElementGroup}, \hyperpage{577} 2893 \item \texttt {LargestElementStabChain}, \hyperpage{649} 2894 \item \texttt {LargestImageOfMovedPoint} 2895 \subitem for a partial permutation, \hyperpage{856} 2896 \subitem for a partial permutation coll, \hyperpage{856} 2897 \subitem for a transformation, \hyperpage{834} 2898 \subitem for a transformation coll, \hyperpage{834} 2899 \item \texttt {LargestMovedPoint} 2900 \subitem for a list or collection of permutations, \hyperpage{632} 2901 \subitem for a partial perm, \hyperpage{855} 2902 \subitem for a partial perm coll, \hyperpage{855} 2903 \subitem for a permutation, \hyperpage{632} 2904 \subitem for a transformation, \hyperpage{833} 2905 \subitem for a transformation coll, \hyperpage{833} 2906 \item \texttt {LargestUnknown}, \hyperpage{1225} 2907 \item \texttt{last}, \hyperpage{80} 2908 \item \texttt{last2}, \hyperpage{80} 2909 \item \texttt{last3}, \hyperpage{80} 2910 \item \texttt {LastSystemError}, \hyperpage{133} 2911 \item LaTeX 2912 \subitem for a decomposition matrix, \hyperpage{1123} 2913 \subitem for GAP objects, \hyperpage{395} 2914 \subitem for permutation characters, \hyperpage{1188} 2915 \subitem for the result of a straight line program, \hyperpage{514} 2916 \item \texttt {LaTeXStringDecompositionMatrix}, \hyperpage{1123} 2917 \item lattice base reduction, \hyperpage{367, 368} 2918 \item lattice basis reduction 2919 \subitem for virtual characters, \hyperpage{1176} 2920 \item \texttt {LatticeByCyclicExtension}, \hyperpage{573} 2921 \item \texttt {LatticeGeneratorsInUEA}, \hyperpage{1011} 2922 \item \texttt {LatticeSubgroups}, \hyperpage{569} 2923 \item \texttt {LatticeSubgroupsByTom}, \hyperpage{1077} 2924 \item \texttt {LaurentPolynomialByCoefficients}, \hyperpage{1038} 2925 \item \texttt {LaurentPolynomialByExtRep}, \hyperpage{1053} 2926 \item \texttt {LaurentPolynomialByExtRepNC}, \hyperpage{1053} 2927 \item \texttt {LClassOfHClass}, \hyperpage{802} 2928 \item \texttt {Lcm} 2929 \subitem for (a ring and) a list of elements, \hyperpage{891} 2930 \subitem for (a ring and) several elements, \hyperpage{891} 2931 \item \texttt {LcmInt}, \hyperpage{194} 2932 \item \texttt {LcmOp}, \hyperpage{891} 2933 \item \texttt {LdExp}, \hyperpage{255} 2934 \item \texttt {LeadCoeffsIGS}, \hyperpage{672} 2935 \item \texttt {LeadingCoefficient}, \hyperpage{1033} 2936 \item \texttt {LeadingCoefficientOfPolynomial}, \hyperpage{1044} 2937 \item \texttt {LeadingExponentOfPcElement}, \hyperpage{668} 2938 \item \texttt {LeadingMonomial}, \hyperpage{1033} 2939 \item \texttt {LeadingMonomialOfPolynomial}, \hyperpage{1043} 2940 \item \texttt {LeadingTermOfPolynomial}, \hyperpage{1044} 2941 \item left cosets, \hyperpage{538} 2942 \item \texttt {LeftActingAlgebra}, \hyperpage{977} 2943 \item \texttt {LeftActingDomain}, \hyperpage{898} 2944 \item \texttt {LeftActingRingOfIdeal}, \hyperpage{882} 2945 \item \texttt {LeftAlgebraModule}, \hyperpage{975} 2946 \item \texttt {LeftAlgebraModuleByGenerators}, \hyperpage{974} 2947 \item \texttt {LeftDerivations}, \hyperpage{989} 2948 \item \texttt {LeftIdeal}, \hyperpage{879} 2949 \item \texttt {LeftIdealByGenerators}, \hyperpage{881} 2950 \item \texttt {LeftIdealNC}, \hyperpage{880} 2951 \item \texttt {LeftModuleByGenerators}, \hyperpage{898} 2952 \item \texttt {LeftModuleByHomomorphismToMatAlg}, \hyperpage{979} 2953 \item \texttt {LeftModuleGeneralMappingByImages}, \hyperpage{942} 2954 \item \texttt {LeftModuleHomomorphismByImages}, \hyperpage{943} 2955 \item \texttt {LeftModuleHomomorphismByImagesNC}, \hyperpage{943} 2956 \item \texttt {LeftModuleHomomorphismByMatrix}, \hyperpage{943} 2957 \item \texttt {LeftOne} 2958 \subitem for a partial perm, \hyperpage{858} 2959 \subitem for a transformation, \hyperpage{838} 2960 \item \texttt {LeftQuotient}, \hyperpage{441} 2961 \item \texttt{LeftQuotient} 2962 \subitem for words, \hyperpage{505} 2963 \item \texttt {LeftShiftRowVector}, \hyperpage{327} 2964 \item legacy, \hyperpage{1272} 2965 \item \texttt {Legendre}, \hyperpage{212} 2966 \item \texttt {Length}, \hyperpage{293} 2967 \subitem for a associative word, \hyperpage{506} 2968 \item length 2969 \subitem of a word, \hyperpage{506} 2970 \item \texttt {LengthsTom}, \hyperpage{1082} 2971 \item \texttt {LengthWPObj}, \hyperpage{1358} 2972 \item \texttt {LenstraBase}, \hyperpage{925} 2973 \item \texttt {LessThanFunction}, \hyperpage{481} 2974 \item \texttt {LessThanOrEqualFunction}, \hyperpage{481} 2975 \item \texttt {LetterRepAssocWord}, \hyperpage{510} 2976 \item \texttt {LevelsOfGenerators}, \hyperpage{485} 2977 \item \texttt {LeviMalcevDecomposition} 2978 \subitem for Lie algebras, \hyperpage{967} 2979 \item \texttt {LexicographicOrdering}, \hyperpage{482} 2980 \item \texttt {LGFirst}, \hyperpage{682} 2981 \item \texttt {LGLayers}, \hyperpage{682} 2982 \item \texttt {LGLength}, \hyperpage{682} 2983 \item \texttt {LGWeights}, \hyperpage{682} 2984 \item library tables, \hyperpage{1100} 2985 \item \texttt {LieAlgebra} 2986 \subitem for an associative algebra, \hyperpage{988} 2987 \subitem for field and generators, \hyperpage{988} 2988 \item \texttt {LieAlgebraByStructureConstants}, \hyperpage{987} 2989 \item \texttt {LieBracket}, \hyperpage{441} 2990 \item \texttt {LieCenter}, \hyperpage{991} 2991 \item \texttt {LieCentralizer}, \hyperpage{991} 2992 \item \texttt {LieCentre}, \hyperpage{991} 2993 \item \texttt {LieCoboundaryOperator}, \hyperpage{1008} 2994 \item \texttt {LieDerivedSeries}, \hyperpage{992} 2995 \item \texttt {LieDerivedSubalgebra}, \hyperpage{991} 2996 \item \texttt {LieFamily}, \hyperpage{986} 2997 \item \texttt {LieLowerCentralSeries}, \hyperpage{993} 2998 \item \texttt {LieNilRadical}, \hyperpage{992} 2999 \item \texttt {LieNormalizer}, \hyperpage{991} 3000 \item \texttt {LieObject}, \hyperpage{986} 3001 \item \texttt {LieSolvableRadical}, \hyperpage{992} 3002 \item \texttt {LieUpperCentralSeries}, \hyperpage{993} 3003 \item \texttt {LiftedInducedPcgs}, \hyperpage{676} 3004 \item \texttt {LiftedPcElement}, \hyperpage{676} 3005 \item \texttt {LinearAction}, \hyperpage{684} 3006 \item \texttt {LinearActionLayer}, \hyperpage{684} 3007 \item \texttt {LinearCharacters} 3008 \subitem for a character table, \hyperpage{1110} 3009 \subitem for a group, \hyperpage{1110} 3010 \item \texttt {LinearCombination}, \hyperpage{934} 3011 \item \texttt {LinearCombinationPcgs}, \hyperpage{668} 3012 \item \texttt {LinearIndependentColumns}, \hyperpage{366} 3013 \item \texttt {LinearOperation}, \hyperpage{684} 3014 \item \texttt {LinearOperationLayer}, \hyperpage{684} 3015 \item \texttt {LinesOfStraightLineProgram}, \hyperpage{512} 3016 \item \texttt {List} 3017 \subitem for a collection, \hyperpage{414} 3018 \subitem for a list (and a function), \hyperpage{304} 3019 \item list 3020 \subitem sorted, \hyperpage{292} 3021 \item list and non-list 3022 \subitem difference, \hyperpage{281} 3023 \subitem left quotient, \hyperpage{284} 3024 \subitem mod, \hyperpage{284} 3025 \subitem product, \hyperpage{282} 3026 \subitem quotient, \hyperpage{283} 3027 \item list assignment 3028 \subitem operation, \hyperpage{265} 3029 \item list boundedness test 3030 \subitem operation, \hyperpage{265} 3031 \item list element 3032 \subitem access, \hyperpage{266} 3033 \subitem assignment, \hyperpage{267} 3034 \subitem operation, \hyperpage{265} 3035 \item list equal 3036 \subitem comparison, \hyperpage{276} 3037 \item list of available books, \hyperpage{29} 3038 \item list smaller 3039 \subitem comparison, \hyperpage{277} 3040 \item list unbind 3041 \subitem operation, \hyperpage{265} 3042 \item \texttt {ListBlist}, \hyperpage{316} 3043 \item \texttt {ListN}, \hyperpage{308} 3044 \item \texttt {ListOfDigits}, \hyperpage{192} 3045 \item \texttt {ListOp} 3046 \subitem for IsVectorObj, IsFunction, \hyperpage{372} 3047 \item \texttt {ListPerm}, \hyperpage{633} 3048 \item \texttt {ListStabChain}, \hyperpage{648} 3049 \item \texttt {ListTransformation}, \hyperpage{831} 3050 \item \texttt {ListWithIdenticalEntries}, \hyperpage{285} 3051 \item \texttt {ListX}, \hyperpage{308} 3052 \item \texttt {LLL}, \hyperpage{1176} 3053 \item LLL algorithm 3054 \subitem for Gram matrices, \hyperpage{368} 3055 \subitem for vectors, \hyperpage{367} 3056 \subitem for virtual characters, \hyperpage{1176} 3057 \item \texttt {LLLReducedBasis}, \hyperpage{367} 3058 \item \texttt {LLLReducedGramMat}, \hyperpage{368} 3059 \item \texttt {LoadAllPackages}, \hyperpage{1266} 3060 \item \texttt {LoadDynamicModule}, \hyperpage{1244} 3061 \item \texttt {LoadPackage}, \hyperpage{1237} 3062 \item \texttt{local}, \hyperpage{65} 3063 \item local namespace 3064 \subitem for a GAP package, \hyperpage{1255} 3065 \item \texttt {LocationFunc}, \hyperpage{72} 3066 \item \texttt {Log}, \hyperpage{255} 3067 \item \texttt {Log10}, \hyperpage{255} 3068 \item \texttt {Log1p}, \hyperpage{255} 3069 \item \texttt {Log2}, \hyperpage{255} 3070 \item logarithm 3071 \subitem discrete, \hyperpage{210} 3072 \subitem of a root of unity, \hyperpage{240} 3073 \item \texttt {LogFFE}, \hyperpage{913} 3074 \item logical, \hyperpage{259} 3075 \item Logical conjunction, \hyperpage{261} 3076 \item Logical disjunction, \hyperpage{260} 3077 \item Logical negation, \hyperpage{261} 3078 \item logical operations, \hyperpage{260} 3079 \item \texttt {LogInt}, \hyperpage{191} 3080 \item \texttt {LogMod}, \hyperpage{210} 3081 \item \texttt {LogModShanks}, \hyperpage{210} 3082 \item \texttt {LogPackageLoadingMessage}, \hyperpage{1239} 3083 \item \texttt{LogPackageLoadingMessage}, \hyperpage{1261} 3084 \item \texttt {LogTo} 3085 \subitem for a filename, \hyperpage{140} 3086 \subitem for streams, \hyperpage{148} 3087 \subitem stop logging, \hyperpage{140} 3088 \item \texttt {LongestWeylWordPerm}, \hyperpage{999} 3089 \item \texttt {LookupDictionary}, \hyperpage{399} 3090 \item loop 3091 \subitem for, \hyperpage{62} 3092 \subitem read eval print, \hyperpage{80} 3093 \subitem repeat, \hyperpage{62} 3094 \subitem while, \hyperpage{61} 3095 \item loop over iterator, \hyperpage{63} 3096 \item loop over object, \hyperpage{64} 3097 \item loop over range, \hyperpage{63} 3098 \item loops 3099 \subitem leaving, \hyperpage{64} 3100 \subitem restarting, \hyperpage{64} 3101 \item \texttt {LowercaseChar}, \hyperpage{385} 3102 \item \texttt {LowercaseString}, \hyperpage{384} 3103 \item \texttt {LowerCentralSeriesOfGroup}, \hyperpage{562} 3104 \item \texttt {LowIndexSubgroups}, \hyperpage{567} 3105 \item \texttt {LowIndexSubgroupsFpGroup}, \hyperpage{713} 3106 \item \texttt {LowIndexSubgroupsFpGroupIterator}, \hyperpage{713} 3107 \item \texttt {LowLayerSubgroups}, \hyperpage{571} 3108 \item \texttt{LQUO} 3109 \subitem for a permutation and transformation, \hyperpage{829} 3110 \subitem for a permutation or partial permutation and partial permutation, 3111 \hyperpage{861} 3112 \item \texttt {Lucas}, \hyperpage{231} 3113 3114 \indexspace 3115 3116 \item $m_N$ (irrational value), \hyperpage{244} 3117 \item \texttt {Magma}, \hyperpage{487} 3118 \item \texttt {MagmaByGenerators}, \hyperpage{488} 3119 \item \texttt {MagmaByMultiplicationTable}, \hyperpage{490} 3120 \item \texttt {MagmaElement}, \hyperpage{491} 3121 \item \texttt {MagmaHomomorphismByFunctionNC}, \hyperpage{462} 3122 \item \texttt {MagmaRingModuloSpanOfZero}, \hyperpage{1020} 3123 \item \texttt {MagmaWithInverses}, \hyperpage{488} 3124 \item \texttt {MagmaWithInversesByGenerators}, \hyperpage{488} 3125 \item \texttt {Magma}\discretionary {-}{}{}\texttt {With}\discretionary {-}{}{}\texttt {Inverses}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Multiplication}\discretionary {-}{}{}\texttt {Table}, 3126 \hyperpage{491} 3127 \item \texttt {MagmaWithOne}, \hyperpage{487} 3128 \item \texttt {MagmaWithOneByGenerators}, \hyperpage{488} 3129 \item \texttt {MagmaWithOneByMultiplicationTable}, \hyperpage{491} 3130 \item \texttt {MagmaWithZeroAdjoined}, \hyperpage{489} 3131 \item \texttt {MakeBitfields}, \hyperpage{206} 3132 \item \texttt {MakeConfluent}, \hyperpage{521} 3133 \item \texttt {MakeConstantGlobal}, \hyperpage{52} 3134 \item \texttt {MakeFloat}, \hyperpage{252} 3135 \item \texttt {MakeImmutable}, \hyperpage{164} 3136 \item \texttt {MakeReadOnlyGlobal}, \hyperpage{51} 3137 \item \texttt {MakeReadWriteGlobal}, \hyperpage{51} 3138 \item map 3139 \subitem parametrized, \hyperpage{1208} 3140 \item \texttt {MappedWord}, \hyperpage{499} 3141 \item \texttt {MappingByFunction} 3142 \subitem by function (and inverse function) between two domains, 3143 \hyperpage{453} 3144 \subitem by function and function that computes one preimage, 3145 \hyperpage{453} 3146 \item \texttt {MappingGeneratorsImages}, \hyperpage{604} 3147 \item \texttt {MappingPermListList}, \hyperpage{634} 3148 \item maps, \hyperpage{1197} 3149 \item \texttt {MarksTom}, \hyperpage{1081} 3150 \item \texttt {MatAlgebra}, \hyperpage{956} 3151 \item \texttt {MatClassMultCoeffsCharTable}, \hyperpage{1127} 3152 \item \texttt {MathieuGroup}, \hyperpage{765} 3153 \item \texttt {MatLieAlgebra}, \hyperpage{989} 3154 \item matrices 3155 \subitem commutator, \hyperpage{335} 3156 \item \texttt {Matrix}, \hyperpage{809} 3157 \item matrix automorphisms, \hyperpage{1201} 3158 \item matrix spaces, \hyperpage{939} 3159 \item \texttt {MatrixAlgebra}, \hyperpage{955} 3160 \item \texttt {MatrixAutomorphisms}, \hyperpage{1150} 3161 \item \texttt {MatrixByBlockMatrix}, \hyperpage{358} 3162 \item \texttt {MatrixLieAlgebra}, \hyperpage{989} 3163 \item \texttt {MatrixOfAction}, \hyperpage{978} 3164 \item \texttt {MatScalarProducts}, \hyperpage{1168} 3165 \item \texttt {MatTom}, \hyperpage{1084} 3166 \item \texttt {MaximalAbelianQuotient}, \hyperpage{565} 3167 \item \texttt {MaximalBlocks} 3168 \subitem for a group, an action domain, etc., \hyperpage{623} 3169 \subitem for an external set, \hyperpage{623} 3170 \item \texttt {MaximalNormalSubgroups}, \hyperpage{568} 3171 \item \texttt {MaximalSubgroupClassReps}, \hyperpage{567} 3172 \item \texttt {MaximalSubgroups}, \hyperpage{568} 3173 \item \texttt{MaximalSubgroups} 3174 \subitem for groups with pcgs, \hyperpage{685} 3175 \item \texttt {MaximalSubgroupsLattice}, \hyperpage{570} 3176 \item \texttt {MaximalSubgroupsTom}, \hyperpage{1090} 3177 \item \texttt {Maximum} 3178 \subitem for a list, \hyperpage{302} 3179 \subitem for various objects, \hyperpage{302} 3180 \item \texttt {MaximumList}, \hyperpage{303} 3181 \item meet strategy, \hyperpage{1368} 3182 \item \texttt {MeetEquivalenceRelations}, \hyperpage{477} 3183 \item \texttt {MeetMaps}, \hyperpage{1212} 3184 \item \texttt {MeetOfPartialPerms}, \hyperpage{850} 3185 \item \texttt {MemoizePosIntFunction}, \hyperpage{74} 3186 \item \texttt{memory{\textunderscore}allocated}, \hyperpage{80} 3187 \item \texttt {MemoryUsage}, \hyperpage{167} 3188 \item \texttt {memory{\textunderscore }allocated}, \hyperpage{113} 3189 \item method, \hyperpage{1276} 3190 \item \texttt {MicroSleep}, \hyperpage{112} 3191 \item \texttt {Mid}, \hyperpage{257} 3192 \item \texttt {MinimalElementCosetStabChain}, \hyperpage{649} 3193 \item \texttt {MinimalFaithfulPermutationDegree}, \hyperpage{572} 3194 \item \texttt {MinimalGeneratingSet}, \hyperpage{577} 3195 \item \texttt{MinimalGeneratingSet} 3196 \subitem for groups with pcgs, \hyperpage{685} 3197 \item \texttt {MinimalNonmonomialGroup}, \hyperpage{1235} 3198 \item \texttt {MinimalNormalSubgroups}, \hyperpage{569} 3199 \item \texttt {MinimalPolynomial}, \hyperpage{1035} 3200 \subitem over a field, \hyperpage{907} 3201 \item \texttt{MinimalPolynomial} 3202 \subitem over a ring, \hyperpage{1035} 3203 \item \texttt {MinimalStabChain}, \hyperpage{646} 3204 \item \texttt {MinimalSupergroupsLattice}, \hyperpage{571} 3205 \item \texttt {MinimalSupergroupsTom}, \hyperpage{1091} 3206 \item \texttt {MinimizedBombieriNorm}, \hyperpage{1038} 3207 \item \texttt {Minimum} 3208 \subitem for a list, \hyperpage{302} 3209 \subitem for various objects, \hyperpage{302} 3210 \item \texttt {MinimumList}, \hyperpage{303} 3211 \item \texttt {MinusCharacter}, \hyperpage{1219} 3212 \item mod 3213 \subitem Integers, \hyperpage{201} 3214 \subitem Laurent polynomials, \hyperpage{1025} 3215 \subitem lists, \hyperpage{284} 3216 \subitem rationals, \hyperpage{57} 3217 \item \texttt{mod}, \hyperpage{57} 3218 \subitem arithmetic operators, \hyperpage{57} 3219 \subitem for character tables, \hyperpage{1108} 3220 \subitem residue class rings, \hyperpage{200} 3221 \item modular inverse, \hyperpage{57} 3222 \item modular remainder, \hyperpage{57} 3223 \item modular roots, \hyperpage{213} 3224 \item \texttt {ModuleByRestriction}, \hyperpage{980} 3225 \item \texttt {ModuleOfExtension}, \hyperpage{696} 3226 \item modulo, \hyperpage{57} 3227 \subitem arithmetic operators, \hyperpage{57} 3228 \subitem residue class rings, \hyperpage{200} 3229 \item \texttt {ModuloPcgs}, \hyperpage{673} 3230 \item \texttt {MoebiusMu}, \hyperpage{215} 3231 \item \texttt {MoebiusTom}, \hyperpage{1085} 3232 \item \texttt {MolienSeries}, \hyperpage{1185} 3233 \item \texttt {MolienSeriesInfo}, \hyperpage{1185} 3234 \item \texttt {MolienSeriesWithGivenDenominator}, \hyperpage{1187} 3235 \item \texttt {Monoid} 3236 \subitem for a list, \hyperpage{793} 3237 \subitem for various generators, \hyperpage{793} 3238 \item \texttt {MonoidByGenerators}, \hyperpage{793} 3239 \item \texttt {MonoidByMultiplicationTable}, \hyperpage{794} 3240 \item \texttt {MonoidOfRewritingSystem}, \hyperpage{819} 3241 \item \texttt {MonomialComparisonFunction}, \hyperpage{1044} 3242 \item \texttt {MonomialExtGrlexLess}, \hyperpage{1047} 3243 \item \texttt {MonomialExtrepComparisonFun}, \hyperpage{1044} 3244 \item \texttt {MonomialGrevlexOrdering}, \hyperpage{1045} 3245 \item \texttt {MonomialGrlexOrdering}, \hyperpage{1045} 3246 \item \texttt {MonomialLexOrdering}, \hyperpage{1044} 3247 \item \texttt{MonomialTotalDegreeLess}, \hyperpage{1273} 3248 \item monomorphisms 3249 \subitem find all, \hyperpage{602} 3250 \item \texttt {MorClassLoop}, \hyperpage{602} 3251 \item \texttt {MostFrequentGeneratorFpGroup}, \hyperpage{710} 3252 \item \texttt {MovedPoints} 3253 \subitem for a list or collection of permutations, \hyperpage{632} 3254 \subitem for a partial perm, \hyperpage{854} 3255 \subitem for a partial perm coll, \hyperpage{854} 3256 \subitem for a permutation, \hyperpage{632} 3257 \subitem for a transformation, \hyperpage{832} 3258 \subitem for a transformation coll, \hyperpage{832} 3259 \item \texttt {MTX}, \hyperpage{1063} 3260 \item \texttt {MTX.BasesCompositionSeries}, \hyperpage{1066} 3261 \item \texttt {MTX.BasesMaximalSubmodules}, \hyperpage{1066} 3262 \item \texttt {MTX.BasesMinimalSubmodules}, \hyperpage{1066} 3263 \item \texttt {MTX.BasesMinimalSupermodules}, \hyperpage{1066} 3264 \item \texttt {MTX.BasesSubmodules}, \hyperpage{1066} 3265 \item \texttt {MTX.BasisInOrbit}, \hyperpage{1070} 3266 \item \texttt {MTX.BasisModuleEndomorphisms}, \hyperpage{1068} 3267 \item \texttt {MTX.BasisModuleHomomorphisms}, \hyperpage{1068} 3268 \item \texttt {MTX.BasisRadical}, \hyperpage{1066} 3269 \item \texttt {MTX.BasisSocle}, \hyperpage{1066} 3270 \item \texttt {MTX.CollectedFactors}, \hyperpage{1067} 3271 \item \texttt {MTX.CompositionFactors}, \hyperpage{1067} 3272 \item \texttt {MTX.DegreeSplittingField}, \hyperpage{1064} 3273 \item \texttt {MTX.Dimension}, \hyperpage{1064} 3274 \item \texttt {MTX.Distinguish}, \hyperpage{1069} 3275 \item \texttt {MTX.Field}, \hyperpage{1064} 3276 \item \texttt {MTX.Generators}, \hyperpage{1064} 3277 \item \texttt {MTX.HomogeneousComponents}, \hyperpage{1065} 3278 \item \texttt {MTX.Homomorphism}, \hyperpage{1069} 3279 \item \texttt {MTX.Homomorphisms}, \hyperpage{1069} 3280 \item \texttt {MTX.Indecomposition}, \hyperpage{1065} 3281 \item \texttt {MTX.InducedAction}, \hyperpage{1068} 3282 \item \texttt {MTX.InducedActionFactorMatrix}, \hyperpage{1067} 3283 \item \texttt {MTX.InducedActionFactorModule}, \hyperpage{1067} 3284 \item \texttt {MTX.InducedActionSubMatrix}, \hyperpage{1067} 3285 \item \texttt {MTX.InducedActionSubMatrixNB}, \hyperpage{1067} 3286 \item \texttt {MTX.InducedActionSubmodule}, \hyperpage{1067} 3287 \item \texttt {MTX.InducedActionSubmoduleNB}, \hyperpage{1067} 3288 \item \texttt {MTX.InvariantBilinearForm}, \hyperpage{1069} 3289 \item \texttt {MTX.InvariantQuadraticForm}, \hyperpage{1070} 3290 \item \texttt {MTX.InvariantSesquilinearForm}, \hyperpage{1070} 3291 \item \texttt {MTX.IsAbsolutelyIrreducible}, \hyperpage{1064} 3292 \item \texttt {MTX.IsEquivalent}, \hyperpage{1069} 3293 \item \texttt {MTX.IsIndecomposable}, \hyperpage{1065} 3294 \item \texttt {MTX.IsIrreducible}, \hyperpage{1064} 3295 \item \texttt {MTX.IsomorphismIrred}, \hyperpage{1069} 3296 \item \texttt {MTX.IsomorphismModules}, \hyperpage{1068} 3297 \item \texttt {MTX.ModuleAutomorphisms}, \hyperpage{1068} 3298 \item \texttt {MTX.NormedBasisAndBaseChange}, \hyperpage{1067} 3299 \item \texttt {MTX.OrthogonalSign}, \hyperpage{1070} 3300 \item \texttt {MTX.ProperSubmoduleBasis}, \hyperpage{1066} 3301 \item \texttt {MTX.SubGModule}, \hyperpage{1065} 3302 \item \texttt {MTX.SubmoduleGModule}, \hyperpage{1065} 3303 \item multiplication, \hyperpage{57} 3304 \subitem matrices, \hyperpage{335} 3305 \subitem matrix and matrix list, \hyperpage{335} 3306 \subitem matrix and scalar, \hyperpage{334} 3307 \subitem matrix and vector, \hyperpage{334} 3308 \subitem operation, \hyperpage{440} 3309 \subitem scalar and matrix, \hyperpage{334} 3310 \subitem scalar and matrix list, \hyperpage{335} 3311 \subitem scalar and vector, \hyperpage{323} 3312 \subitem vector and matrix, \hyperpage{334} 3313 \subitem vector and matrix list, \hyperpage{336} 3314 \subitem vector and scalar, \hyperpage{323} 3315 \subitem vectors, \hyperpage{324} 3316 \item \texttt {MultiplicationTable} 3317 \subitem for a list of elements, \hyperpage{491} 3318 \subitem for a magma, \hyperpage{491} 3319 \item multiplicative order of an integer, \hyperpage{210} 3320 \item \texttt {MultiplicativeNeutralElement}, \hyperpage{494} 3321 \item \texttt {MultiplicativeZero}, \hyperpage{494} 3322 \subitem for a partial perm, \hyperpage{859} 3323 \item \texttt {MultiplicativeZeroOp}, \hyperpage{437} 3324 \item multiplicity 3325 \subitem of constituents of a group character, \hyperpage{1168} 3326 \item Multiplier, \hyperpage{582} 3327 \item multisets, \hyperpage{295} 3328 \item \texttt{MultRowVector}, \hyperpage{1274} 3329 \item \texttt {MultVector}, \hyperpage{327} 3330 \item \texttt {MultVectorLeft}, \hyperpage{327} 3331 \item Murnaghan components, \hyperpage{1183, 1184} 3332 \item \texttt {MutableBasis}, \hyperpage{937} 3333 \item \texttt {MutableBasisOfClosureUnderAction}, \hyperpage{963} 3334 \item \texttt {Mutable}\discretionary {-}{}{}\texttt {Basis}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Ideal}\discretionary {-}{}{}\texttt {In}\discretionary {-}{}{}\texttt {Nonassociative}\discretionary {-}{}{}\texttt {Algebra}, 3335 \hyperpage{965} 3336 \item \texttt {MutableBasisOfNonassociativeAlgebra}, \hyperpage{964} 3337 \item \texttt{MutableIdentityMat}, \hyperpage{1273} 3338 \item \texttt{MutableNullMat}, \hyperpage{1273} 3339 3340 \indexspace 3341 3342 \item \texttt {Name}, \hyperpage{166} 3343 \item \texttt {NameFunction}, \hyperpage{70} 3344 \item \texttt {NameRNam}, \hyperpage{408} 3345 \item \texttt {NamesFilter}, \hyperpage{171} 3346 \item \texttt {NamesGVars}, \hyperpage{53} 3347 \item \texttt {NamesLocalVariablesFunction}, \hyperpage{71} 3348 \item \texttt {NamesOfComponents}, \hyperpage{1289} 3349 \item \texttt {NamesOfFusionSources}, \hyperpage{1205} 3350 \item namespace, \hyperpage{48}, \hyperpage{50} 3351 \item \texttt {NamesSystemGVars}, \hyperpage{53} 3352 \item \texttt {NamesUserGVars}, \hyperpage{53} 3353 \item \texttt {NanosecondsSinceEpoch}, \hyperpage{112} 3354 \item \texttt {NanosecondsSinceEpochInfo}, \hyperpage{112} 3355 \item \texttt {NaturalCharacter} 3356 \subitem for a group, \hyperpage{1165} 3357 \subitem for a homomorphism, \hyperpage{1165} 3358 \item \texttt {NaturalHomomorphismByGenerators}, \hyperpage{462} 3359 \item \texttt {NaturalHomomorphismByIdeal}, \hyperpage{893} 3360 \subitem for an algebra and an ideal, \hyperpage{971} 3361 \item \texttt {NaturalHomomorphismByNormalSubgroup}, \hyperpage{564} 3362 \item \texttt {Natural}\discretionary {-}{}{}\texttt {Homomorphism}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Normal}\discretionary {-}{}{}\texttt {SubgroupNC}, 3363 \hyperpage{564} 3364 \item \texttt {Natural}\discretionary {-}{}{}\texttt {Homomorphism}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Sub}\discretionary {-}{}{}\texttt {Algebra}\discretionary {-}{}{}\texttt {Module}, 3365 \hyperpage{981} 3366 \item \texttt {NaturalHomomorphismBySubspace}, \hyperpage{944} 3367 \item \texttt {Natural}\discretionary {-}{}{}\texttt {Homomorphism}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Lie}\discretionary {-}{}{}\texttt {Algebra}\discretionary {-}{}{}\texttt {From}\discretionary {-}{}{}\texttt {Nilpotent}\discretionary {-}{}{}\texttt {Group}, 3368 \hyperpage{1002} 3369 \item \texttt {NaturalLeqPartialPerm}, \hyperpage{862} 3370 \item \texttt {NaturalPartialOrder}, \hyperpage{867} 3371 \item \texttt {NearAdditiveGroup}, \hyperpage{872} 3372 \item \texttt {NearAdditiveGroupByGenerators}, \hyperpage{873} 3373 \item \texttt {NearAdditiveMagma}, \hyperpage{872} 3374 \item \texttt {NearAdditiveMagmaByGenerators}, \hyperpage{872} 3375 \item \texttt {NearAdditiveMagmaWithZero}, \hyperpage{872} 3376 \item \texttt {Near}\discretionary {-}{}{}\texttt {Additive}\discretionary {-}{}{}\texttt {Magma}\discretionary {-}{}{}\texttt {With}\discretionary {-}{}{}\texttt {Zero}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Generators}, 3377 \hyperpage{872} 3378 \item \texttt {NearlyCharacterTablesFamily}, \hyperpage{1104} 3379 \item needed package, \hyperpage{1257} 3380 \item negative number, \hyperpage{57} 3381 \item \texttt {NegativeRoots}, \hyperpage{996} 3382 \item \texttt {NegativeRootVectors}, \hyperpage{996} 3383 \item \texttt {NestingDepthA}, \hyperpage{279} 3384 \item \texttt {NestingDepthM}, \hyperpage{279} 3385 \item \texttt {NewAttribute}, \hyperpage{179} 3386 \item \texttt{NewAttribute} 3387 \subitem example, \hyperpage{1306} 3388 \item \texttt {NewCategory}, \hyperpage{175} 3389 \item \texttt {NewConstructor}, \hyperpage{1279} 3390 \item \texttt {NewDictionary}, \hyperpage{398} 3391 \item \texttt {NewFamily}, \hyperpage{170} 3392 \item \texttt {NewFilter}, \hyperpage{186} 3393 \item \texttt {NewFloat}, \hyperpage{252} 3394 \item \texttt {NewInfoClass}, \hyperpage{108} 3395 \item newline, \hyperpage{46} 3396 \item \texttt {NewmanInfinityCriterion}, \hyperpage{725} 3397 \item \texttt {NewOperation}, \hyperpage{1277} 3398 \item \texttt {NewProperty}, \hyperpage{185} 3399 \item \texttt {NewRepresentation}, \hyperpage{177} 3400 \item \texttt{NewRepresentation} 3401 \subitem example, \hyperpage{1307} 3402 \item \texttt {NewType}, \hyperpage{187} 3403 \item \texttt {NextIterator}, \hyperpage{425} 3404 \item \texttt {NextPrimeInt}, \hyperpage{197} 3405 \item \texttt {NF}, \hyperpage{921} 3406 \item \texttt {NiceAlgebraMonomorphism}, \hyperpage{972} 3407 \item \texttt {NiceBasis}, \hyperpage{946} 3408 \item \texttt {NiceBasisFiltersInfo}, \hyperpage{948} 3409 \item \texttt {NiceFreeLeftModule}, \hyperpage{946} 3410 \item \texttt {NiceFreeLeftModuleInfo}, \hyperpage{946} 3411 \item \texttt {NiceMonomorphism}, \hyperpage{595} 3412 \item \texttt {NiceMonomorphismAutomGroup}, \hyperpage{600} 3413 \item \texttt {NiceObject}, \hyperpage{595} 3414 \item \texttt {NiceVector}, \hyperpage{946} 3415 \item \texttt {NilpotencyClassOfGroup}, \hyperpage{552} 3416 \item \texttt {NilpotentQuotientOfFpLieAlgebra}, \hyperpage{1005} 3417 \item \texttt {NK}, \hyperpage{244} 3418 \item \texttt{NOAUTO}, \hyperpage{1238} 3419 \item \texttt {NonabelianExteriorSquare}, \hyperpage{583} 3420 \item \texttt {NonnegativeIntegers}, \hyperpage{188} 3421 \item \texttt {NonnegIntScalarProducts}, \hyperpage{1215} 3422 \item \texttt {NonNilpotentElement}, \hyperpage{1004} 3423 \item \texttt {Norm}, \hyperpage{908} 3424 \subitem for a class function, \hyperpage{1168} 3425 \subitem for floats, \hyperpage{255} 3426 \item \texttt{Norm} 3427 \subitem of character, \hyperpage{1168} 3428 \item \texttt {NormalBase}, \hyperpage{909} 3429 \item \texttt {NormalClosure}, \hyperpage{545} 3430 \item \texttt {NormalFormIntMat}, \hyperpage{364} 3431 \item \texttt {NormalIntersection}, \hyperpage{545} 3432 \item \texttt {Normalized}\discretionary {-}{}{}\texttt {Element}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Magma}\discretionary {-}{}{}\texttt {Ring}\discretionary {-}{}{}\texttt {Modulo}\discretionary {-}{}{}\texttt {Relations}, 3433 \hyperpage{1020} 3434 \item \texttt {NormalizedWhitespace}, \hyperpage{386} 3435 \item \texttt {Normalizer} 3436 \subitem for a group and a group element, \hyperpage{544} 3437 \subitem for two groups, \hyperpage{544} 3438 \item normalizer, \hyperpage{544} 3439 \item \texttt {NormalizerInGLnZ}, \hyperpage{662} 3440 \item \texttt {NormalizerInGLnZBravaisGroup}, \hyperpage{663} 3441 \item \texttt {NormalizersTom}, \hyperpage{1087} 3442 \item \texttt {NormalizerTom}, \hyperpage{1087} 3443 \item \texttt {NormalizerViaRadical}, \hyperpage{588} 3444 \item \texttt {NormalizeWhitespace}, \hyperpage{386} 3445 \item \texttt {NormalSeriesByPcgs}, \hyperpage{680} 3446 \item \texttt {NormalSubgroupClasses}, \hyperpage{1153} 3447 \item \texttt {NormalSubgroupClassesInfo}, \hyperpage{1152} 3448 \item \texttt {NormalSubgroups}, \hyperpage{568} 3449 \item \texttt {NormedRowVector}, \hyperpage{324} 3450 \item \texttt {NormedRowVectors}, \hyperpage{942} 3451 \item \texttt{NormedVectors}, \hyperpage{1273} 3452 \item \texttt{not}, \hyperpage{261} 3453 \item \texttt {NrArrangements}, \hyperpage{222} 3454 \item \texttt {NrBasisVectors}, \hyperpage{937} 3455 \item \texttt {NrCombinations}, \hyperpage{222} 3456 \item \texttt {NrComponentsOfPartialPerm}, \hyperpage{857} 3457 \item \texttt {NrComponentsOfTransformation}, \hyperpage{837} 3458 \item \texttt {NrConjugacyClasses}, \hyperpage{542} 3459 \subitem for a character table, \hyperpage{1111} 3460 \item \texttt {NrConjugacyClassesGL}, \hyperpage{772} 3461 \item \texttt {NrConjugacyClassesGU}, \hyperpage{772} 3462 \item \texttt {NrConjugacyClassesPGL}, \hyperpage{772} 3463 \item \texttt {NrConjugacyClassesPGU}, \hyperpage{772} 3464 \item \texttt {NrConjugacyClassesPSL}, \hyperpage{772} 3465 \item \texttt {NrConjugacyClassesPSU}, \hyperpage{772} 3466 \item \texttt {NrConjugacyClassesSL}, \hyperpage{772} 3467 \item \texttt {NrConjugacyClassesSLIsogeneous}, \hyperpage{772} 3468 \item \texttt {NrConjugacyClassesSU}, \hyperpage{772} 3469 \item \texttt {NrConjugacyClassesSUIsogeneous}, \hyperpage{772} 3470 \item \texttt {NrDerangements}, \hyperpage{225} 3471 \item \texttt {NrFixedPoints} 3472 \subitem for a partial perm, \hyperpage{854} 3473 \subitem for a partial perm coll, \hyperpage{854} 3474 \item \texttt {NrInputsOfStraightLineProgram}, \hyperpage{512} 3475 \item \texttt {NrMovedPoints} 3476 \subitem for a list or collection of permutations, \hyperpage{632} 3477 \subitem for a partial perm, \hyperpage{854} 3478 \subitem for a partial perm coll, \hyperpage{854} 3479 \subitem for a permutation, \hyperpage{632} 3480 \subitem for a transformation, \hyperpage{832} 3481 \subitem for a transformation coll, \hyperpage{832} 3482 \item \texttt {NrOrderedPartitions}, \hyperpage{228} 3483 \item \texttt {NrPartitions}, \hyperpage{227} 3484 \item \texttt {NrPartitionsSet}, \hyperpage{226} 3485 \item \texttt {NrPartitionTuples}, \hyperpage{230} 3486 \item \texttt {NrPermutationsList}, \hyperpage{225} 3487 \item \texttt {NrPolyhedralSubgroups}, \hyperpage{1126} 3488 \item \texttt {NrRestrictedPartitions}, \hyperpage{229} 3489 \item \texttt {NrSubsTom}, \hyperpage{1082} 3490 \item \texttt {NrTuples}, \hyperpage{224} 3491 \item \texttt {NrUnorderedTuples}, \hyperpage{223} 3492 \item \texttt {NthRootsInGroup}, \hyperpage{544} 3493 \item \texttt {NullAlgebra}, \hyperpage{956} 3494 \item \texttt {NullMat}, \hyperpage{339} 3495 \item \texttt {NullspaceIntMat}, \hyperpage{360} 3496 \item \texttt {NullspaceMat}, \hyperpage{343} 3497 \item \texttt {NullspaceMatDestructive}, \hyperpage{343} 3498 \item \texttt {NullspaceModN}, \hyperpage{357} 3499 \item \texttt {NullspaceModQ}, \hyperpage{357} 3500 \item \texttt {Number}, \hyperpage{305} 3501 \item number 3502 \subitem Bell, \hyperpage{219} 3503 \subitem binomial, \hyperpage{218} 3504 \subitem Stirling, of the first kind, \hyperpage{220} 3505 \subitem Stirling, of the second kind, \hyperpage{220} 3506 \item number field, \hyperpage{922} 3507 \item number fields 3508 \subitem Galois group, \hyperpage{925} 3509 \item \texttt {NumberArgumentsFunction}, \hyperpage{71} 3510 \item \texttt {NumberFFVector}, \hyperpage{326} 3511 \item \texttt {NumberPerfectGroups}, \hyperpage{776} 3512 \item \texttt {NumberPerfectLibraryGroups}, \hyperpage{776} 3513 \item \texttt {NumberSmallRings}, \hyperpage{894} 3514 \item \texttt {NumbersString}, \hyperpage{389} 3515 \item \texttt {NumberSyllables}, \hyperpage{508} 3516 \item \texttt {NumberTransformation}, \hyperpage{825} 3517 \item numerator 3518 \subitem of a rational, \hyperpage{234} 3519 \item \texttt {NumeratorOfModuloPcgs}, \hyperpage{674} 3520 \item \texttt {NumeratorOfRationalFunction}, \hyperpage{1027} 3521 \item \texttt {NumeratorRat}, \hyperpage{234} 3522 3523 \indexspace 3524 3525 \item \texttt {ObjByExtRep}, \hyperpage{1297} 3526 \subitem for creating a UEALattice element, \hyperpage{1011} 3527 \item \texttt {Objectify}, \hyperpage{1287} 3528 \item \texttt {ObjectifyWithAttributes}, \hyperpage{1287} 3529 \item obsolete, \hyperpage{1272} 3530 \item \texttt {OCOneCocycles}, \hyperpage{580} 3531 \item octal character codes, \hyperpage{378} 3532 \item \texttt {OctaveAlgebra}, \hyperpage{955} 3533 \item \texttt{od}, \hyperpage{62} 3534 \item \texttt {OldGeneratorsOfPresentation}, \hyperpage{746} 3535 \item \texttt {Omega}, \hyperpage{551} 3536 \subitem construct an orthogonal group, \hyperpage{769} 3537 \item OmniGraffle, \hyperpage{570} 3538 \item \texttt {ONanScottType}, \hyperpage{639} 3539 \item \texttt {OnBreak}, \hyperpage{87} 3540 \item \texttt {OnBreakMessage}, \hyperpage{89} 3541 \item \texttt {One}, \hyperpage{436} 3542 \subitem for a partial perm, \hyperpage{858} 3543 \item one cohomology, \hyperpage{578} 3544 \item \texttt {OneAttr}, \hyperpage{436} 3545 \item \texttt {OneCoboundaries}, \hyperpage{579} 3546 \item \texttt {OneCocycles} 3547 \subitem for a group and a pcgs, \hyperpage{579} 3548 \subitem for generators and a group, \hyperpage{579} 3549 \subitem for generators and a pcgs, \hyperpage{579} 3550 \subitem for two groups, \hyperpage{579} 3551 \item \texttt {OneFactorBound}, \hyperpage{1038} 3552 \item \texttt {OneImmutable}, \hyperpage{436} 3553 \item \texttt{One\mbox{\texttt{\mdseries\slshape Library}}Group}, 3554 \hyperpage{774} 3555 \item \texttt {OneMutable}, \hyperpage{436} 3556 \item \texttt {OneOfPcgs}, \hyperpage{667} 3557 \item \texttt {OneOp}, \hyperpage{436} 3558 \item \texttt{OnePrimitiveGroup}, \hyperpage{774} 3559 \item \texttt {OneSameMutability}, \hyperpage{436} 3560 \item \texttt {OneSM}, \hyperpage{436} 3561 \item \texttt{OneTransitiveGroup}, \hyperpage{774} 3562 \item \texttt {OnIndeterminates} 3563 \subitem as a permutation action, \hyperpage{610} 3564 \item \texttt {OnLeftInverse}, \hyperpage{608} 3565 \item \texttt {OnLines}, \hyperpage{610} 3566 \item \texttt{OnLines} 3567 \subitem example, \hyperpage{766} 3568 \item \texttt{OnlyNeeded} 3569 \subitem option, \hyperpage{1258} 3570 \item \texttt {OnPairs}, \hyperpage{608} 3571 \item \texttt {OnPoints}, \hyperpage{607} 3572 \item \texttt {OnQuit}, \hyperpage{131} 3573 \item \texttt {OnRight}, \hyperpage{607} 3574 \item \texttt {OnSets}, \hyperpage{608} 3575 \item \texttt {OnSetsDisjointSets}, \hyperpage{609} 3576 \item \texttt {OnSetsSets}, \hyperpage{608} 3577 \item \texttt {OnSetsTuples}, \hyperpage{609} 3578 \item \texttt {OnSubspacesByCanonicalBasis}, \hyperpage{611} 3579 \item \texttt {OnSubspaces}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Canonical}\discretionary {-}{}{}\texttt {Basis}\discretionary {-}{}{}\texttt {Concatenations}, 3580 \hyperpage{611} 3581 \item \texttt {OnTuples}, \hyperpage{608} 3582 \item \texttt {OnTuplesSets}, \hyperpage{609} 3583 \item \texttt {OnTuplesTuples}, \hyperpage{609} 3584 \item $O_p(G)$ 3585 \subitem see PCore, \hyperpage{544} 3586 \item \texttt{Operation}, \hyperpage{1272} 3587 \item operation, \hyperpage{1276} 3588 \item \texttt {OperationAlgebraHomomorphism} 3589 \subitem action on a free left module, \hyperpage{971} 3590 \subitem action w.r.t. a basis of the module, \hyperpage{971} 3591 \item \texttt{OperationHomomorphism}, \hyperpage{1272} 3592 \item operations 3593 \subitem for booleans, \hyperpage{260} 3594 \item Operations for algebraic elements, \hyperpage{1056} 3595 \item operators, \hyperpage{48} 3596 \subitem arithmetic, \hyperpage{57} 3597 \subitem associativity, \hyperpage{58} 3598 \subitem for cyclotomics, \hyperpage{242} 3599 \subitem for lists, \hyperpage{277} 3600 \subitem precedence, \hyperpage{57} 3601 \item options, \hyperpage{33} 3602 \subitem command line, filenames, \hyperpage{37} 3603 \subitem command line, internal, \hyperpage{37} 3604 \subitem under UNIX, \hyperpage{33} 3605 \item \texttt{or}, \hyperpage{260} 3606 \item \texttt {Orbit}, \hyperpage{611} 3607 \item \texttt {OrbitFusions}, \hyperpage{1208} 3608 \item \texttt {OrbitishFO}, \hyperpage{1355} 3609 \item \texttt {OrbitLength}, \hyperpage{613} 3610 \item \texttt {OrbitLengths} 3611 \subitem for a group, a set of seeds, etc., \hyperpage{613} 3612 \subitem for a permutation group, \hyperpage{613} 3613 \subitem for an external set, \hyperpage{613} 3614 \item \texttt {OrbitLengthsDomain} 3615 \subitem for a group and a set of seeds, \hyperpage{613} 3616 \subitem for a permutation group, \hyperpage{613} 3617 \subitem of an external set, \hyperpage{613} 3618 \item \texttt {OrbitPerms}, \hyperpage{637} 3619 \item \texttt {OrbitPowerMaps}, \hyperpage{1201} 3620 \item \texttt {Orbits} 3621 \subitem attribute, \hyperpage{612} 3622 \subitem for a permutation group, \hyperpage{612} 3623 \subitem operation, \hyperpage{612} 3624 \item \texttt{Orbits} 3625 \subitem as attributes for external sets, \hyperpage{1353} 3626 \item \texttt {OrbitsDomain} 3627 \subitem for a group and an action domain, \hyperpage{612} 3628 \subitem for a permutation group, \hyperpage{612} 3629 \subitem of an external set, \hyperpage{612} 3630 \item \texttt {OrbitsishOperation}, \hyperpage{1354} 3631 \item \texttt {OrbitsPerms}, \hyperpage{637} 3632 \item \texttt {OrbitStabChain}, \hyperpage{648} 3633 \item \texttt {OrbitStabilizer}, \hyperpage{614} 3634 \item \texttt {OrbitStabilizerAlgorithm}, \hyperpage{614} 3635 \item \texttt {Order}, \hyperpage{439} 3636 \subitem for a class function, \hyperpage{1163} 3637 \item order 3638 \subitem of a group, \hyperpage{525} 3639 \subitem of a list, collection or domain, \hyperpage{419} 3640 \subitem of the prime residue group, \hyperpage{209} 3641 \item ordered partitions 3642 \subitem internal representation, \hyperpage{1362} 3643 \item \texttt {OrderedPartitions}, \hyperpage{227} 3644 \item ordering 3645 \subitem booleans, \hyperpage{260} 3646 \subitem of records, \hyperpage{407} 3647 \item \texttt {OrderingByLessThanFunctionNC}, \hyperpage{479} 3648 \item \texttt {OrderingByLessThanOrEqualFunctionNC}, \hyperpage{479} 3649 \item \texttt {OrderingOfRewritingSystem}, \hyperpage{520} 3650 \item \texttt {OrderingOnGenerators}, \hyperpage{482} 3651 \item \texttt {OrderingsFamily}, \hyperpage{479} 3652 \item \texttt {OrderMod}, \hyperpage{210} 3653 \item \texttt {OrderOfRewritingSystem}, \hyperpage{520} 3654 \item \texttt {OrdersClassRepresentatives}, \hyperpage{1113} 3655 \item \texttt {OrdersTom}, \hyperpage{1082} 3656 \item \texttt {Ordinal}, \hyperpage{392} 3657 \item ordinary character, \hyperpage{1167} 3658 \item \texttt {OrdinaryCharacterTable} 3659 \subitem for a character table, \hyperpage{1110} 3660 \subitem for a group, \hyperpage{1110} 3661 \item \texttt {OrthogonalComponents}, \hyperpage{1183} 3662 \item \texttt {OrthogonalEmbeddings}, \hyperpage{369} 3663 \item \texttt {Orthogonal}\discretionary {-}{}{}\texttt {Embeddings}\discretionary {-}{}{}\texttt {Special}\discretionary {-}{}{}\texttt {Dimension}, 3664 \hyperpage{1178} 3665 \item output 3666 \subitem suppressing, \hyperpage{80} 3667 \item \texttt {OutputLogTo} 3668 \subitem for a filename, \hyperpage{140} 3669 \subitem for streams, \hyperpage{149} 3670 \subitem stop logging output, \hyperpage{140} 3671 \item \texttt {OutputTextFile}, \hyperpage{150} 3672 \item \texttt {OutputTextNone}, \hyperpage{154} 3673 \item \texttt {OutputTextString}, \hyperpage{152} 3674 \item \texttt {OutputTextUser}, \hyperpage{151} 3675 \item overload, \hyperpage{1285} 3676 3677 \indexspace 3678 3679 \item $p$-group, \hyperpage{557} 3680 \item package, \hyperpage{1236} 3681 \item \texttt{PackageInfo.g} 3682 \subitem for a GAP package, \hyperpage{1250} 3683 \item \texttt {PACKAGE{\textunderscore }DEBUG}, \hyperpage{1239} 3684 \item \texttt {PACKAGE{\textunderscore }ERROR}, \hyperpage{1239} 3685 \item \texttt {PACKAGE{\textunderscore }INFO}, \hyperpage{1239} 3686 \item \texttt {PACKAGE{\textunderscore }WARNING}, \hyperpage{1239} 3687 \item \texttt {PackageVariablesInfo}, \hyperpage{1245} 3688 \item \texttt {PadicCoefficients}, \hyperpage{367} 3689 \item \texttt {PadicExtensionNumberFamily}, \hyperpage{1060} 3690 \item \texttt {PadicNumber} 3691 \subitem for a p-adic extension family and a list, \hyperpage{1060} 3692 \subitem for a p-adic extension family and a rational, 3693 \hyperpage{1060} 3694 \subitem for a pure p-adic numbers family and a list, 3695 \hyperpage{1060} 3696 \subitem for pure padics, \hyperpage{1058} 3697 \item \texttt {PadicValuation}, \hyperpage{888} 3698 \item \texttt {Pager}, \hyperpage{31} 3699 \item \texttt {PageSource}, \hyperpage{72} 3700 \item \texttt {Parametrized}, \hyperpage{1210} 3701 \item parametrized maps, \hyperpage{1197} 3702 \item \texttt {Parent}, \hyperpage{433} 3703 \item \texttt {ParentPcgs}, \hyperpage{671} 3704 \item \texttt {ParseRelators}, \hyperpage{702} 3705 \item partial order, \hyperpage{472} 3706 \item \texttt {PartialFactorization}, \hyperpage{199} 3707 \item \texttt {PartialOrderByOrderingFunction}, \hyperpage{475} 3708 \item \texttt {PartialOrderOfHasseDiagram}, \hyperpage{473} 3709 \item \texttt {PartialPerm} 3710 \subitem for a dense image, \hyperpage{847} 3711 \subitem for a domain and image, \hyperpage{847} 3712 \item \texttt {PartialPermFamily}, \hyperpage{847} 3713 \item \texttt {PartialPermOp}, \hyperpage{848} 3714 \item \texttt {PartialPermOpNC}, \hyperpage{848} 3715 \item \texttt {Partitions}, \hyperpage{227} 3716 \item partitions 3717 \subitem improper, of an integer, \hyperpage{228} 3718 \subitem ordered, of an integer, \hyperpage{228} 3719 \subitem restricted, of an integer, \hyperpage{228} 3720 \item \texttt {PartitionsGreatestEQ}, \hyperpage{228} 3721 \item \texttt {PartitionsGreatestLE}, \hyperpage{228} 3722 \item \texttt {PartitionsSet}, \hyperpage{226} 3723 \item \texttt {PartitionTuples}, \hyperpage{230} 3724 \item \texttt {PcElementByExponents}, \hyperpage{668} 3725 \item \texttt {PcElementByExponentsNC}, \hyperpage{668} 3726 \item \texttt {PCentralLieAlgebra}, \hyperpage{1001} 3727 \item \texttt {PCentralNormalSeriesByPcgsPGroup}, \hyperpage{679} 3728 \item \texttt {PCentralSeries}, \hyperpage{563} 3729 \item \texttt {PcGroupCode}, \hyperpage{699} 3730 \item \texttt {PcGroupFpGroup}, \hyperpage{690} 3731 \item \texttt {PcGroupWithPcgs}, \hyperpage{693} 3732 \item \texttt {Pcgs}, \hyperpage{665} 3733 \item \texttt {PcgsByPcSequence}, \hyperpage{666} 3734 \item \texttt {PcgsByPcSequenceNC}, \hyperpage{666} 3735 \item \texttt {PcgsCentralSeries}, \hyperpage{677} 3736 \item \texttt {PcgsChiefSeries}, \hyperpage{679} 3737 \item \texttt {PcgsElementaryAbelianSeries} 3738 \subitem for a group, \hyperpage{676} 3739 \subitem for a list of normal subgroups, \hyperpage{676} 3740 \item \texttt {PcgsPCentralSeriesPGroup}, \hyperpage{678} 3741 \item \texttt {Pcgs{\textunderscore }}\discretionary {-}{}{}\texttt {Orbit}\discretionary {-}{}{}\texttt {Stabilizer}, 3742 \hyperpage{685} 3743 \item \texttt {PClassPGroup}, \hyperpage{558} 3744 \item \texttt {PCore}, \hyperpage{544} 3745 \item \texttt {PcSeries}, \hyperpage{667} 3746 \item perfect groups, \hyperpage{774} 3747 \item \texttt {PerfectGroup} 3748 \subitem for a pair [ order, index ], \hyperpage{775} 3749 \subitem for group order (and index), \hyperpage{775} 3750 \item \texttt {PerfectIdentification}, \hyperpage{775} 3751 \item \texttt {PerfectResiduum}, \hyperpage{548} 3752 \item \texttt {Perform}, \hyperpage{301} 3753 \item \texttt {Permanent}, \hyperpage{232} 3754 \item \texttt {PermBounds}, \hyperpage{1193} 3755 \item \texttt {PermCharInfo}, \hyperpage{1188} 3756 \item \texttt {PermCharInfoRelative}, \hyperpage{1189} 3757 \item \texttt {PermChars}, \hyperpage{1190} 3758 \item \texttt {PermCharsTom} 3759 \subitem from a character table, \hyperpage{1094} 3760 \subitem via fusion map, \hyperpage{1094} 3761 \item \texttt {PermComb}, \hyperpage{1194} 3762 \item \texttt {PermLeftQuoPartialPerm}, \hyperpage{861} 3763 \item \texttt {PermLeftQuoPartialPermNC}, \hyperpage{861} 3764 \item \texttt {PermLeftQuoTransformation}, \hyperpage{829} 3765 \item \texttt {PermLeftQuoTransformationNC}, \hyperpage{829} 3766 \item \texttt {PermList}, \hyperpage{633} 3767 \item \texttt {PermListList}, \hyperpage{302} 3768 \item \texttt {PER}\discretionary {-}{}{}\texttt {M{\textunderscore }}\discretionary {-}{}{}\texttt {I}\discretionary {-}{}{}\texttt {N}\discretionary {-}{}{}\texttt {V}\discretionary {-}{}{}\texttt {E}\discretionary {-}{}{}\texttt {R}\discretionary {-}{}{}\texttt {S}\discretionary {-}{}{}\texttt {E{\textunderscore }}\discretionary {-}{}{}\texttt {T}\discretionary {-}{}{}\texttt {H}\discretionary {-}{}{}\texttt {R}\discretionary {-}{}{}\texttt {E}\discretionary {-}{}{}\texttt {S}\discretionary {-}{}{}\texttt {HOLD}, 3769 \hyperpage{630} 3770 \item \texttt {Permutation} 3771 \subitem for a group, an action domain, etc., \hyperpage{619} 3772 \subitem for an external set, \hyperpage{619} 3773 \item permutation character, \hyperpage{1221} 3774 \item permutation characters 3775 \subitem possible, \hyperpage{1187} 3776 \item \texttt {PermutationCharacter} 3777 \subitem for a group, an action domain, and a function, 3778 \hyperpage{1166} 3779 \subitem for two groups, \hyperpage{1166} 3780 \item \texttt {PermutationCycle}, \hyperpage{619} 3781 \item \texttt {PermutationGModule}, \hyperpage{1063} 3782 \item \texttt {PermutationMat}, \hyperpage{340} 3783 \item \texttt {PermutationOfImage}, \hyperpage{828} 3784 \item \texttt {PermutationsFamily}, \hyperpage{630} 3785 \item \texttt {PermutationsList}, \hyperpage{224} 3786 \item \texttt {PermutationTom}, \hyperpage{1080} 3787 \item \texttt {Permuted}, \hyperpage{304} 3788 \subitem as a permutation action, \hyperpage{610} 3789 \subitem for a class function, \hyperpage{1162} 3790 \item \texttt {PGL}, \hyperpage{770} 3791 \item \texttt {PGU}, \hyperpage{771} 3792 \item \texttt {Phi}, \hyperpage{209} 3793 \item point stabilizer, \hyperpage{614} 3794 \item \texttt {PolynomialByExtRep}, \hyperpage{1052} 3795 \item \texttt {PolynomialByExtRepNC}, \hyperpage{1052} 3796 \item \texttt {PolynomialCoefficientsOfPolynomial}, \hyperpage{1032} 3797 \item \texttt {PolynomialDivisionAlgorithm}, \hyperpage{1046} 3798 \item \texttt {PolynomialModP}, \hyperpage{1036} 3799 \item \texttt {PolynomialReducedRemainder}, \hyperpage{1046} 3800 \item \texttt {PolynomialReduction}, \hyperpage{1046} 3801 \item \texttt {PolynomialRing} 3802 \subitem for a ring and a list of indeterminate numbers, 3803 \hyperpage{1040} 3804 \subitem for a ring and a list of indeterminates, \hyperpage{1040} 3805 \subitem for a ring and a list of names (and an exclusion list), 3806 \hyperpage{1040} 3807 \subitem for a ring and a rank (and an exclusion list), 3808 \hyperpage{1040} 3809 \item \texttt {POmega}, \hyperpage{771} 3810 \item \texttt {PopOptions}, \hyperpage{131} 3811 \item \texttt {Position}, \hyperpage{286} 3812 \item \texttt {PositionBound}, \hyperpage{290} 3813 \item \texttt {PositionCanonical}, \hyperpage{286} 3814 \item \texttt{PositionFirstComponent}, \hyperpage{1274} 3815 \item \texttt {PositionLastNonZero}, \hyperpage{372} 3816 \item \texttt {PositionMaximum}, \hyperpage{289} 3817 \item \texttt {PositionMinimum}, \hyperpage{289} 3818 \item \texttt {PositionNonZero}, \hyperpage{290} 3819 \subitem for vectors, \hyperpage{372} 3820 \item \texttt {PositionNot}, \hyperpage{290} 3821 \item \texttt {PositionNthOccurrence}, \hyperpage{287} 3822 \item \texttt {PositionProperty}, \hyperpage{289} 3823 \item \texttt {Positions}, \hyperpage{286} 3824 \item \texttt {PositionsBound}, \hyperpage{290} 3825 \item \texttt {PositionSet}, \hyperpage{288} 3826 \item \texttt {PositionsOp}, \hyperpage{286} 3827 \item \texttt {PositionSorted}, \hyperpage{287} 3828 \item \texttt {PositionSortedBy}, \hyperpage{288} 3829 \item \texttt{PositionSortedByOp}, \hyperpage{288} 3830 \item \texttt{PositionSortedOp}, \hyperpage{287} 3831 \item \texttt {PositionsProperty}, \hyperpage{289} 3832 \item \texttt {PositionStream}, \hyperpage{147} 3833 \item \texttt {PositionSublist}, \hyperpage{291} 3834 \item \texttt {PositionWord}, \hyperpage{506} 3835 \item positive number, \hyperpage{57} 3836 \item \texttt {PositiveIntegers}, \hyperpage{188} 3837 \item \texttt {PositiveRoots}, \hyperpage{996} 3838 \item \texttt {PositiveRootVectors}, \hyperpage{996} 3839 \item possible permutation characters, \hyperpage{1187} 3840 \item \texttt {PossibleClassFusions}, \hyperpage{1206} 3841 \item \texttt {PossibleFusionsCharTableTom}, \hyperpage{1094} 3842 \item \texttt {PossiblePowerMaps}, \hyperpage{1199} 3843 \item power, \hyperpage{57} 3844 \subitem matrix, \hyperpage{335} 3845 \subitem meaning for class functions, \hyperpage{1161} 3846 \subitem of words, \hyperpage{505} 3847 \item power set, \hyperpage{221} 3848 \item Powerful $p$-group, \hyperpage{557} 3849 \item \texttt {PowerMap}, \hyperpage{1198} 3850 \item \texttt {PowerMapByComposition}, \hyperpage{1201} 3851 \item \texttt {PowerMapOp}, \hyperpage{1198} 3852 \item \texttt {PowerMapsAllowedBySymmetrizations}, \hyperpage{1220} 3853 \item \texttt {PowerMod}, \hyperpage{892} 3854 \item \texttt {PowerModCoeffs}, \hyperpage{331} 3855 \item \texttt {PowerModInt}, \hyperpage{195} 3856 \item \texttt {PowerPartition}, \hyperpage{230} 3857 \item \texttt {PowerSubalgebraSeries}, \hyperpage{962} 3858 \item \texttt {PQuotient}, \hyperpage{720} 3859 \item Pragmas, \hyperpage{78} 3860 \item precedence, \hyperpage{57} 3861 \item precedence test 3862 \subitem for permutations, \hyperpage{631} 3863 \item \texttt {PrecisionFloat}, \hyperpage{254} 3864 \item Prefix, \hyperpage{388} 3865 \item \texttt {PrefrattiniSubgroup}, \hyperpage{547} 3866 \item \texttt{PrefrattiniSubgroup} 3867 \subitem for groups with pcgs, \hyperpage{685} 3868 \item \texttt {PreImage} 3869 \subitem set of preimages of a collection under a general mapping, 3870 \hyperpage{460} 3871 \subitem set of preimages of the range of a general mapping, 3872 \hyperpage{460} 3873 \subitem unique preimage of an element under a general mapping, 3874 \hyperpage{460} 3875 \item \texttt {PreImageElm}, \hyperpage{460} 3876 \item \texttt {PreImagePartialPerm}, \hyperpage{861} 3877 \item \texttt {PreImages} 3878 \subitem set of preimages of a collection under a general mapping, 3879 \hyperpage{461} 3880 \subitem set of preimages of an elm under a general mapping, 3881 \hyperpage{461} 3882 \subitem set of preimages of the range of a general mapping, 3883 \hyperpage{461} 3884 \item \texttt {PreImagesElm}, \hyperpage{459} 3885 \item \texttt {PreImagesOfTransformation}, \hyperpage{830} 3886 \item \texttt {PreImagesRange}, \hyperpage{459} 3887 \item \texttt {PreImagesRepresentative}, \hyperpage{460} 3888 \item \texttt {PreImagesSet}, \hyperpage{460} 3889 \item preorder, \hyperpage{472} 3890 \item \texttt {PresentationFpGroup}, \hyperpage{726} 3891 \item \texttt {PresentationNormalClosure}, \hyperpage{733} 3892 \item \texttt {PresentationNormalClosureRrs}, \hyperpage{733} 3893 \item \texttt {PresentationSubgroup}, \hyperpage{729} 3894 \item \texttt {PresentationSubgroupMtc}, \hyperpage{731} 3895 \item \texttt {PresentationSubgroupRrs} 3896 \subitem for a group and a coset table (and a string), 3897 \hyperpage{729} 3898 \subitem for two groups (and a string), \hyperpage{729} 3899 \item \texttt {PresentationViaCosetTable}, \hyperpage{727} 3900 \item previous result, \hyperpage{80} 3901 \item \texttt {PrevPrimeInt}, \hyperpage{197} 3902 \item \texttt {PrimalityProof}, \hyperpage{196} 3903 \item primary subgroup generators, \hyperpage{748} 3904 \item \texttt {PrimaryGeneratorWords}, \hyperpage{731} 3905 \item prime residue group, \hyperpage{208} 3906 \subitem exponent, \hyperpage{209} 3907 \subitem generator, \hyperpage{211} 3908 \subitem order, \hyperpage{209} 3909 \item \texttt {PrimeBlocks}, \hyperpage{1120} 3910 \item \texttt {PrimeBlocksOp}, \hyperpage{1120} 3911 \item \texttt {PrimeDivisors}, \hyperpage{198} 3912 \item \texttt {PrimeField}, \hyperpage{905} 3913 \item \texttt {PrimePGroup}, \hyperpage{558} 3914 \item \texttt {PrimePowersInt}, \hyperpage{200} 3915 \item \texttt {PrimeResidues}, \hyperpage{208} 3916 \item \texttt {Primes}, \hyperpage{195} 3917 \item primitive, \hyperpage{622} 3918 \item primitive root modulo an integer, \hyperpage{211} 3919 \item \texttt {PrimitiveElement}, \hyperpage{905} 3920 \item \texttt {PrimitivePolynomial}, \hyperpage{1036} 3921 \item \texttt {PrimitiveRoot}, \hyperpage{916} 3922 \item \texttt {PrimitiveRootMod}, \hyperpage{211} 3923 \item \texttt {Print}, \hyperpage{84} 3924 \item \texttt {PrintAmbiguity}, \hyperpage{1215} 3925 \item \texttt {PrintArray}, \hyperpage{341} 3926 \item \texttt {PrintCharacterTable}, \hyperpage{1131} 3927 \item \texttt {PrintCSV}, \hyperpage{156} 3928 \item \texttt {PrintFactorsInt}, \hyperpage{200} 3929 \item \texttt {PrintFormatted}, \hyperpage{388} 3930 \item \texttt {PrintFormattingStatus}, \hyperpage{149} 3931 \item \texttt {PrintObj}, \hyperpage{85} 3932 \subitem for a character table, \hyperpage{1128} 3933 \subitem for a ffe, \hyperpage{918} 3934 \subitem for a string, \hyperpage{376} 3935 \subitem for a table of marks, \hyperpage{1078} 3936 \subitem for class functions, \hyperpage{1163} 3937 \item \texttt {PrintString}, \hyperpage{383} 3938 \item \texttt {PrintTo}, \hyperpage{139} 3939 \subitem for streams, \hyperpage{148} 3940 \item \texttt {PrintToFormatted}, \hyperpage{388} 3941 \item \texttt {ProbabilityShapes}, \hyperpage{1037} 3942 \item procedure call, \hyperpage{59} 3943 \item procedure call with arguments, \hyperpage{59} 3944 \item \texttt {Process}, \hyperpage{157} 3945 \item \texttt {Product}, \hyperpage{307} 3946 \item product 3947 \subitem of words, \hyperpage{505} 3948 \subitem rational functions, \hyperpage{1025} 3949 \item \texttt {ProductCoeffs}, \hyperpage{330} 3950 \item \texttt {ProductOfStraightLinePrograms}, \hyperpage{516} 3951 \item \texttt {ProductSpace}, \hyperpage{961} 3952 \item \texttt {ProductX}, \hyperpage{310} 3953 \item \texttt {PRO}\discretionary {-}{}{}\texttt {D{\textunderscore }}\discretionary {-}{}{}\texttt {G}\discretionary {-}{}{}\texttt {F2}\discretionary {-}{}{}\texttt {M}\discretionary {-}{}{}\texttt {A}\discretionary {-}{}{}\texttt {T{\textunderscore }}\discretionary {-}{}{}\texttt {G}\discretionary {-}{}{}\texttt {F2}\discretionary {-}{}{}\texttt {M}\discretionary {-}{}{}\texttt {A}\discretionary {-}{}{}\texttt {T{\textunderscore }}\discretionary {-}{}{}\texttt {A}\discretionary {-}{}{}\texttt {D}\discretionary {-}{}{}\texttt {V}\discretionary {-}{}{}\texttt {A}\discretionary {-}{}{}\texttt {NCED}, 3954 \hyperpage{357} 3955 \item \texttt {PRO}\discretionary {-}{}{}\texttt {D{\textunderscore }}\discretionary {-}{}{}\texttt {G}\discretionary {-}{}{}\texttt {F2}\discretionary {-}{}{}\texttt {M}\discretionary {-}{}{}\texttt {A}\discretionary {-}{}{}\texttt {T{\textunderscore }}\discretionary {-}{}{}\texttt {G}\discretionary {-}{}{}\texttt {F2}\discretionary {-}{}{}\texttt {M}\discretionary {-}{}{}\texttt {A}\discretionary {-}{}{}\texttt {T{\textunderscore }}\discretionary {-}{}{}\texttt {S}\discretionary {-}{}{}\texttt {I}\discretionary {-}{}{}\texttt {MPLE}, 3956 \hyperpage{357} 3957 \item \texttt {ProfileFunctions}, \hyperpage{114} 3958 \item \texttt {ProfileGlobalFunctions}, \hyperpage{114} 3959 \item \texttt {ProfileLineByLine}, \hyperpage{120} 3960 \item \texttt {ProfileMethods}, \hyperpage{115} 3961 \item \texttt {ProfileOperations}, \hyperpage{114} 3962 \item \texttt {ProfileOperationsAndMethods}, \hyperpage{114} 3963 \item \texttt {ProjectedInducedPcgs}, \hyperpage{675} 3964 \item \texttt {ProjectedPcElement}, \hyperpage{675} 3965 \item \texttt {Projection} 3966 \subitem for a domain, \hyperpage{455} 3967 \subitem for a domain and a positive integer, \hyperpage{455} 3968 \subitem for group products, \hyperpage{759} 3969 \subitem for two domains, \hyperpage{455} 3970 \item \texttt{Projection} 3971 \subitem example for direct products, \hyperpage{754} 3972 \subitem example for semidirect products, \hyperpage{755} 3973 \subitem example for subdirect products, \hyperpage{756} 3974 \subitem example for wreath products, \hyperpage{757} 3975 \item \texttt {ProjectionMap}, \hyperpage{1210} 3976 \item projections 3977 \subitem find all, \hyperpage{601} 3978 \item \texttt {Projective}\discretionary {-}{}{}\texttt {Action}\discretionary {-}{}{}\texttt {Homomorphism}\discretionary {-}{}{}\texttt {Matrix}\discretionary {-}{}{}\texttt {Group}, 3979 \hyperpage{657} 3980 \item \texttt {ProjectiveActionOnFullSpace}, \hyperpage{657} 3981 \item \texttt {ProjectiveGeneralLinearGroup}, \hyperpage{770} 3982 \item \texttt {ProjectiveGeneralUnitaryGroup}, \hyperpage{771} 3983 \item \texttt {ProjectiveOmega}, \hyperpage{771} 3984 \item \texttt {ProjectiveOrder}, \hyperpage{356} 3985 \item \texttt {ProjectiveSpecialLinearGroup}, \hyperpage{770} 3986 \item \texttt {ProjectiveSpecialUnitaryGroup}, \hyperpage{771} 3987 \item \texttt {ProjectiveSymplecticGroup}, \hyperpage{771} 3988 \item prompt, \hyperpage{80} 3989 \subitem partial, \hyperpage{80} 3990 \item \texttt {PRump}, \hyperpage{548} 3991 \item \texttt {PseudoRandom}, \hyperpage{423} 3992 \subitem for finitely presented groups, \hyperpage{706} 3993 \item \texttt {PSL}, \hyperpage{770} 3994 \item \texttt {PSP}, \hyperpage{771} 3995 \item \texttt {PSp}, \hyperpage{771} 3996 \item \texttt {PSU}, \hyperpage{771} 3997 \item \texttt {PthPowerImage} 3998 \subitem for basis and element, \hyperpage{1001} 3999 \subitem for element, \hyperpage{1001} 4000 \subitem for element and integer, \hyperpage{1001} 4001 \item \texttt {PthPowerImages}, \hyperpage{1000} 4002 \item \texttt {PurePadicNumberFamily}, \hyperpage{1058} 4003 \item \texttt {PushOptions}, \hyperpage{130} 4004 \item \texttt {PValuation}, \hyperpage{216} 4005 4006 \indexspace 4007 4008 \item \texttt {Quadratic}, \hyperpage{246} 4009 \item quadratic residue, \hyperpage{211, 212} 4010 \item \texttt {QuaternionAlgebra}, \hyperpage{954} 4011 \item \texttt {QuaternionGenerators}, \hyperpage{763} 4012 \item \texttt {QuaternionGroup}, \hyperpage{763} 4013 \item \texttt{QUIET}, \hyperpage{1273} 4014 \item \texttt {QUIT}, \hyperpage{93} 4015 \item \texttt{QUIT} 4016 \subitem emergency quit, \hyperpage{93} 4017 \item quit 4018 \subitem in emergency, \hyperpage{93} 4019 \item \texttt {QUITTING}, \hyperpage{94} 4020 \item \texttt {QUIT{\textunderscore }GAP}, \hyperpage{93} 4021 \item \texttt {QuoInt}, \hyperpage{192} 4022 \item \texttt {Quotient}, \hyperpage{878} 4023 \item quotient 4024 \subitem for finitely presented groups, \hyperpage{702} 4025 \subitem matrices, \hyperpage{335} 4026 \subitem matrix and matrix list, \hyperpage{336} 4027 \subitem matrix and scalar, \hyperpage{335} 4028 \subitem of free monoid, \hyperpage{815} 4029 \subitem of free semigroup, \hyperpage{815} 4030 \subitem of words, \hyperpage{505} 4031 \subitem rational functions, \hyperpage{1025} 4032 \subitem scalar and matrix, \hyperpage{335} 4033 \subitem scalar and matrix list, \hyperpage{335} 4034 \subitem vector and matrix, \hyperpage{335} 4035 \item \texttt {QuotientFromSCTable}, \hyperpage{954} 4036 \item \texttt {QuotientMod}, \hyperpage{892} 4037 \item \texttt {QuotientPolynomialsExtRep}, \hyperpage{1053} 4038 \item \texttt {QuotientRemainder}, \hyperpage{889} 4039 \item \texttt {QuotientSemigroupCongruence}, \hyperpage{800} 4040 \item \texttt {QuotientSemigroupHomomorphism}, \hyperpage{800} 4041 \item \texttt {QuotientSemigroupPreimage}, \hyperpage{800} 4042 \item \texttt {QuotRemLaurpols}, \hyperpage{1031} 4043 4044 \indexspace 4045 4046 \item $r_N$ (irrational value), \hyperpage{243} 4047 \item \texttt {RadicalGroup}, \hyperpage{548} 4048 \item \texttt {RadicalOfAlgebra}, \hyperpage{966} 4049 \item \texttt {Random} 4050 \subitem for a list or collection, \hyperpage{422} 4051 \subitem for integers, \hyperpage{192} 4052 \subitem for lower and upper bound, \hyperpage{422} 4053 \subitem for random source and collection, \hyperpage{204} 4054 \subitem for random source and list, \hyperpage{204} 4055 \subitem for random source and two integers, \hyperpage{204} 4056 \subitem for rationals, \hyperpage{235} 4057 \item \texttt{Random}, \hyperpage{422} 4058 \item random seed, \hyperpage{423} 4059 \item \texttt {RandomBinaryRelationOnPoints}, \hyperpage{474} 4060 \item \texttt {RandomInvertibleMat}, \hyperpage{341} 4061 \item \texttt {RandomIsomorphismTest}, \hyperpage{699} 4062 \item \texttt {Randomize} 4063 \subitem for a matrix object, \hyperpage{373} 4064 \subitem for a vector object, \hyperpage{373} 4065 \item \texttt {RandomList}, \hyperpage{423} 4066 \item \texttt {RandomMat}, \hyperpage{341} 4067 \item \texttt {RandomPartialPerm} 4068 \subitem for a positive integer, \hyperpage{851} 4069 \subitem for a set of positive integers, \hyperpage{851} 4070 \subitem for domain and image, \hyperpage{851} 4071 \item \texttt {RandomPrimitivePolynomial}, \hyperpage{918} 4072 \item \texttt {RandomSource}, \hyperpage{205} 4073 \item \texttt {RandomTransformation}, \hyperpage{826} 4074 \item \texttt {RandomUnimodularMat}, \hyperpage{342} 4075 \item \texttt {Range} 4076 \subitem of a general mapping, \hyperpage{457} 4077 \item range, \hyperpage{310} 4078 \item \texttt {RankAction} 4079 \subitem for a group, an action domain, etc., \hyperpage{621} 4080 \subitem for an external set, \hyperpage{621} 4081 \item \texttt {RankFilter}, \hyperpage{171} 4082 \item \texttt {RankMat}, \hyperpage{342} 4083 \item \texttt {RankOfPartialPerm}, \hyperpage{852} 4084 \item \texttt {RankOfPartialPermCollection}, \hyperpage{852} 4085 \item \texttt {RankOfPartialPermSemigroup}, \hyperpage{866} 4086 \item \texttt {RankOfTransformation} 4087 \subitem for a transformation and a list, \hyperpage{831} 4088 \subitem for a transformation and a positive integer, 4089 \hyperpage{831} 4090 \item \texttt {RankPGroup}, \hyperpage{558} 4091 \item \texttt {Rat}, \hyperpage{235} 4092 \subitem for floats, \hyperpage{252} 4093 \subitem for strings, \hyperpage{391} 4094 \item \texttt {RationalCanonicalFormTransform}, \hyperpage{352} 4095 \item \texttt {RationalClass}, \hyperpage{543} 4096 \item \texttt {RationalClasses}, \hyperpage{543} 4097 \item \texttt {RationalFunctionByExtRep}, \hyperpage{1052} 4098 \item \texttt {RationalFunctionByExtRepNC}, \hyperpage{1052} 4099 \item \texttt {Rational}\discretionary {-}{}{}\texttt {Function}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Ext}\discretionary {-}{}{}\texttt {Rep}\discretionary {-}{}{}\texttt {With}\discretionary {-}{}{}\texttt {Cancellation}, 4100 \hyperpage{1054} 4101 \item \texttt {RationalFunctionsFamily}, \hyperpage{1049} 4102 \item \texttt {RationalizedMat}, \hyperpage{248} 4103 \item \texttt {Rationals}, \hyperpage{233} 4104 \item \texttt {RClassOfHClass}, \hyperpage{802} 4105 \item \texttt {Read}, \hyperpage{138} 4106 \subitem for streams, \hyperpage{145} 4107 \item read eval print loop, \hyperpage{80} 4108 \item \texttt{read.g} 4109 \subitem for a GAP package, \hyperpage{1250} 4110 \item \texttt {ReadAll}, \hyperpage{146} 4111 \item \texttt {ReadAllLine}, \hyperpage{153} 4112 \item \texttt {ReadAsFunction}, \hyperpage{139} 4113 \subitem for streams, \hyperpage{145} 4114 \item \texttt {ReadByte}, \hyperpage{145} 4115 \item \texttt {ReadCommandLineHistory}, \hyperpage{98} 4116 \item \texttt {ReadCSV}, \hyperpage{155} 4117 \item \texttt {ReadLine}, \hyperpage{145} 4118 \item \texttt{ReadlineInitLine}, \hyperpage{97} 4119 \item \texttt{README} 4120 \subitem for a GAP package, \hyperpage{1249} 4121 \item \texttt {ReadPackage}, \hyperpage{1240} 4122 \item \texttt{ReadPkg}, \hyperpage{1273} 4123 \item \texttt {RealClasses}, \hyperpage{1116} 4124 \item \texttt {RealizableBrauerCharacters}, \hyperpage{1196} 4125 \item \texttt {RealPart}, \hyperpage{246} 4126 \item \texttt {RecNames}, \hyperpage{403} 4127 \item record 4128 \subitem component access, \hyperpage{403} 4129 \subitem component assignment, \hyperpage{404} 4130 \subitem component variable, \hyperpage{403} 4131 \subitem component variable assignment, \hyperpage{404} 4132 \item record assignment 4133 \subitem operation, \hyperpage{409} 4134 \item record boundness test 4135 \subitem operation, \hyperpage{409} 4136 \item record component 4137 \subitem operation, \hyperpage{409} 4138 \item record unbind 4139 \subitem operation, \hyperpage{409} 4140 \item recursion, \hyperpage{65} 4141 \item \texttt {RedispatchOnCondition}, \hyperpage{1283} 4142 \item redisplay a help section, \hyperpage{29} 4143 \item redisplay with next help viewer, \hyperpage{29} 4144 \item \texttt {ReduceCoeffs}, \hyperpage{330} 4145 \item \texttt {ReduceCoeffsMod}, \hyperpage{331} 4146 \item \texttt {ReducedAdditiveInverse}, \hyperpage{521} 4147 \item \texttt {ReducedCharacters}, \hyperpage{1176} 4148 \item \texttt {ReducedClassFunctions}, \hyperpage{1175} 4149 \item \texttt {ReducedComm}, \hyperpage{521} 4150 \item \texttt {ReducedConfluentRewritingSystem}, \hyperpage{818} 4151 \item \texttt {ReducedConjugate}, \hyperpage{521} 4152 \item \texttt {ReducedDifference}, \hyperpage{521} 4153 \item \texttt {ReducedForm}, \hyperpage{520} 4154 \item \texttt {ReducedGroebnerBasis} 4155 \subitem for a list and a monomial ordering, \hyperpage{1048} 4156 \subitem for an ideal and a monomial ordering, \hyperpage{1048} 4157 \item \texttt {ReducedInverse}, \hyperpage{521} 4158 \item \texttt {ReducedLeftQuotient}, \hyperpage{521} 4159 \item \texttt {ReducedOne}, \hyperpage{521} 4160 \item \texttt {ReducedPcElement}, \hyperpage{669} 4161 \item \texttt {ReducedPower}, \hyperpage{521} 4162 \item \texttt {ReducedProduct}, \hyperpage{521} 4163 \item \texttt {ReducedQuotient}, \hyperpage{521} 4164 \item \texttt {ReducedScalarProduct}, \hyperpage{521} 4165 \item \texttt {ReducedSum}, \hyperpage{521} 4166 \item \texttt {ReducedZero}, \hyperpage{521} 4167 \item \texttt {ReduceRules}, \hyperpage{520} 4168 \item \texttt {ReduceStabChain}, \hyperpage{650} 4169 \item \texttt {Ree}, \hyperpage{765} 4170 \item \texttt {ReeGroup}, \hyperpage{765} 4171 \item \texttt {ReesCongruenceOfSemigroupIdeal}, \hyperpage{799} 4172 \item \texttt {ReesMatrixSemigroup}, \hyperpage{805} 4173 \item \texttt {ReesMatrixSemigroupElement}, \hyperpage{807} 4174 \item \texttt {ReesMatrixSubsemigroup}, \hyperpage{805} 4175 \item \texttt {ReesZeroMatrixSemigroup}, \hyperpage{805} 4176 \item \texttt {ReesZeroMatrixSemigroupElement}, \hyperpage{807} 4177 \item \texttt {ReesZeroMatrixSubsemigroup}, \hyperpage{805} 4178 \item \texttt {RefinedPcGroup}, \hyperpage{692} 4179 \item \texttt {ReflectionMat}, \hyperpage{341} 4180 \item reflexive relation, \hyperpage{471} 4181 \item \texttt {ReflexiveClosureBinaryRelation}, \hyperpage{474} 4182 \item regular, \hyperpage{622} 4183 \item regular action, \hyperpage{617} 4184 \item \texttt {RegularActionHomomorphism}, \hyperpage{618} 4185 \item \texttt {RegularModule}, \hyperpage{1135} 4186 \item relations, \hyperpage{451} 4187 \item \texttt {RelationsOfFpMonoid}, \hyperpage{817} 4188 \item \texttt {RelationsOfFpSemigroup}, \hyperpage{817} 4189 \item \texttt {RelativeBasis}, \hyperpage{933} 4190 \item \texttt {RelativeBasisNC}, \hyperpage{933} 4191 \item \texttt {RelativeDiameter}, \hyperpage{257} 4192 \item relatively prime, \hyperpage{57} 4193 \item \texttt {RelativeOrderOfPcElement}, \hyperpage{667} 4194 \item \texttt {RelativeOrders}, \hyperpage{666} 4195 \item \texttt{RelativeOrders} 4196 \subitem of a pcgs, \hyperpage{666} 4197 \item \texttt {RelatorsOfFpGroup}, \hyperpage{705} 4198 \item remainder 4199 \subitem operation, \hyperpage{440} 4200 \item remainder of a quotient, \hyperpage{193} 4201 \item \texttt {RemInt}, \hyperpage{193} 4202 \item \texttt {Remove}, \hyperpage{270} 4203 \item remove 4204 \subitem an element from a set, \hyperpage{297} 4205 \item \texttt {RemoveCharacters}, \hyperpage{386} 4206 \item \texttt {RemoveFile}, \hyperpage{141} 4207 \item \texttt {RemoveOuterCoeffs}, \hyperpage{328} 4208 \item \texttt {RemoveRelator}, \hyperpage{737} 4209 \item \texttt {RemoveSet}, \hyperpage{297} 4210 \item \texttt {RemoveStabChain}, \hyperpage{651} 4211 \item \texttt{repeat} loop, \hyperpage{62} 4212 \item \texttt {ReplacedString}, \hyperpage{386} 4213 \item representation 4214 \subitem as a sum of two squares, \hyperpage{216} 4215 \item \texttt {RepresentationsOfObject}, \hyperpage{177} 4216 \item \texttt {Representative}, \hyperpage{419} 4217 \item representative 4218 \subitem of a list or collection, \hyperpage{419} 4219 \item \texttt {RepresentativeAction}, \hyperpage{615} 4220 \item \texttt {RepresentativeLinearOperation}, \hyperpage{973} 4221 \item \texttt{RepresentativeOperation}, \hyperpage{1272} 4222 \item \texttt {RepresentativesContainedRightCosets}, \hyperpage{539} 4223 \item \texttt {RepresentativesFusions}, \hyperpage{1208} 4224 \item \texttt {RepresentativeSmallest}, \hyperpage{419} 4225 \item \texttt {RepresentativesMinimalBlocks} 4226 \subitem for a group, an action domain, etc., \hyperpage{623} 4227 \subitem for an external set, \hyperpage{623} 4228 \item \texttt {RepresentativesPerfectSubgroups}, \hyperpage{572} 4229 \item \texttt {RepresentativesPowerMaps}, \hyperpage{1201} 4230 \item \texttt {RepresentativesSimpleSubgroups}, \hyperpage{572} 4231 \item \texttt {RepresentativeTom}, \hyperpage{1093} 4232 \item \texttt {RepresentativeTomByGenerators}, \hyperpage{1093} 4233 \item \texttt {RepresentativeTomByGeneratorsNC}, \hyperpage{1093} 4234 \item \texttt{RequirePackage}, \hyperpage{1273} 4235 \item \texttt {Reread}, \hyperpage{141} 4236 \item \texttt {REREADING}, \hyperpage{141} 4237 \item \texttt {RereadPackage}, \hyperpage{1240} 4238 \item \texttt{RereadPkg}, \hyperpage{1273} 4239 \item \texttt {Reset}, \hyperpage{204} 4240 \item \texttt {ResetFilterObj}, \hyperpage{186} 4241 \item \texttt {ResetMethodReordering}, \hyperpage{1285} 4242 \item \texttt {ResetOptionsStack}, \hyperpage{131} 4243 \item residue 4244 \subitem quadratic, \hyperpage{211, 212} 4245 \item \texttt {RespectsAddition}, \hyperpage{464} 4246 \item \texttt {RespectsAdditiveInverses}, \hyperpage{464} 4247 \item \texttt {RespectsInverses}, \hyperpage{463} 4248 \item \texttt {RespectsMultiplication}, \hyperpage{462} 4249 \item \texttt {RespectsOne}, \hyperpage{463} 4250 \item \texttt {RespectsScalarMultiplication}, \hyperpage{465} 4251 \item \texttt {RespectsZero}, \hyperpage{464} 4252 \item \texttt {RestrictedClassFunction}, \hyperpage{1173} 4253 \item \texttt {RestrictedClassFunctions}, \hyperpage{1173} 4254 \item \texttt {RestrictedInverseGeneralMapping}, \hyperpage{453} 4255 \item \texttt {Restricted}\discretionary {-}{}{}\texttt {Lie}\discretionary {-}{}{}\texttt {Algebra}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Structure}\discretionary {-}{}{}\texttt {Constants}, 4256 \hyperpage{988} 4257 \item \texttt {RestrictedMapping}, \hyperpage{456} 4258 \item \texttt {RestrictedPartialPerm}, \hyperpage{849} 4259 \item \texttt {RestrictedPartitions}, \hyperpage{228} 4260 \item \texttt {RestrictedPerm}, \hyperpage{634} 4261 \item \texttt {RestrictedPermNC}, \hyperpage{634} 4262 \item \texttt {RestrictedTransformation}, \hyperpage{828} 4263 \item \texttt {RestrictOutputsOfSLP}, \hyperpage{516} 4264 \item \texttt {Resultant}, \hyperpage{1034} 4265 \item \texttt {ResultOfStraightLineProgram}, \hyperpage{513} 4266 \item \texttt {ResumeMethodReordering}, \hyperpage{1285} 4267 \item \texttt{return}, \hyperpage{87} 4268 \subitem no value, \hyperpage{69} 4269 \subitem with value, \hyperpage{69} 4270 \item return from break loop, \hyperpage{87} 4271 \item \texttt {ReturnFail}, \hyperpage{76} 4272 \item \texttt {ReturnFalse}, \hyperpage{75} 4273 \item \texttt {ReturnFirst}, \hyperpage{76} 4274 \item \texttt {ReturnNothing}, \hyperpage{76} 4275 \item \texttt {ReturnTrue}, \hyperpage{75} 4276 \item \texttt {Reversed}, \hyperpage{300} 4277 \item \texttt {ReverseNaturalPartialOrder}, \hyperpage{867} 4278 \item \texttt {RewindStream}, \hyperpage{147} 4279 \item \texttt {RewriteWord}, \hyperpage{713} 4280 \item right cosets, \hyperpage{536} 4281 \item \texttt {RightActingAlgebra}, \hyperpage{977} 4282 \item \texttt {RightActingRingOfIdeal}, \hyperpage{882} 4283 \item \texttt {RightAlgebraModule}, \hyperpage{975} 4284 \item \texttt {RightAlgebraModuleByGenerators}, \hyperpage{974} 4285 \item \texttt {RightCoset}, \hyperpage{536} 4286 \item \texttt {RightCosets}, \hyperpage{537} 4287 \item \texttt {RightCosetsNC}, \hyperpage{537} 4288 \item \texttt {RightDerivations}, \hyperpage{989} 4289 \item \texttt {RightIdeal}, \hyperpage{879} 4290 \item \texttt {RightIdealByGenerators}, \hyperpage{881} 4291 \item \texttt {RightIdealNC}, \hyperpage{880} 4292 \item \texttt {RightModuleByHomomorphismToMatAlg}, \hyperpage{979} 4293 \item \texttt {RightOne} 4294 \subitem for a partial perm, \hyperpage{858} 4295 \subitem for a transformation, \hyperpage{838} 4296 \item \texttt {RightShiftRowVector}, \hyperpage{328} 4297 \item \texttt {RightTransversal}, \hyperpage{538} 4298 \item \texttt {Ring} 4299 \subitem for a collection, \hyperpage{876} 4300 \subitem for ring elements, \hyperpage{876} 4301 \item \texttt {RingByGenerators}, \hyperpage{877} 4302 \item \texttt {RingByStructureConstants}, \hyperpage{895} 4303 \item \texttt {RingGeneralMappingByImages}, \hyperpage{893} 4304 \item \texttt {RingHomomorphismByImages}, \hyperpage{893} 4305 \item \texttt {RingHomomorphismByImagesNC}, \hyperpage{893} 4306 \item \texttt {RingWithOne} 4307 \subitem for a collection, \hyperpage{883} 4308 \subitem for ring elements, \hyperpage{883} 4309 \item \texttt {RingWithOneByGenerators}, \hyperpage{883} 4310 \item \texttt {RNamObj} 4311 \subitem for a positive integer, \hyperpage{408} 4312 \subitem for a string, \hyperpage{408} 4313 \item root 4314 \subitem of 1 modulo an integer, \hyperpage{213} 4315 \subitem of an integer, \hyperpage{191} 4316 \subitem of an integer modulo another, \hyperpage{212} 4317 \subitem of an integer, smallest, \hyperpage{191} 4318 \item \texttt {RootInt}, \hyperpage{191} 4319 \item \texttt {RootMod}, \hyperpage{212} 4320 \item \texttt {RootOfDefiningPolynomial}, \hyperpage{905} 4321 \item roots of unity, \hyperpage{236} 4322 \item \texttt {RootsMod}, \hyperpage{213} 4323 \item \texttt {RootsOfPolynomial}, \hyperpage{1030} 4324 \item \texttt {RootsOfUPol}, \hyperpage{1031} 4325 \item \texttt {RootsUnityMod}, \hyperpage{213} 4326 \item \texttt {RootSystem}, \hyperpage{995} 4327 \item \texttt {Round}, \hyperpage{255} 4328 \item \texttt {RoundCyc}, \hyperpage{239} 4329 \item row spaces, \hyperpage{939} 4330 \item \texttt {Rows}, \hyperpage{810} 4331 \item \texttt {RREF}, \hyperpage{342} 4332 \item \texttt {Rules}, \hyperpage{519} 4333 \item \texttt {Runtime}, \hyperpage{112} 4334 \item \texttt {Runtimes}, \hyperpage{111} 4335 4336 \indexspace 4337 4338 \item $s_N$ (irrational value), \hyperpage{243} 4339 \item \texttt {SameBlock}, \hyperpage{1121} 4340 \item save, \hyperpage{41} 4341 \item \texttt {SaveCommandLineHistory}, \hyperpage{98} 4342 \item \texttt {SaveOnExitFile}, \hyperpage{94} 4343 \item \texttt {SaveWorkspace}, \hyperpage{41} 4344 \item saving on exit, \hyperpage{93} 4345 \item \texttt {ScalarProduct} 4346 \subitem for characters, \hyperpage{1168} 4347 \item Schreier, \hyperpage{729} 4348 \item Schreier-Sims 4349 \subitem random, \hyperpage{641} 4350 \item Schur multiplier, \hyperpage{582} 4351 \item \texttt {SchurCover}, \hyperpage{581} 4352 \item \texttt {SchurCoverOfSymmetricGroup}, \hyperpage{584} 4353 \item scope, \hyperpage{49} 4354 \item \texttt {Sec}, \hyperpage{255} 4355 \item \texttt {Sech}, \hyperpage{255} 4356 \item \texttt {SecHMSM}, \hyperpage{394} 4357 \item secondary subgroup generators, \hyperpage{748} 4358 \item \texttt {SecondsDMYhms}, \hyperpage{395} 4359 \item \texttt {SeekPositionStream}, \hyperpage{147} 4360 \item \texttt {SemidirectProduct} 4361 \subitem for a group of automorphisms and a group, \hyperpage{754} 4362 \subitem for acting group, action, and a group, \hyperpage{754} 4363 \item \texttt {SemiEchelonBasis}, \hyperpage{941} 4364 \item \texttt {SemiEchelonBasisNC}, \hyperpage{941} 4365 \item \texttt {SemiEchelonMat}, \hyperpage{347} 4366 \item \texttt {SemiEchelonMatDestructive}, \hyperpage{347} 4367 \item \texttt {SemiEchelonMats}, \hyperpage{348} 4368 \item \texttt {SemiEchelonMatsDestructive}, \hyperpage{348} 4369 \item \texttt {SemiEchelonMatTransformation}, \hyperpage{348} 4370 \item \texttt {Semigroup} 4371 \subitem for a list, \hyperpage{789} 4372 \subitem for various generators, \hyperpage{789} 4373 \item semigroup, \hyperpage{789} 4374 \item \texttt {SemigroupByGenerators}, \hyperpage{790} 4375 \item \texttt {SemigroupByMultiplicationTable}, \hyperpage{792} 4376 \item \texttt {SemigroupIdealByGenerators}, \hyperpage{799} 4377 \item \texttt {SemigroupOfRewritingSystem}, \hyperpage{819} 4378 \item semiregular, \hyperpage{621} 4379 \item \texttt {SemiSimpleType}, \hyperpage{994} 4380 \item sequence 4381 \subitem Bernoulli, \hyperpage{219} 4382 \subitem Fibonacci, \hyperpage{231} 4383 \subitem Lucas, \hyperpage{231} 4384 \item \texttt {Set}, \hyperpage{415} 4385 \item set difference 4386 \subitem of collections, \hyperpage{422} 4387 \item set stabilizer, \hyperpage{614} 4388 \item \texttt {SetAllBlist}, \hyperpage{319} 4389 \item \texttt {SetAssertionLevel}, \hyperpage{110} 4390 \item \texttt {SetCommutator}, \hyperpage{691} 4391 \item \texttt {SetConjugate}, \hyperpage{691} 4392 \item \texttt {SetCrystGroupDefaultAction}, \hyperpage{663} 4393 \item \texttt {SetCyclotomicsLimit}, \hyperpage{249} 4394 \item \texttt {SetDefaultInfoOutput}, \hyperpage{109} 4395 \item \texttt {SetElmWPObj}, \hyperpage{1358} 4396 \item \texttt {SetEntrySCTable}, \hyperpage{953} 4397 \item \texttt {SetFilterObj}, \hyperpage{186} 4398 \item \texttt {SetFloats}, \hyperpage{253} 4399 \item \texttt {SetGasmanMessageStatus}, \hyperpage{129} 4400 \item \texttt {SetHelpViewer}, \hyperpage{30} 4401 \item \texttt {SetIndeterminateName}, \hyperpage{1024} 4402 \item \texttt {SetInfoHandler}, \hyperpage{109} 4403 \item \texttt {SetInfoLevel}, \hyperpage{108} 4404 \item \texttt {SetInfoOutput}, \hyperpage{109} 4405 \item \texttt {SetName}, \hyperpage{166} 4406 \item \texttt {SetNameObject}, \hyperpage{86} 4407 \item \texttt {SetPackagePath}, \hyperpage{1238} 4408 \item \texttt {SetParent}, \hyperpage{433} 4409 \item \texttt {SetPower}, \hyperpage{691} 4410 \item \texttt {SetPrintFormattingStatus}, \hyperpage{149} 4411 \item \texttt {SetRecursionTrapInterval}, \hyperpage{127} 4412 \item \texttt {SetReducedMultiplication}, \hyperpage{704} 4413 \item Sets, \hyperpage{263} 4414 \item sets, \hyperpage{295} 4415 \item \texttt {Setter}, \hyperpage{181} 4416 \item setter, \hyperpage{180} 4417 \item \texttt {SetUserPreference}, \hyperpage{39} 4418 \item \texttt {SetX}, \hyperpage{310} 4419 \item \texttt {ShallowCopy}, \hyperpage{165} 4420 \item \texttt{ShallowCopy} 4421 \subitem for lists, \hyperpage{274} 4422 \item \texttt {ShiftedCoeffs}, \hyperpage{331} 4423 \item \texttt {ShiftedPadicNumber}, \hyperpage{1059} 4424 \item short vectors spanning a lattice, \hyperpage{367}, 4425 \hyperpage{1176} 4426 \item \texttt {ShortestVectors}, \hyperpage{369} 4427 \item \texttt {ShortLexLeqPartialPerm}, \hyperpage{863} 4428 \item \texttt {ShortLexOrdering}, \hyperpage{483} 4429 \item \texttt {ShowAdditionTable}, \hyperpage{875} 4430 \item \texttt {ShowArgument}, \hyperpage{104} 4431 \item \texttt {ShowArguments}, \hyperpage{103} 4432 \item \texttt {ShowDeclarationsOfOperation}, \hyperpage{1277} 4433 \item \texttt {ShowDetails}, \hyperpage{104} 4434 \item \texttt {ShowGcd}, \hyperpage{891} 4435 \item \texttt {ShowImpliedFilters}, \hyperpage{172} 4436 \item \texttt {ShowMethods}, \hyperpage{104} 4437 \item \texttt {ShowMultiplicationTable}, \hyperpage{875} 4438 \item \texttt {ShowOtherMethods}, \hyperpage{104} 4439 \item \texttt {ShowPackageVariables}, \hyperpage{1245} 4440 \item \texttt{ShowPackageVariables}, \hyperpage{1256} 4441 \item \texttt {ShowUsedInfoClasses}, \hyperpage{108} 4442 \item \texttt {ShowUserPreferences}, \hyperpage{39} 4443 \item \texttt {ShrinkAllocationPlist}, \hyperpage{276} 4444 \item \texttt {ShrinkAllocationString}, \hyperpage{380} 4445 \item \texttt {ShrinkRowVector}, \hyperpage{328} 4446 \item \texttt {Shuffle}, \hyperpage{301} 4447 \item \texttt {SiftedPcElement}, \hyperpage{668} 4448 \item \texttt {SiftedPermutation}, \hyperpage{649} 4449 \item \texttt {SiftedVector}, \hyperpage{942} 4450 \item \texttt {Sigma}, \hyperpage{214} 4451 \item \texttt {SigmaL}, \hyperpage{770} 4452 \item sign 4453 \subitem of an integer, \hyperpage{190} 4454 \item \texttt {SignBit}, \hyperpage{254} 4455 \item \texttt {SignFloat}, \hyperpage{254} 4456 \item \texttt {SignInt}, \hyperpage{190} 4457 \item \texttt {SignPartition}, \hyperpage{229} 4458 \item \texttt {SignPerm}, \hyperpage{633} 4459 \item \texttt {SimpleGroup}, \hyperpage{555} 4460 \item \texttt {SimpleGroupsIterator}, \hyperpage{556} 4461 \item \texttt {SimpleLieAlgebra}, \hyperpage{990} 4462 \item \texttt {SimpleSystem}, \hyperpage{996} 4463 \item \texttt {SimplexMethod}, \hyperpage{358} 4464 \item \texttt {SimplifiedFpGroup}, \hyperpage{729} 4465 \item \texttt {SimplifyPresentation}, \hyperpage{737} 4466 \item \texttt {SimultaneousEigenvalues}, \hyperpage{356} 4467 \item \texttt {Sin}, \hyperpage{255} 4468 \item \texttt {SinCos}, \hyperpage{255} 4469 \item \texttt {SingleCollector}, \hyperpage{691} 4470 \item singlequote character, \hyperpage{378} 4471 \item singlequotes, \hyperpage{375} 4472 \item \texttt {Sinh}, \hyperpage{255} 4473 \item \texttt {SIntChar}, \hyperpage{390} 4474 \item \texttt {Size}, \hyperpage{419} 4475 \subitem for a character table, \hyperpage{1111} 4476 \item \texttt{Size} 4477 \subitem for groups with pcgs, \hyperpage{685} 4478 \item size 4479 \subitem of a list or collection, \hyperpage{419} 4480 \item \texttt {SizeBlist}, \hyperpage{316} 4481 \item \texttt {SizeConsiderFunction}, \hyperpage{576} 4482 \item \texttt {SizeNumbersPerfectGroups}, \hyperpage{776} 4483 \item \texttt {SizeOfFieldOfDefinition}, \hyperpage{1196} 4484 \item \texttt {SizesCentralisers}, \hyperpage{1113} 4485 \item \texttt {SizesCentralizers}, \hyperpage{1113} 4486 \item \texttt {SizesConjugacyClasses}, \hyperpage{1113} 4487 \item \texttt {SizeScreen}, \hyperpage{101} 4488 \item \texttt {SizesPerfectGroups}, \hyperpage{775} 4489 \item \texttt {SizeStabChain}, \hyperpage{648} 4490 \item \texttt {SL} 4491 \subitem for dimension and a field size, \hyperpage{767} 4492 \subitem for dimension and a ring, \hyperpage{767} 4493 \item \texttt {Sleep}, \hyperpage{112} 4494 \item \texttt {SlotUsagePattern}, \hyperpage{517} 4495 \item small integer, \hyperpage{188} 4496 \item smaller 4497 \subitem associative words, \hyperpage{505} 4498 \subitem elements of finitely presented groups, \hyperpage{704} 4499 \subitem for pcwords, \hyperpage{689} 4500 \subitem for transformations, \hyperpage{829} 4501 \subitem nonassociative words, \hyperpage{498} 4502 \subitem rational functions, \hyperpage{1026} 4503 \item smaller or equal, \hyperpage{56} 4504 \item smaller test, \hyperpage{56} 4505 \item \texttt {Smaller}\discretionary {-}{}{}\texttt {Degree}\discretionary {-}{}{}\texttt {Permutation}\discretionary {-}{}{}\texttt {Representation}, 4506 \hyperpage{638} 4507 \item \texttt {SmallestGeneratorPerm}, \hyperpage{631} 4508 \item \texttt {SmallestIdempotentPower} 4509 \subitem for a partial perm, \hyperpage{857} 4510 \subitem for a transformation, \hyperpage{836} 4511 \item \texttt {SmallestImageOfMovedPoint} 4512 \subitem for a partial permutation, \hyperpage{855} 4513 \subitem for a partial permutation coll, \hyperpage{855} 4514 \subitem for a transformation, \hyperpage{833} 4515 \subitem for a transformation coll, \hyperpage{833} 4516 \item \texttt {SmallestMovedPoint} 4517 \subitem for a list or collection of permutations, \hyperpage{631} 4518 \subitem for a partial perm, \hyperpage{855} 4519 \subitem for a partial perm coll, \hyperpage{855} 4520 \subitem for a permutation, \hyperpage{631} 4521 \subitem for a transformation, \hyperpage{833} 4522 \subitem for a transformation coll, \hyperpage{833} 4523 \item \texttt {SmallestRootInt}, \hyperpage{191} 4524 \item \texttt {SmallGeneratingSet}, \hyperpage{577} 4525 \item \texttt {SmallRing}, \hyperpage{894} 4526 \item \texttt {SmallSimpleGroup}, \hyperpage{556} 4527 \item Smith normal form, \hyperpage{1273} 4528 \item \texttt {SmithNormalFormIntegerMat}, \hyperpage{363} 4529 \item \texttt {SmithNormalFormIntegerMatTransforms}, \hyperpage{363} 4530 \item \texttt {SMTX.AbsoluteIrreducibilityTest}, \hyperpage{1071} 4531 \item \texttt {SMTX.AlgEl}, \hyperpage{1072} 4532 \item \texttt {SMTX.AlgElCharPol}, \hyperpage{1072} 4533 \item \texttt {SMTX.AlgElCharPolFac}, \hyperpage{1073} 4534 \item \texttt {SMTX.AlgElMat}, \hyperpage{1072} 4535 \item \texttt {SMTX.AlgElNullspaceDimension}, \hyperpage{1073} 4536 \item \texttt {SMTX.AlgElNullspaceVec}, \hyperpage{1073} 4537 \item \texttt {SMTX.CentMat}, \hyperpage{1073} 4538 \item \texttt {SMTX.CentMatMinPoly}, \hyperpage{1073} 4539 \item \texttt {SMTX.CompleteBasis}, \hyperpage{1072} 4540 \item \texttt {SMTX.Getter}, \hyperpage{1071} 4541 \item \texttt {SMTX.GoodElementGModule}, \hyperpage{1071} 4542 \item \texttt {SMTX.IrreducibilityTest}, \hyperpage{1071} 4543 \item \texttt {SMTX.MatrixSum}, \hyperpage{1072} 4544 \item \texttt {SMTX.MinimalSubGModule}, \hyperpage{1072} 4545 \item \texttt {SMTX.MinimalSubGModules}, \hyperpage{1071} 4546 \item \texttt {SMTX.RandomIrreducibleSubGModule}, \hyperpage{1070} 4547 \item \texttt {SMTX.Setter}, \hyperpage{1071} 4548 \item \texttt {SMTX.SortHomGModule}, \hyperpage{1071} 4549 \item \texttt {SMTX.Subbasis}, \hyperpage{1072} 4550 \item \texttt {SO}, \hyperpage{769} 4551 \item \texttt {Socle}, \hyperpage{548} 4552 \item \texttt {SocleTypePrimitiveGroup}, \hyperpage{640} 4553 \item \texttt {SolutionIntMat}, \hyperpage{360} 4554 \item \texttt {SolutionMat}, \hyperpage{344} 4555 \item \texttt {SolutionMatDestructive}, \hyperpage{344} 4556 \item \texttt {SolutionNullspaceIntMat}, \hyperpage{360} 4557 \item \texttt {SolvableQuotient} 4558 \subitem for a f.p. group and a list of primes, \hyperpage{721} 4559 \subitem for a f.p. group and a list of tuples, \hyperpage{721} 4560 \subitem for a f.p. group and a size, \hyperpage{721} 4561 \item \texttt {Sort}, \hyperpage{293} 4562 \item \texttt {SortBy}, \hyperpage{293} 4563 \item Sorted Lists as Collections, \hyperpage{412} 4564 \item \texttt {SortedCharacters}, \hyperpage{1147} 4565 \item \texttt {SortedCharacterTable} 4566 \subitem relative to the table of a factor group, \hyperpage{1148} 4567 \subitem w.r.t. a normal subgroup, \hyperpage{1148} 4568 \subitem w.r.t. a series of normal subgroups, \hyperpage{1148} 4569 \item \texttt {SortedList}, \hyperpage{415} 4570 \item \texttt {SortedSparseActionHomomorphism}, \hyperpage{617} 4571 \item \texttt {SortedTom}, \hyperpage{1079} 4572 \item \texttt {Sortex}, \hyperpage{294} 4573 \item \texttt {SortingPerm}, \hyperpage{295} 4574 \item \texttt {SortParallel}, \hyperpage{294} 4575 \item \texttt {Source}, \hyperpage{457} 4576 \item \texttt {SourceOfIsoclinicTable}, \hyperpage{1142} 4577 \item \texttt {SP} 4578 \subitem for dimension and a ring, \hyperpage{768} 4579 \subitem for dimension and field size, \hyperpage{768} 4580 \item \texttt {Sp} 4581 \subitem for dimension and a ring, \hyperpage{768} 4582 \subitem for dimension and field size, \hyperpage{768} 4583 \item space, \hyperpage{46} 4584 \item \texttt {SparseActionHomomorphism}, \hyperpage{617} 4585 \item \texttt {SparseCartanMatrix}, \hyperpage{998} 4586 \item \texttt {SparseHashTable}, \hyperpage{401} 4587 \item \texttt {SparseIntKey}, \hyperpage{400} 4588 \item special character sequences, \hyperpage{377} 4589 \item \texttt {SpecialLinearGroup} 4590 \subitem for dimension and a field size, \hyperpage{767} 4591 \subitem for dimension and a ring, \hyperpage{767} 4592 \item \texttt {SpecialOrthogonalGroup}, \hyperpage{769} 4593 \item \texttt {SpecialPcgs} 4594 \subitem for a group, \hyperpage{682} 4595 \subitem for a pcgs, \hyperpage{682} 4596 \item \texttt {SpecialSemilinearGroup}, \hyperpage{770} 4597 \item \texttt {SpecialUnitaryGroup}, \hyperpage{768} 4598 \item \texttt {SplitCharacters}, \hyperpage{1138} 4599 \item \texttt {SplitExtension}, \hyperpage{696} 4600 \subitem with specified homomorphism, \hyperpage{698} 4601 \item \texttt {SplitString}, \hyperpage{385} 4602 \item \texttt {SplittingField}, \hyperpage{1029} 4603 \item Spreadsheet, \hyperpage{155} 4604 \item \texttt {SQ} 4605 \subitem synonym of SolvableQuotient, \hyperpage{721} 4606 \item \texttt {Sqrt}, \hyperpage{441} 4607 \item \texttt {Square}, \hyperpage{255} 4608 \item square root 4609 \subitem of an integer, \hyperpage{191} 4610 \item \texttt {SquareRoots}, \hyperpage{495} 4611 \item \texttt {SSortedList}, \hyperpage{415} 4612 \item \texttt {StabChain} 4613 \subitem for a group (and a record), \hyperpage{644} 4614 \subitem for a group and a base, \hyperpage{644} 4615 \item \texttt {StabChainBaseStrongGenerators}, \hyperpage{645} 4616 \item \texttt {StabChainImmutable}, \hyperpage{644} 4617 \item \texttt {StabChainMutable} 4618 \subitem for a group, \hyperpage{644} 4619 \subitem for a homomorphism, \hyperpage{644} 4620 \item \texttt {StabChainOp}, \hyperpage{644} 4621 \item \texttt {StabChainOptions}, \hyperpage{645} 4622 \item \texttt {Stabilizer}, \hyperpage{614} 4623 \item \texttt {StabilizerOfExternalSet}, \hyperpage{626} 4624 \item \texttt {StabilizerPcgs}, \hyperpage{685} 4625 \item \texttt {StableSort}, \hyperpage{293} 4626 \item \texttt {StableSortBy}, \hyperpage{293} 4627 \item \texttt {StableSortParallel}, \hyperpage{294} 4628 \item Stack trace, \hyperpage{90} 4629 \item \texttt {StandardAssociate}, \hyperpage{887} 4630 \item \texttt {StandardAssociateUnit}, \hyperpage{887} 4631 \item \texttt {StandardizeTable}, \hyperpage{711} 4632 \item \texttt {StandardWreathProduct}, \hyperpage{757} 4633 \item \texttt {StarCyc}, \hyperpage{246} 4634 \item \texttt {StartlineFunc}, \hyperpage{72} 4635 \item \texttt {StartsWith}, \hyperpage{388} 4636 \item \texttt {START{\textunderscore }TEST}, \hyperpage{121} 4637 \item \texttt {State}, \hyperpage{204} 4638 \item Stirling number of the first kind, \hyperpage{220} 4639 \item Stirling number of the second kind, \hyperpage{220} 4640 \item \texttt {Stirling1}, \hyperpage{220} 4641 \item \texttt {Stirling2}, \hyperpage{220} 4642 \item \texttt {STOP{\textunderscore }TEST}, \hyperpage{121} 4643 \item \texttt {StoredGroebnerBasis}, \hyperpage{1048} 4644 \item \texttt {StoreFusion}, \hyperpage{1205} 4645 \item \texttt {StraightLineProgElm}, \hyperpage{517} 4646 \item \texttt {StraightLineProgGens}, \hyperpage{518} 4647 \item \texttt {StraightLineProgram} 4648 \subitem for a list of lines (and the number of generators), 4649 \hyperpage{512} 4650 \subitem for a string and a list of generators names, 4651 \hyperpage{512} 4652 \item \texttt {StraightLineProgramNC} 4653 \subitem for a list of lines (and the number of generators), 4654 \hyperpage{512} 4655 \subitem for a string and a list of generators names, 4656 \hyperpage{512} 4657 \item \texttt {StraightLineProgramsTom}, \hyperpage{1091} 4658 \item \texttt {StreamsFamily}, \hyperpage{143} 4659 \item \texttt {StretchImportantSLPElement}, \hyperpage{518} 4660 \item strictly sorted list, \hyperpage{292} 4661 \item \texttt {String}, \hyperpage{383} 4662 \subitem for a cyclotomic, \hyperpage{238} 4663 \item \texttt {StringDate}, \hyperpage{394} 4664 \item \texttt {StringFactorizationWord}, \hyperpage{703} 4665 \item \texttt {StringFormatted}, \hyperpage{388} 4666 \item \texttt {StringNumbers}, \hyperpage{389} 4667 \item \texttt {StringOfMemoryAmount}, \hyperpage{389} 4668 \item \texttt {StringOfResultOfStraightLineProgram}, \hyperpage{514} 4669 \item \texttt {StringPP}, \hyperpage{384} 4670 \item strings 4671 \subitem equality of, \hyperpage{381} 4672 \subitem inequality of, \hyperpage{381} 4673 \subitem lexicographic ordering of, \hyperpage{382} 4674 \item \texttt {StringTime}, \hyperpage{394} 4675 \item \texttt {StripLineBreakCharacters}, \hyperpage{384} 4676 \item \texttt {StrongGeneratorsStabChain}, \hyperpage{648} 4677 \item \texttt {StronglyConnectedComponents}, \hyperpage{475} 4678 \item \mbox{\texttt{\mdseries\slshape Struct}}, \hyperpage{430} 4679 \item \texttt{\mbox{\texttt{\mdseries\slshape Struct}}ByGenerators}, 4680 \hyperpage{430} 4681 \item \texttt {StructuralCopy}, \hyperpage{165} 4682 \item \texttt{StructuralCopy} 4683 \subitem for lists, \hyperpage{274} 4684 \item structure constant, \hyperpage{1126, 1127} 4685 \item \texttt {StructureConstantsTable}, \hyperpage{952} 4686 \item \texttt {StructureDescription}, \hyperpage{534} 4687 \item \texttt{\mbox{\texttt{\mdseries\slshape Struct}}WithGenerators}, 4688 \hyperpage{430} 4689 \item \texttt {SU}, \hyperpage{768} 4690 \item \texttt {SubadditiveGroup}, \hyperpage{873} 4691 \item \texttt {SubadditiveGroupNC}, \hyperpage{873} 4692 \item \texttt {SubadditiveMagma}, \hyperpage{873} 4693 \item \texttt {SubadditiveMagmaNC}, \hyperpage{873} 4694 \item \texttt {SubadditiveMagmaWithZero}, \hyperpage{873} 4695 \item \texttt {SubadditiveMagmaWithZeroNC}, \hyperpage{873} 4696 \item \texttt {Subalgebra}, \hyperpage{956} 4697 \item \texttt {SubAlgebraModule}, \hyperpage{978} 4698 \item \texttt {SubalgebraNC}, \hyperpage{956} 4699 \item \texttt {SubalgebraWithOne}, \hyperpage{957} 4700 \item \texttt {SubalgebraWithOneNC}, \hyperpage{957} 4701 \item \texttt {SubdirectProduct}, \hyperpage{756} 4702 \item \texttt {SubdirectProducts}, \hyperpage{756} 4703 \item Subdomains, \hyperpage{433} 4704 \item \texttt {Subfield}, \hyperpage{904} 4705 \item \texttt {SubfieldNC}, \hyperpage{904} 4706 \item \texttt {Subfields}, \hyperpage{906} 4707 \item \texttt {Subgroup}, \hyperpage{528} 4708 \subitem for a group, \hyperpage{528} 4709 \item subgroup fusions, \hyperpage{1202} 4710 \item subgroup generators tree, \hyperpage{748} 4711 \item \texttt {SubgroupByPcgs}, \hyperpage{672} 4712 \item \texttt {SubgroupByProperty}, \hyperpage{530} 4713 \item \texttt {SubgroupNC}, \hyperpage{528} 4714 \item \texttt {SubgroupOfWholeGroupByCosetTable}, \hyperpage{712} 4715 \item \texttt {Subgroup}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Whole}\discretionary {-}{}{}\texttt {Group}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Quotient}\discretionary {-}{}{}\texttt {Subgroup}, 4716 \hyperpage{719} 4717 \item \texttt {SubgroupProperty}, \hyperpage{652} 4718 \item subgroups 4719 \subitem polyhedral, \hyperpage{1126} 4720 \item \texttt {SubgroupShell}, \hyperpage{531} 4721 \item \texttt {SubgroupsSolvableGroup}, \hyperpage{574} 4722 \item sublist, \hyperpage{266} 4723 \subitem access, \hyperpage{266} 4724 \subitem assignment, \hyperpage{268} 4725 \subitem operation, \hyperpage{267} 4726 \item sublist assignment 4727 \subitem operation, \hyperpage{269} 4728 \item \texttt {Submagma}, \hyperpage{488} 4729 \item \texttt {SubmagmaNC}, \hyperpage{488} 4730 \item \texttt {SubmagmaWithInverses}, \hyperpage{488} 4731 \item \texttt {SubmagmaWithInversesNC}, \hyperpage{488} 4732 \item \texttt {SubmagmaWithOne}, \hyperpage{488} 4733 \item \texttt {SubmagmaWithOneNC}, \hyperpage{488} 4734 \item \texttt {Submodule}, \hyperpage{898} 4735 \item \texttt {SubmoduleNC}, \hyperpage{898} 4736 \item \texttt {Submonoid}, \hyperpage{793} 4737 \item \texttt {SubmonoidNC}, \hyperpage{793} 4738 \item \texttt {SubnearAdditiveGroup}, \hyperpage{873} 4739 \item \texttt {SubnearAdditiveGroupNC}, \hyperpage{873} 4740 \item \texttt {SubnearAdditiveMagma}, \hyperpage{873} 4741 \item \texttt {SubnearAdditiveMagmaNC}, \hyperpage{873} 4742 \item \texttt {SubnearAdditiveMagmaWithZero}, \hyperpage{873} 4743 \item \texttt {SubnearAdditiveMagmaWithZeroNC}, \hyperpage{873} 4744 \item \texttt {SubnormalSeries}, \hyperpage{561} 4745 \item \texttt {Subring}, \hyperpage{878} 4746 \item \texttt {SubringNC}, \hyperpage{878} 4747 \item \texttt {Subrings}, \hyperpage{894} 4748 \item \texttt {SubringWithOne}, \hyperpage{883} 4749 \item \texttt {SubringWithOneNC}, \hyperpage{883} 4750 \item \texttt {Subsemigroup}, \hyperpage{789} 4751 \item \texttt {SubsemigroupNC}, \hyperpage{789} 4752 \item subset test 4753 \subitem for collections, \hyperpage{420} 4754 \item subsets, \hyperpage{221} 4755 \item \texttt {Subspace}, \hyperpage{929} 4756 \item \texttt {SubspaceNC}, \hyperpage{929} 4757 \item \texttt {Subspaces}, \hyperpage{930} 4758 \item \texttt {SubstitutedWord} 4759 \subitem replace a subword by a given word, \hyperpage{507} 4760 \subitem replace an interval by a given word, \hyperpage{507} 4761 \item \texttt {SubsTom}, \hyperpage{1081} 4762 \item \texttt{Sub\mbox{\texttt{\mdseries\slshape struct}}}, 4763 \hyperpage{434} 4764 \item \texttt{Sub\mbox{\texttt{\mdseries\slshape struct}}NC}, 4765 \hyperpage{434} 4766 \item \texttt {SubSyllables}, \hyperpage{508} 4767 \item subtract 4768 \subitem a set from another, \hyperpage{298} 4769 \item \texttt {SubtractBlist}, \hyperpage{319} 4770 \item subtraction, \hyperpage{57} 4771 \subitem matrices, \hyperpage{334} 4772 \subitem matrix and scalar, \hyperpage{334} 4773 \subitem rational functions, \hyperpage{1025} 4774 \subitem scalar and matrix, \hyperpage{334} 4775 \subitem scalar and matrix list, \hyperpage{335} 4776 \subitem scalar and vector, \hyperpage{323} 4777 \subitem vector and scalar, \hyperpage{323} 4778 \subitem vectors, \hyperpage{323} 4779 \item \texttt {SubtractSet}, \hyperpage{298} 4780 \item \texttt {Subword}, \hyperpage{506} 4781 \item \texttt {Successors}, \hyperpage{473} 4782 \item Suffix, \hyperpage{388} 4783 \item suggested package, \hyperpage{1257} 4784 \item \texttt {Sum}, \hyperpage{307} 4785 \item \texttt {SumFactorizationFunctionPcgs}, \hyperpage{680} 4786 \item \texttt {SumIntersectionMat}, \hyperpage{349} 4787 \item \texttt {SumX}, \hyperpage{310} 4788 \item \texttt {Sup}, \hyperpage{257} 4789 \item \texttt {SupersolvableResiduum}, \hyperpage{548} 4790 \item support 4791 \subitem email address, \hyperpage{27} 4792 \item \texttt {SupportedCharacterTableInfo}, \hyperpage{1102} 4793 \item \texttt {SurjectiveActionHomomorphismAttr}, \hyperpage{628} 4794 \item \texttt {SuspendMethodReordering}, \hyperpage{1285} 4795 \item \texttt {SuzukiGroup}, \hyperpage{765} 4796 \item \texttt {SylowComplement}, \hyperpage{549} 4797 \item \texttt {SylowSubgroup}, \hyperpage{549} 4798 \item \texttt {SylowSystem}, \hyperpage{550} 4799 \item symmetric group 4800 \subitem power map, \hyperpage{230} 4801 \item symmetric power, \hyperpage{1183} 4802 \item symmetric relation, \hyperpage{471} 4803 \item \texttt {SymmetricClosureBinaryRelation}, \hyperpage{475} 4804 \item \texttt {SymmetricGroup} 4805 \subitem for a degree, \hyperpage{764} 4806 \subitem for a domain, \hyperpage{764} 4807 \item \texttt {SymmetricInverseMonoid}, \hyperpage{867} 4808 \item \texttt {SymmetricInverseSemigroup}, \hyperpage{867} 4809 \item \texttt {SymmetricParentGroup}, \hyperpage{639} 4810 \item \texttt {SymmetricParts}, \hyperpage{1183} 4811 \item \texttt {SymmetricPowerOfAlgebraModule}, \hyperpage{1014} 4812 \item \texttt {Symmetrizations}, \hyperpage{1182} 4813 \item symmetrizations 4814 \subitem orthogonal, \hyperpage{1183} 4815 \subitem symplectic, \hyperpage{1184} 4816 \item \texttt {SymplecticComponents}, \hyperpage{1184} 4817 \item \texttt {SymplecticGroup} 4818 \subitem for dimension and a ring, \hyperpage{768} 4819 \subitem for dimension and field size, \hyperpage{768} 4820 \item syntax errors, \hyperpage{80} 4821 \item \texttt {SyntaxTree}, \hyperpage{69} 4822 \item \texttt{sysinfo.gap}, \hyperpage{1260} 4823 \item system getter, \hyperpage{180} 4824 \item system setter, \hyperpage{180} 4825 \item \texttt {Sz}, \hyperpage{765} 4826 4827 \indexspace 4828 4829 \item $t_N$ (irrational value), \hyperpage{243} 4830 \item table automorphisms, \hyperpage{1208}, \hyperpage{1222} 4831 \item table of chapters for help books, \hyperpage{29} 4832 \item table of sections for help books, \hyperpage{29} 4833 \item \texttt {TableAutomorphisms}, \hyperpage{1150} 4834 \item \texttt {TableOfMarks} 4835 \subitem for a group, \hyperpage{1076} 4836 \subitem for a matrix, \hyperpage{1076} 4837 \subitem for a string, \hyperpage{1076} 4838 \item \texttt {TableOfMarksByLattice}, \hyperpage{1077} 4839 \item \texttt {TableOfMarksComponents}, \hyperpage{1081} 4840 \item \texttt {TableOfMarksCyclic}, \hyperpage{1095} 4841 \item \texttt {TableOfMarksDihedral}, \hyperpage{1095} 4842 \item \texttt {TableOfMarksFamily}, \hyperpage{1080} 4843 \item \texttt {TableOfMarksFrobenius}, \hyperpage{1096} 4844 \item tables, \hyperpage{1097}, \hyperpage{1100} 4845 \item tabulator, \hyperpage{46} 4846 \item \texttt {Tan}, \hyperpage{255} 4847 \item \texttt {Tanh}, \hyperpage{255} 4848 \item \texttt {Tau}, \hyperpage{214} 4849 \item \texttt{TCENUM}, \hyperpage{708} 4850 \item \texttt {TeachingMode}, \hyperpage{101} 4851 \item \texttt{TemporaryGlobalVarName}, \hyperpage{1274} 4852 \item \texttt {Tensored}, \hyperpage{1172} 4853 \item \texttt {TensorProductGModule}, \hyperpage{1063} 4854 \item \texttt {TensorProductOfAlgebraModules} 4855 \subitem for a list of algebra modules, \hyperpage{1013} 4856 \subitem for two algebra modules, \hyperpage{1013} 4857 \item \texttt {Test}, \hyperpage{122} 4858 \item test 4859 \subitem for a primitive root, \hyperpage{211} 4860 \subitem for a rational, \hyperpage{234} 4861 \subitem for records, \hyperpage{402} 4862 \subitem for set equality, \hyperpage{296} 4863 \item \texttt {TestConsistencyMaps}, \hyperpage{1214} 4864 \item \texttt {TestDirectory}, \hyperpage{125} 4865 \item \texttt {Tester}, \hyperpage{180} 4866 \item tester, \hyperpage{180} 4867 \item \texttt {TestHomogeneous}, \hyperpage{1229} 4868 \item \texttt {TestInducedFromNormalSubgroup}, \hyperpage{1231} 4869 \item \texttt {TestJacobi}, \hyperpage{953} 4870 \item \texttt {TestMonomial} 4871 \subitem for a character, \hyperpage{1231} 4872 \subitem for a character and a Boolean, \hyperpage{1231} 4873 \subitem for a group, \hyperpage{1231} 4874 \subitem for a group and a Boolean, \hyperpage{1231} 4875 \item \texttt {TestMonomialQuick} 4876 \subitem for a character, \hyperpage{1233} 4877 \subitem for a group, \hyperpage{1233} 4878 \item \texttt {TestMonomialUseLattice}, \hyperpage{1232} 4879 \item \texttt {TestPackage}, \hyperpage{1241} 4880 \item \texttt {TestPackageAvailability}, \hyperpage{1240} 4881 \item \texttt {TestPerm1}, \hyperpage{1192} 4882 \item \texttt {TestPerm2}, \hyperpage{1192} 4883 \item \texttt {TestPerm3}, \hyperpage{1192} 4884 \item \texttt {TestPerm4}, \hyperpage{1192} 4885 \item \texttt {TestPerm5}, \hyperpage{1192} 4886 \item \texttt {TestQuasiPrimitive}, \hyperpage{1230} 4887 \item \texttt {TestRelativelySM} 4888 \subitem for a character, \hyperpage{1234} 4889 \subitem for a character and a normal subgroup, \hyperpage{1234} 4890 \subitem for a group, \hyperpage{1234} 4891 \subitem for a group and a normal subgroup, \hyperpage{1234} 4892 \item \texttt {TestSubnormallyMonomial} 4893 \subitem for a character, \hyperpage{1233} 4894 \subitem for a group, \hyperpage{1233} 4895 \item \texttt{then}, \hyperpage{60} 4896 \item \texttt {TietzeWordAbstractWord}, \hyperpage{733} 4897 \item \texttt {time}, \hyperpage{112} 4898 \item \texttt{time}, \hyperpage{80} 4899 \item \texttt {TotalMemoryAllocated}, \hyperpage{113} 4900 \item \texttt {Trace} 4901 \subitem for a field element, \hyperpage{908} 4902 \subitem for a matrix, \hyperpage{908} 4903 \subitem of a matrix, \hyperpage{336} 4904 \item \texttt {TraceAllMethods}, \hyperpage{106} 4905 \item \texttt {TracedCosetFpGroup}, \hyperpage{707} 4906 \item \texttt {TraceImmediateMethods}, \hyperpage{106} 4907 \item \texttt {TraceMat}, \hyperpage{336} 4908 \item \texttt {TraceMethods} 4909 \subitem for a list of operations, \hyperpage{105} 4910 \subitem for operations, \hyperpage{105} 4911 \item \texttt {TracePolynomial}, \hyperpage{907} 4912 \item \texttt {TransferDiagram}, \hyperpage{1213} 4913 \item \texttt {Transformation} 4914 \subitem for a list and function, \hyperpage{823} 4915 \subitem for a source and destination, \hyperpage{823} 4916 \subitem for an image list, \hyperpage{823} 4917 \item \texttt {TransformationByImageAndKernel} 4918 \subitem for an image and kernel, \hyperpage{824} 4919 \item \texttt {TransformationFamily}, \hyperpage{823} 4920 \item \texttt {TransformationList} 4921 \subitem for an image list, \hyperpage{823} 4922 \item \texttt {TransformationListList} 4923 \subitem for a source and destination, \hyperpage{823} 4924 \item \texttt {TransformationNumber}, \hyperpage{825} 4925 \item \texttt {TransformationOp}, \hyperpage{824} 4926 \item \texttt {TransformationOpNC}, \hyperpage{824} 4927 \item \texttt {TransformingPermutations}, \hyperpage{1151} 4928 \item \texttt {Transforming}\discretionary {-}{}{}\texttt {Permutations}\discretionary {-}{}{}\texttt {Character}\discretionary {-}{}{}\texttt {Tables}, 4929 \hyperpage{1151} 4930 \item transitive, \hyperpage{621} 4931 \item transitive relation, \hyperpage{472} 4932 \item \texttt {TransitiveClosureBinaryRelation}, \hyperpage{475} 4933 \item \texttt {Transitivity} 4934 \subitem for a character, \hyperpage{1171} 4935 \subitem for a group and an action domain, \hyperpage{621} 4936 \subitem for a permutation group, \hyperpage{621} 4937 \subitem for an external set, \hyperpage{621} 4938 \item \texttt {TranslatorSubalgebra}, \hyperpage{982} 4939 \item transporter, \hyperpage{615} 4940 \item \texttt {TransposedMat}, \hyperpage{340} 4941 \item \texttt {TransposedMatAttr}, \hyperpage{340} 4942 \item \texttt {TransposedMatDestructive}, \hyperpage{340} 4943 \item \texttt {TransposedMatImmutable}, \hyperpage{340} 4944 \item \texttt {TransposedMatMutable}, \hyperpage{340} 4945 \item \texttt {TransposedMatOp}, \hyperpage{340} 4946 \item \texttt {TransposedMatrixGroup}, \hyperpage{656} 4947 \item \texttt {TriangulizedIntegerMat}, \hyperpage{362} 4948 \item \texttt {TriangulizedIntegerMatTransform}, \hyperpage{362} 4949 \item \texttt {TriangulizedMat}, \hyperpage{342} 4950 \item \texttt {TriangulizedNullspaceMat}, \hyperpage{343} 4951 \item \texttt {TriangulizedNullspaceMatDestructive}, \hyperpage{343} 4952 \item \texttt {TriangulizeIntegerMat}, \hyperpage{362} 4953 \item \texttt {TriangulizeMat}, \hyperpage{343} 4954 \item \texttt {TrimPartialPerm}, \hyperpage{863} 4955 \item \texttt {TrimTransformation}, \hyperpage{839} 4956 \item \texttt {TrivialCharacter} 4957 \subitem for a character table, \hyperpage{1165} 4958 \subitem for a group, \hyperpage{1165} 4959 \item \texttt {TrivialGroup}, \hyperpage{761} 4960 \item \texttt {TrivialIterator}, \hyperpage{426} 4961 \item \texttt {TrivialSubalgebra}, \hyperpage{957} 4962 \item \texttt {TrivialSubgroup}, \hyperpage{546} 4963 \item \texttt {TrivialSubmagmaWithOne}, \hyperpage{495} 4964 \item \texttt {TrivialSubmodule}, \hyperpage{899} 4965 \item \texttt {TrivialSubmonoid}, \hyperpage{794} 4966 \item \texttt {TrivialSubnearAdditiveMagmaWithZero}, \hyperpage{875} 4967 \item \texttt {TrivialSubspace}, \hyperpage{930} 4968 \item \texttt {Trunc}, \hyperpage{255} 4969 \item \texttt {TryCosetTableInWholeGroup}, \hyperpage{712} 4970 \item \texttt {TryGcdCancelExtRepPolynomials}, \hyperpage{1054} 4971 \item \texttt {TryNextMethod}, \hyperpage{1282} 4972 \item tuple stabilizer, \hyperpage{614} 4973 \item \texttt {Tuples}, \hyperpage{223} 4974 \item \texttt {TwoClosure}, \hyperpage{652} 4975 \item \texttt {TwoCoboundaries}, \hyperpage{695} 4976 \item \texttt {TwoCocycles}, \hyperpage{695} 4977 \item \texttt {TwoCohomology}, \hyperpage{695} 4978 \item \texttt {TwoCohomologyGeneric}, \hyperpage{584} 4979 \item \texttt {TwoSidedIdeal}, \hyperpage{879} 4980 \item \texttt {TwoSidedIdealByGenerators}, \hyperpage{881} 4981 \item \texttt {TwoSidedIdealNC}, \hyperpage{880} 4982 \item \texttt {TwoSquares}, \hyperpage{216} 4983 \item type 4984 \subitem boolean, \hyperpage{259} 4985 \subitem cyclotomic, \hyperpage{236} 4986 \subitem records, \hyperpage{402} 4987 \subitem strings, \hyperpage{375} 4988 \item \texttt {TypeObj}, \hyperpage{186} 4989 \item \texttt {TypeOfDefaultGeneralMapping}, \hyperpage{469} 4990 \item \texttt {TypeOfOperation}, \hyperpage{1277} 4991 \item \texttt {TzEliminate} 4992 \subitem for a presentation (and a generator), \hyperpage{740} 4993 \subitem for a presentation (and an integer), \hyperpage{740} 4994 \item \texttt {TzFindCyclicJoins}, \hyperpage{741} 4995 \item \texttt {TzGo}, \hyperpage{737} 4996 \item \texttt {TzGoGo}, \hyperpage{738} 4997 \item \texttt {TzImagesOldGens}, \hyperpage{746} 4998 \item \texttt {TzInitGeneratorImages}, \hyperpage{746} 4999 \item \texttt {TzNewGenerator}, \hyperpage{736} 5000 \item \texttt {TzOptions}, \hyperpage{750} 5001 \item \texttt {TzPreImagesNewGens}, \hyperpage{746} 5002 \item \texttt {TzPrint}, \hyperpage{735} 5003 \item \texttt {TzPrintGeneratorImages}, \hyperpage{747} 5004 \item \texttt {TzPrintGenerators}, \hyperpage{734} 5005 \item \texttt {TzPrintLengths}, \hyperpage{734} 5006 \item \texttt {TzPrintOptions}, \hyperpage{752} 5007 \item \texttt {TzPrintPairs}, \hyperpage{735} 5008 \item \texttt {TzPrintPresentation}, \hyperpage{735} 5009 \item \texttt {TzPrintRelators}, \hyperpage{734} 5010 \item \texttt {TzPrintStatus}, \hyperpage{735} 5011 \item \texttt {TzSearch}, \hyperpage{740} 5012 \item \texttt {TzSearchEqual}, \hyperpage{741} 5013 \item \texttt {TzSort}, \hyperpage{727} 5014 \item \texttt {TzSubstitute} 5015 \subitem for a presentation (and an integer and 0/1/2), 5016 \hyperpage{742} 5017 \subitem for a presentation and a word, \hyperpage{742} 5018 \item \texttt {TzSubstituteCyclicJoins}, \hyperpage{745} 5019 5020 \indexspace 5021 5022 \item $u_N$ (irrational value), \hyperpage{243} 5023 \item \texttt {UglyVector}, \hyperpage{946} 5024 \item \texttt {Unbind} 5025 \subitem unbind a list entry, \hyperpage{272} 5026 \subitem unbind a record component, \hyperpage{407} 5027 \subitem unbind a variable, \hyperpage{50} 5028 \item \texttt {Unbind\texttt {\char 92\relax }.}, \hyperpage{409} 5029 \item \texttt {Unbind\texttt {\char 92\relax }[\texttt {\char 92\relax }]}, 5030 \hyperpage{266} 5031 \item \texttt {UnbindElmWPObj}, \hyperpage{1358} 5032 \item \texttt {UnbindGlobal}, \hyperpage{52} 5033 \item \texttt {UnbindInfoOutput}, \hyperpage{109} 5034 \item \texttt {UncoverageLineByLine}, \hyperpage{120} 5035 \item \texttt {UnderlyingCharacteristic} 5036 \subitem for a character, \hyperpage{1114} 5037 \subitem for a character table, \hyperpage{1114} 5038 \item \texttt {UnderlyingCharacterTable}, \hyperpage{1158} 5039 \item \texttt {UnderlyingElement} 5040 \subitem fp group elements, \hyperpage{705} 5041 \subitem of an element in a fp semigroup or monoid, \hyperpage{816} 5042 \item \texttt {UnderlyingExternalSet}, \hyperpage{628} 5043 \item \texttt {UnderlyingFamily}, \hyperpage{987} 5044 \item \texttt {UnderlyingGeneralMapping}, \hyperpage{457} 5045 \item \texttt {UnderlyingGroup} 5046 \subitem for character tables, \hyperpage{1105} 5047 \subitem for tables of marks, \hyperpage{1083} 5048 \item \texttt {UnderlyingInjectionZeroMagma}, \hyperpage{490} 5049 \item \texttt {UnderlyingLeftModule}, \hyperpage{934} 5050 \item \texttt {UnderlyingLieAlgebra}, \hyperpage{995} 5051 \item \texttt {UnderlyingMagma}, \hyperpage{1017} 5052 \item \texttt {UnderlyingRelation}, \hyperpage{457} 5053 \item \texttt {UnderlyingRingElement}, \hyperpage{987} 5054 \item \texttt {UnderlyingSemigroup} 5055 \subitem for a Rees 0-matrix semigroup, \hyperpage{810} 5056 \subitem for a Rees matrix semigroup, \hyperpage{810} 5057 \item \texttt {UnInstallCharReadHookFunc}, \hyperpage{155} 5058 \item \texttt {Union} 5059 \subitem for a list, \hyperpage{421} 5060 \subitem for various collections, \hyperpage{421} 5061 \item union 5062 \subitem of collections, \hyperpage{421} 5063 \subitem of sets, \hyperpage{297} 5064 \item \texttt {Union2}, \hyperpage{421} 5065 \item \texttt {UnionBlist} 5066 \subitem for a list, \hyperpage{317} 5067 \subitem for various boolean lists, \hyperpage{317} 5068 \item \texttt {Unique}, \hyperpage{299} 5069 \item \texttt {UniteBlist}, \hyperpage{318} 5070 \item \texttt {UniteBlistList}, \hyperpage{318} 5071 \item \texttt {UniteSet}, \hyperpage{297} 5072 \item \texttt {Units}, \hyperpage{886} 5073 \item \texttt {UnivariatenessTestRationalFunction}, \hyperpage{1031} 5074 \item \texttt {UnivariatePolynomial}, \hyperpage{1030} 5075 \item \texttt {UnivariatePolynomialByCoefficients}, \hyperpage{1030} 5076 \item \texttt {UnivariatePolynomialRing} 5077 \subitem for a ring (and a name and an exclusion list), 5078 \hyperpage{1042} 5079 \subitem for a ring (and an indeterminate number), \hyperpage{1042} 5080 \item \texttt {Univariate}\discretionary {-}{}{}\texttt {Rational}\discretionary {-}{}{}\texttt {Function}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Coefficients}, 5081 \hyperpage{1039} 5082 \item \texttt {UniversalEnvelopingAlgebra}, \hyperpage{1004} 5083 \item UNIX 5084 \subitem features, \hyperpage{33} 5085 \subitem options, \hyperpage{33} 5086 \item \texttt {UNIXSelect}, \hyperpage{144} 5087 \item \texttt {Unknown}, \hyperpage{1224} 5088 \item \texttt {UnorderedTuples}, \hyperpage{223} 5089 \item \texttt {Unpack} 5090 \subitem for IsVectorObj, \hyperpage{373} 5091 \item \texttt {UnprofileFunctions}, \hyperpage{114} 5092 \item \texttt {UnprofileLineByLine}, \hyperpage{120} 5093 \item \texttt {UnprofileMethods}, \hyperpage{115} 5094 \item \texttt{until}, \hyperpage{62} 5095 \item \texttt {UntraceAllMethods}, \hyperpage{106} 5096 \item \texttt {UntraceImmediateMethods}, \hyperpage{106} 5097 \item \texttt {UntraceMethods} 5098 \subitem for a list of operations, \hyperpage{106} 5099 \subitem for operations, \hyperpage{106} 5100 \item \texttt {UpdateMap}, \hyperpage{1211} 5101 \item \texttt {UpEnv}, \hyperpage{91} 5102 \item \texttt {UppercaseChar}, \hyperpage{385} 5103 \item \texttt {UppercaseString}, \hyperpage{385} 5104 \item \texttt {UpperCentralSeriesOfGroup}, \hyperpage{563} 5105 \item \texttt {UpperSubdiagonal}, \hyperpage{350} 5106 \item \texttt {UseBasis}, \hyperpage{900} 5107 \item \texttt {UseFactorRelation}, \hyperpage{442} 5108 \item \texttt {UseIsomorphismRelation}, \hyperpage{443} 5109 \item \texttt {UserHomeExpand}, \hyperpage{141} 5110 \item \texttt {UserPreference}, \hyperpage{39} 5111 \item \texttt {UseSubsetRelation}, \hyperpage{442} 5112 \item utilities for editing GAP files, \hyperpage{100} 5113 5114 \indexspace 5115 5116 \item $v_N$ (irrational value), \hyperpage{243} 5117 \item \texttt {ValidatePackageInfo}, \hyperpage{1244} 5118 \item \texttt{ValidatePackageInfo}, \hyperpage{1254} 5119 \item \texttt {Valuation}, \hyperpage{1059} 5120 \item \texttt {Value} 5121 \subitem for a univariate rat. function, a value (and a one), 5122 \hyperpage{1034} 5123 \subitem for rat. function, a list of indeterminates, a value (and a one), 5124 \hyperpage{1034} 5125 \item \texttt {ValueCochain}, \hyperpage{1008} 5126 \item \texttt {ValueGlobal}, \hyperpage{52} 5127 \item \texttt {ValueMolienSeries}, \hyperpage{1186} 5128 \item \texttt {ValueOption}, \hyperpage{131} 5129 \item \texttt {ValuePol}, \hyperpage{330} 5130 \item \texttt {ValuesOfClassFunction}, \hyperpage{1158} 5131 \item \texttt {VectorSpace}, \hyperpage{928} 5132 \item \texttt {Vector}\discretionary {-}{}{}\texttt {Space}\discretionary {-}{}{}\texttt {By}\discretionary {-}{}{}\texttt {Pcgs}\discretionary {-}{}{}\texttt {Of}\discretionary {-}{}{}\texttt {Elementary}\discretionary {-}{}{}\texttt {Abelian}\discretionary {-}{}{}\texttt {Group}, 5133 \hyperpage{683} 5134 \item verbosity of GAP output, \hyperpage{107} 5135 \item version number 5136 \subitem for a GAP package, \hyperpage{1262} 5137 \item \texttt{vi}, \hyperpage{100} 5138 \item \texttt {View}, \hyperpage{84} 5139 \item \texttt {ViewObj}, \hyperpage{85} 5140 \subitem for a character table, \hyperpage{1127} 5141 \subitem for a ffe, \hyperpage{918} 5142 \subitem for a string, \hyperpage{376} 5143 \subitem for a table of marks, \hyperpage{1077} 5144 \subitem for class functions, \hyperpage{1163} 5145 \item \texttt {ViewString}, \hyperpage{383} 5146 \item \texttt{vim}, \hyperpage{100} 5147 \item virtual character, \hyperpage{1167} 5148 \item virtual characters, \hyperpage{1155} 5149 \item \texttt {VirtualCharacter} 5150 \subitem for a character table and a list, \hyperpage{1164} 5151 \subitem for a group and a list, \hyperpage{1164} 5152 5153 \indexspace 5154 5155 \item $w_N$ (irrational value), \hyperpage{243} 5156 \item \texttt {WeakPointerObj}, \hyperpage{1357} 5157 \item web sites 5158 \subitem for GAP, \hyperpage{27} 5159 \item \texttt {WedgeGModule}, \hyperpage{1063} 5160 \item \texttt {WeekDay}, \hyperpage{394} 5161 \item \texttt {WeightLexOrdering}, \hyperpage{483} 5162 \item \texttt {WeightOfGenerators}, \hyperpage{484} 5163 \item \texttt {WeightOfVector} 5164 \subitem for IsVectorObj, \hyperpage{373} 5165 \item \texttt {WeightsTom}, \hyperpage{1085} 5166 \item \texttt {WeightVecFFE}, \hyperpage{328} 5167 \item \texttt {WeylGroup}, \hyperpage{998} 5168 \item \texttt {WeylOrbitIterator}, \hyperpage{999} 5169 \item \texttt {Where}, \hyperpage{90} 5170 \item \texttt {WhereWithVars}, \hyperpage{90} 5171 \item \texttt{while} loop, \hyperpage{61} 5172 \item \texttt {WordAlp}, \hyperpage{384} 5173 \item words 5174 \subitem in generators, \hyperpage{532} 5175 \item Wreath product embedding, \hyperpage{758} 5176 \item \texttt {WreathProduct}, \hyperpage{757} 5177 \item \texttt {WreathProductImprimitiveAction}, \hyperpage{757} 5178 \item \texttt {WreathProductOrdering}, \hyperpage{485} 5179 \item \texttt {WreathProductProductAction}, \hyperpage{758} 5180 \item \texttt {WriteAll}, \hyperpage{148} 5181 \item \texttt {WriteByte}, \hyperpage{147} 5182 \item \texttt {WriteGapIniFile}, \hyperpage{39} 5183 \item \texttt {WriteLine}, \hyperpage{147} 5184 5185 \indexspace 5186 5187 \item \texttt {X} 5188 \subitem for a family and a number, \hyperpage{1023} 5189 \subitem for a ring (and a name, and an exclusion list), 5190 \hyperpage{1023} 5191 \subitem for a ring (and a number), \hyperpage{1023} 5192 \item $x_N$ (irrational value), \hyperpage{243} 5193 5194 \indexspace 5195 5196 \item $y_N$ (irrational value), \hyperpage{243} 5197 5198 \indexspace 5199 5200 \item \texttt {Z} 5201 \subitem for field size, \hyperpage{910} 5202 \subitem for prime and degree, \hyperpage{910} 5203 \item \texttt {ZClassRepsQClass}, \hyperpage{662} 5204 \item \texttt {Zero}, \hyperpage{436} 5205 \item \texttt {ZeroAttr}, \hyperpage{436} 5206 \item \texttt {ZeroCoefficient}, \hyperpage{1018} 5207 \item \texttt {ZeroCoefficientRatFun}, \hyperpage{1051} 5208 \item \texttt {ZeroImmutable}, \hyperpage{436} 5209 \item \texttt {ZeroMapping}, \hyperpage{455} 5210 \item \texttt {ZeroMutable}, \hyperpage{436} 5211 \item \texttt {ZeroOp}, \hyperpage{437} 5212 \item \texttt {ZeroSameMutability}, \hyperpage{437} 5213 \item \texttt {ZeroSM}, \hyperpage{437} 5214 \item \texttt {ZeroVector} 5215 \subitem for IsInt,IsVectorObj, \hyperpage{373} 5216 \item \texttt {Zeta}, \hyperpage{255} 5217 \item \texttt {ZippedProduct}, \hyperpage{1053} 5218 \item \texttt {ZippedSum}, \hyperpage{1053} 5219 \item \texttt {ZmodnZ}, \hyperpage{201} 5220 \item \texttt {ZmodnZObj} 5221 \subitem for a residue class family and integer, \hyperpage{201} 5222 \subitem for two integers, \hyperpage{201} 5223 \item \texttt {ZmodpZ}, \hyperpage{201} 5224 \item \texttt {ZmodpZNC}, \hyperpage{201} 5225 \item \texttt {ZumbroichBase}, \hyperpage{924} 5226 \item \texttt {Zuppos}, \hyperpage{573} 5227 5228\end{theindex} 5229