ActionOnRespectedPartition, for a tame rcwa group 3.4-2 AllElementsOfCTZWithGivenModulus 3.1-9 AssignGlobals 7. Ball, for group, element and radius 3.3-9 ClassPairs, m 2.2-3 ClassReflection, cl 2.2-2 ClassRotation, cl, u 2.2-4 ClassShift, cl 2.2-1 ClassTransposition, cl1, cl2 2.2-3 ClassWiseConstantOn 2.4-3 ClassWiseOrderPreservingOn 2.4-3 ClassWiseOrderReversingOn 2.4-3 Coefficients, of an rcwa mapping 2.3 CollatzLikeMappingByOrbitTree, for rcwa group, root point and range of radii 3.3-13 CommonRightInverse, of two injective rcwa mappings 2.7-2 ComputeCycleLength, for an rcwa permutation and a point 3.3-6 CT, subgroup of CT(Z) 3.1-9 CT, the group generated by all class transpositions of Z x Z 5.4 CTCSCRSplit, for an rcwa permutation of Z 2.5-1 CycleRepresentativesAndLengths, for rcwa permutation and set of seed points 3.3-7 CyclesOnFiniteOrbit 3.3-4 DecreasingOn, for an rcwa mapping 2.8-3 DensityOfSetOfFixedPoints, of an rcwa mapping 2.3 DensityOfSupport, of an rcwa mapping 2.3 DerivedSubgroup, of an rcwa group 3.2-1 Determinant, of an rcwa mapping of Z 2.4-4 DirectProduct, for rcwa groups over Z 3.1-2 Display, for an rcwa group 3.1-7 DistanceToNextSmallerPointInOrbit 3.3-2 Div, for an rcwa group 3.1-7 Divisor, of an rcwa group 3.1-7 DrawGrid, P, yrange, xrange, filename 5.4-2 DrawOrbitPicture, for rcwa groups over Z x Z 5.4-1 DrawOrbitPicture, G, p0, bound, h, w, colored, palette, filename 3.3-3 EpimorphismFromFpGroup, for an rcwa group and a search radius 3.2-2 Exponent, of an rcwa group 3.2-1 ExtRepOfObj 2.10-1 Factorization, for an rcwa permutation of Z 2.5-2 FactorizationIntoCSCRCT, for an rcwa permutation of Z 2.5-2 FactorizationOnConnectedComponents, for an rcwa mapping and a modulus 2.8-6 FixedPointsOfAffinePartialMappings, for an rcwa mapping 2.4-2 FixedResidueClasses, for rcwa group and bound on modulus 3.3-8 GluckTaylorInvariant, of a trajectory 2.8-10 Group 3.1 GroupByGenerators 3.1 GroupByResidueClasses, the group `permuting a given list of residue classes' 3.1-5 GroupWithGenerators 3.1 GrowthFunctionOfOrbit, for an rcwa group orbit and bounds on radius and sphere size 3.3-2 GuessedDivergence, of an rcwa mapping 2.8-12 Image, of an rcwa mapping 2.3 ImageDensity, of an rcwa mapping 2.7-3 IncreasingOn, for an rcwa mapping 2.8-3 Index, for rcwa groups 3.2-1 Induction, for an rcwa monoid, by an injective rcwa mapping 4.1-1 Induction, of an rcwa group, by an injective rcwa mapping 3.1-7 InfoRCWA 9.4-1 InjectiveAsMappingFrom, for an rcwa mapping 2.7-3 IntegralConjugate, of a tame rcwa group 3.4-2 IntegralizingConjugator, of a tame rcwa group 3.4-2 IsBalanced, for an rcwa mapping 2.4 IsBijective, for an rcwa mapping 2.3 IsClassReflection, for an rcwa mapping 2.2-4 IsClassRotation, for an rcwa mapping 2.2-4 IsClassShift, for an rcwa mapping 2.2-4 IsClassTransposition, for an rcwa mapping 2.2-4 IsClassWiseOrderPreserving, for an rcwa group 3.1-7 IsClassWiseTranslating, for an rcwa group 3.1-7 IsConjugate, for elements of CT(R) 3.2-1 IsGeneralizedClassTransposition, for an rcwa mapping 2.2-4 IsInjective, for an rcwa mapping 2.3 IsIntegral, for an rcwa group 3.1-7 IsNaturalCT 3.6-1 IsNaturalRCWA 3.6-1 IsomorphismMatrixGroup, for an rcwa group 3.2-1 IsomorphismPermGroup, for a finite rcwa group 3.2-1 IsomorphismRcwaGroup, for a group 3.1-1 IsOne, for an rcwa mapping of Z x Z 5.3 IsPerfectGroup, for an rcwa group 3.2-1 IsPrimeSwitch, for an rcwa mapping 2.5-3 IsRcwaGroup 3.6-1 IsRcwaGroupOverGFqx 3.6-1 IsRcwaGroupOverZ 3.6-1 IsRcwaGroupOverZ_pi 3.6-1 IsRcwaGroupOverZOrZ_pi 3.6-1 IsRcwaMapping 2.10-1 IsRcwaMappingOfGFqx 2.10-1 IsRcwaMappingOfZ 2.10-1 IsRcwaMappingOfZ_pi 2.10-1 IsRcwaMappingOfZOrZ_pi 2.10-1 IsRcwaMappingStandardRep 2.10-1 IsSignPreserving, for an rcwa group 3.1-7 IsSolvableGroup, for an rcwa group 3.2-1 IsSubset, for two rcwa monoids 4.2 IsSurjective, for an rcwa mapping 2.3 IsTame, for an rcwa group 3.2-1 IsTransitive, for an rcwa group, on its underlying ring 3.3 IsTransitiveOnNonnegativeIntegersInSupport, for an rcwa group over Z 3.3 IsZero, for an rcwa mapping of Z x Z 5.3 KernelOfActionOnRespectedPartition, for a tame rcwa group 3.4-2 LargestSourcesOfAffineMappings, for an rcwa mapping 2.4-1 LaTeXAndXDVI, for an rcwa mapping 2.2-6 LaTeXStringRcwaMapping, for an rcwa mapping 2.2-6 LikelyContractionCentre, of an rcwa mapping 2.8-11 LoadDatabaseOfGroupsGeneratedBy3ClassTranspositions, both databases 6.2-2 LoadDatabaseOfGroupsGeneratedBy4ClassTranspositions 6.2-3 LoadDatabaseOfNonbalancedProductsOfClassTranspositions 6.3-2 LoadDatabaseOfProductsOf2ClassTranspositions 6.3-1 LoadRCWAExamples 6.1-1 LoadRCWAExamples 7. LocalizedRcwaMapping, for an rcwa mapping of Z and a prime 2.2-6 Loops, of an rcwa mapping 2.8-9 MaximalShift, of an rcwa mapping of Z 2.4 MergerExtension, for finite permutation groups 3.1-4 Mirrored 3.1-9 mKnot, for an odd integer 2.5-4 Mod, for an rcwa group 3.1-7 Modulus, of an rcwa group 3.1-7 ModulusOfRcwaMonoid, for an rcwa group 3.1-7 Monoid 4.1 MonoidByGenerators 4.1 MovedPoints, of an rcwa group 3.3 Mult, for an rcwa group 3.1-7 Multiplier, of an rcwa group 3.1-7 Multpk, for an rcwa mapping, a prime and an exponent 2.4-3 Multpk, for rcwa mapping of Z x Z, prime and exponent 5.3 NrClassPairs, m 2.2-3 NrConjugacyClassesOfRCWAZOfOrder 3.1-8 NrConjugacyClassesOfCTZOfOrder 3.1-9 NrElementsOfCTZWithGivenModulus 3.1-9 ObjByExtRep 2.10-1 One, for an rcwa mapping of Z x Z 5.3 Orbit, for an rcwa group and a point 3.3-1 OrbitLengthBound 3.2-1 OrbitsModulo, for an rcwa group and a modulus 3.3-11 OrbitsModulo, for an rcwa mapping and a modulus 2.8-5 Order, of an rcwa mapping of Z x Z 5.3 PermutationOpNC, g, P, OnPoints 3.4-1 PreImage, of a residue class union under an rcwa mapping 2.3 PreImageElm, of a ring element under an rcwa mapping 2.3 PreImagesElm, of a ring element under an rcwa mapping 2.3 PreImagesRepresentative, for an epi. from a free group to an rcwa group 3.2-3 PreImagesRepresentatives, for an epi. from a free group to an rcwa group 3.2-3 PrimeSet, of an rcwa group 3.1-7 PrimeSwitch, p 2.5-3 Print, for an rcwa group 3.1-7 ProjectionsToCoordinates, for an rcwa mapping of Z x Z 5.3-1 ProjectionsToInvariantUnionsOfResidueClasses, for rcwa group and modulus 3.3-11 Random, CT(R) 3.5 RankOfKernelOfActionOnRespectedPartition, for a tame rcwa group 3.4-2 RCWA, the group formed by all rcwa permutations of a ring 3.1-8 RCWA, the group formed by all rcwa permutations of Z x Z 5.4 Rcwa, the monoid formed by all rcwa mappings of a ring 4.1-1 Rcwa, the monoid formed by all rcwa permutations of Z x Z 5.4 rcwa monoids, membership test 4.2 RCWAInfo 9.4-1 RcwaMapping, by arithmetical expression 2.2-5 RcwaMapping, by list of coefficients, sparse representation 2.9 RcwaMapping, by modulus and list of values 2.2-5 RcwaMappingsFamily, of a ring 2.10-2 RCWATestAll 9.3-2 RCWATestExamples 9.3-3 RCWATestInstall 9.3-1 RepresentativeAction, for RCWA(R) and 2 partitions of R into residue classes 3.3-12 RepresentativeActionPreImage, G, source, destination, action, F 3.3-10 ResidueClassCyclesThroughResidueClass, for rcwa permutation, residue class and bound on modulus 3.3-5 RespectedPartition, of a tame rcwa group 3.4-1 RespectsPartition, for an rcwa group 3.4-1 RestrictedBall, G, g, r, modulusbound 3.3-9 RestrictedPerm, for an rcwa permutation and a residue class union 2.3 Restriction, for an rcwa monoid, by an injective rcwa mapping 4.1-1 Restriction, of an rcwa group, by an injective rcwa mapping 3.1-6 RightInverse, of an injective rcwa mapping 2.7-1 Root, k-th root of an rcwa mapping 2.6-1 RotationFactor, of a class rotation 2.2-4 SemilocalizedRcwaMapping, for an rcwa mapping of Z and a set of primes 2.2-6 ShiftsDownOn 2.4-3 ShiftsUpOn 2.4-3 ShortCycles, for rcwa perm. of Z x Z, set of points and max. length 5.3 ShortCycles, for rcwa permutation and bound on length 3.3-4 ShortOrbits, for rcwa group, set of points and bound on length 3.3-4 ShortResidueClassCycles, for rcwa permutation and bounds on modulus and length 3.3-5 ShortResidueClassOrbits, for rcwa group and bounds on modulus and length 3.3-5 Sign, of an rcwa permutation of Z 2.4-5 SimplifiedCertificate, for a transitivity certificate of an rcwa groups over Z 3.3 Sinks, of an rcwa mapping 2.8-8 Size, for an rcwa group 3.2-1 SmallGeneratingSet 3.1-7 Sources, of an rcwa mapping 2.8-8 SparseRep, of an rcwa mapping 2.9-1 SparseRepresentation, of an rcwa mapping 2.9-1 SplittedClassTransposition, for a class transposition and a number of factors 2.2-3 StandardRep, of an rcwa mapping 2.9-1 StandardRepresentation, of an rcwa mapping 2.9-1 String, for an rcwa group 3.1-7 StructureDescription, for an rcwa group 3.2-1 SupersetOfOrbitRepresentatives, for an rcwa group over Z and search limits 3.3 Support, of an rcwa group 3.3 Trajectory, for rcwa mapping, starting point, length 2.8-1 Trajectory, for rcwa mappings of Z x Z 5.3 TransitionGraph, for an rcwa mapping and a modulus 2.8-4 TransitionMatrix, for an rcwa mapping and a modulus 2.8-7 TransitivityCertificate, for an rcwa group over Z and a search limit 3.3 TransposedClasses, of a class transposition 2.2-3 TryIsTransitiveOnNonnegativeIntegersInSupport, for an rcwa group over Z and a search limit 3.3 TryToComputeTransitivityCertificate, for an rcwa group over Z and a search limit 3.3 View, for an rcwa group 3.1-7 WreathProduct, for an rcwa group over Z and a permutation group 3.1-3 Zero, for an rcwa mapping of Z x Z 5.3
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