ActionOnRespectedPartition, for a tame rcwa group  3.4-2AllElementsOfCTZWithGivenModulus  3.1-9AssignGlobals  7.Ball, for group, element and radius  3.3-9Ball, for group, point and radius  3.3-9Ball, for group, point, radius and action  3.3-9Ball, for monoid, element and radius  4.2-2Ball, for monoid, point, radius and action  4.2-2ClassPairs, m  2.2-3ClassReflection, cl  2.2-2ClassReflection, r, m  2.2-2ClassRotation, cl, u  2.2-4ClassRotation, cl, u; for Z x Z  5.2-3ClassRotation, r, L, u; for Z x Z  5.2-3ClassRotation, r, m, u  2.2-4ClassShift, cl  2.2-1ClassShift, cl, k; for Z x Z  5.2-4ClassShift, r, L, k; for Z x Z  5.2-4ClassShift, r, m  2.2-1ClassTransposition, cl1, cl2  2.2-3ClassTransposition, cl1, cl2 (for Z x Z)  5.2-2ClassTransposition, r1, L1, r2, L2 (for Z x Z)  5.2-2ClassTransposition, r1, m1, r2, m2  2.2-3ClassWiseConstantOn  2.4-3ClassWiseConstantOn, for rcwa mappings of Z x Z  5.3ClassWiseOrderPreservingOn  2.4-3ClassWiseOrderPreservingOn, for rcwa mappings of Z x Z  5.3ClassWiseOrderReversingOn  2.4-3ClassWiseOrderReversingOn, for rcwa mappings of Z x Z  5.3Coefficients, of an rcwa mapping  2.3Coefficients, of an rcwa mapping of Z x Z  5.3CollatzLikeMappingByOrbitTree, for rcwa group, root point and range of radii  3.3-13CommonRightInverse, of two injective rcwa mappings  2.7-2ComputeCycleLength, for an rcwa permutation and a point  3.3-6CT, subgroup of CT(Z)  3.1-9CT, the group generated by all class transpositions of Z x Z  5.4CT, the group generated by all class transpositions of a ring  3.1-9CycleRepresentativesAndLengths, for rcwa permutation and set of seed points  3.3-7CyclesOnFiniteOrbit  3.3-4DecreasingOn, for an rcwa mapping  2.8-3DensityOfSetOfFixedPoints, of an rcwa mapping  2.3DensityOfSupport, of an rcwa mapping  2.3DerivedSubgroup, of an rcwa group  3.2-1Determinant, of an rcwa mapping of Z  2.4-4DirectProduct, for rcwa groups over Z  3.1-2Display, for an rcwa group  3.1-7Display, for an rcwa mapping  2.2-6Display, for an rcwa mapping of Z x Z  5.3Display, for an rcwa monoid  4.1DistanceToNextSmallerPointInOrbit  3.3-2Div, for an rcwa group  3.1-7Div, for an rcwa mapping  2.4Divisor, of an rcwa group  3.1-7Divisor, of an rcwa group over Z x Z  5.4Divisor, of an rcwa mapping  2.4Divisor, of an rcwa mapping of Z x Z  5.3DrawGrid, P, yrange, xrange, filename  5.4-2DrawGrid, U, yrange, xrange, filename  5.4-2DrawOrbitPicture, G, p0, bound, h, w, colored, palette, filename  3.3-3DrawOrbitPicture, for rcwa groups over Z x Z  5.4-1EpimorphismFromFpGroup, for an rcwa group and a search radius  3.2-2Exponent, of an rcwa group  3.2-1ExtRepOfObj  2.10-1Factorization, for an rcwa permutation of Z  2.5-1FactorizationIntoCSCRCT, for an rcwa permutation of Z  2.5-1FactorizationOnConnectedComponents, for an rcwa mapping and a modulus  2.8-6FixedPointsOfAffinePartialMappings, for an rcwa mapping  2.4-2FixedResidueClasses, for rcwa group and bound on modulus  3.3-8FixedResidueClasses, for rcwa mapping and bound on modulus  3.3-8GluckTaylorInvariant, of a trajectory  2.8-10Group  3.1GroupByGenerators  3.1GroupByResidueClasses, the group `permuting a given list of residue classes'  3.1-5GroupWithGenerators  3.1GrowthFunctionOfOrbit, for an rcwa group orbit and bounds on radius and sphere size  3.3-2GrowthFunctionOfOrbit, for an rcwa group, a point and bounds on radius and sphere size  3.3-2GuessedDivergence, of an rcwa mapping  2.8-12Image, of an rcwa mapping  2.3ImageDensity, of an rcwa mapping  2.7-3IncreasingOn, for an rcwa mapping  2.8-3Index, for rcwa groups  3.2-1Induction, for an rcwa monoid, by an injective rcwa mapping  4.1-1Induction, of an rcwa group, by an injective rcwa mapping  3.1-7Induction, of an rcwa mapping, by an injective rcwa mapping  3.1-7InfoRCWA  9.5-1InjectiveAsMappingFrom, for an rcwa mapping  2.7-3IntegralConjugate, of a tame rcwa group  3.4-2IntegralConjugate, of a tame rcwa permutation  3.4-2IntegralizingConjugator, of a tame rcwa group  3.4-2IntegralizingConjugator, of a tame rcwa permutation  3.4-2IsBalanced, for an rcwa mapping  2.4IsBalanced, for an rcwa mapping of Z x Z  5.3IsBijective, for an rcwa mapping  2.3IsBijective, for an rcwa mapping of Z x Z  5.3IsClassReflection, for an rcwa mapping  2.2-4IsClassRotation, for an rcwa mapping  2.2-4IsClassRotation, for an rcwa mapping of Z x Z  5.2-4IsClassShift, for an rcwa mapping  2.2-4IsClassShift, for an rcwa mapping of Z x Z  5.2-4IsClassTransposition, for an rcwa mapping  2.2-4IsClassTransposition, for an rcwa mapping of Z x Z  5.2-4IsClassWiseOrderPreserving, for an rcwa group  3.1-7IsClassWiseOrderPreserving, for an rcwa mapping  2.4IsClassWiseOrderPreserving, for an rcwa mapping of Z x Z  5.3IsClassWiseOrderPreserving, for an rcwa monoid  4.2IsClassWiseTranslating, for an rcwa group  3.1-7IsClassWiseTranslating, for an rcwa group over Z x Z  5.4IsClassWiseTranslating, for an rcwa mapping  2.4IsConjugate, for elements of CT(R)  3.2-1IsConjugate, for elements of RCWA(R)  3.2-1IsGeneralizedClassTransposition, for an rcwa mapping  2.2-4IsInjective, for an rcwa mapping  2.3IsInjective, for an rcwa mapping of Z x Z  5.3IsIntegral, for an rcwa group  3.1-7IsIntegral, for an rcwa group over Z x Z  5.4IsIntegral, for an rcwa mapping  2.4IsIntegral, for an rcwa mapping of Z x Z  5.3IsIntegral, for an rcwa monoid  4.2IsNaturalCT  3.6-1IsNaturalRCWA  3.6-1IsomorphismMatrixGroup, for an rcwa group  3.2-1IsomorphismPermGroup, for a finite rcwa group  3.2-1IsomorphismRcwaGroup, for GL(2,Z) and a residue class  5.4-1IsomorphismRcwaGroup, for SL(2,Z) and a residue class  5.4-1IsomorphismRcwaGroup, for a group  3.1-1IsomorphismRcwaGroup, for a group, over a given ring  3.1-1IsOne, for an rcwa mapping of Z x Z  5.3IsPerfect, for an rcwa group  3.2-1IsPrimeSwitch, for an rcwa mapping  2.5-2IsRcwaGroup  3.6-1IsRcwaGroupOverGFqx  3.6-1IsRcwaGroupOverZ  3.6-1IsRcwaGroupOverZ_pi  3.6-1IsRcwaGroupOverZOrZ_pi  3.6-1IsRcwaMapping  2.10-1IsRcwaMappingOfGFqx  2.10-1IsRcwaMappingOfZ  2.10-1IsRcwaMappingOfZ_pi  2.10-1IsRcwaMappingOfZOrZ_pi  2.10-1IsRcwaMappingStandardRep  2.10-1IsSignPreserving, for an rcwa group  3.1-7IsSignPreserving, for an rcwa mapping  2.4IsSignPreserving, for an rcwa monoid  4.2IsSolvable, for an rcwa group  3.2-1IsSubset, for two rcwa monoids  4.2IsSurjective, for an rcwa mapping  2.3IsSurjective, for an rcwa mapping of Z x Z  5.3IsTame, for an rcwa group  3.2-1IsTame, for an rcwa group over Z x Z  5.4IsTame, for an rcwa mapping  2.3IsTame, for an rcwa mapping of Z x Z  5.3IsTame, for an rcwa monoid  4.2IsTransitive, for an rcwa group, on its underlying ring  3.3IsTransitiveOnNonnegativeIntegersInSupport, for an rcwa group over Z  3.3IsZero, for an rcwa mapping of Z x Z  5.3KernelOfActionOnRespectedPartition, for a tame rcwa group  3.4-2LargestSourcesOfAffineMappings, for an rcwa mapping  2.4-1LaTeXAndXDVI, for an rcwa mapping  2.2-6LaTeXAndXDVI, for an rcwa mapping of Z x Z  5.3LaTeXStringRcwaMapping, for an rcwa mapping  2.2-6LaTeXStringRcwaMapping, for an rcwa mapping of Z x Z  5.3LikelyContractionCentre, of an rcwa mapping  2.8-11LoadDatabaseOfGroupsGeneratedBy3ClassTranspositions, small database  6.2-1LoadDatabaseOfGroupsGeneratedBy3ClassTranspositions, small or large database  6.2-2LoadDatabaseOfGroupsGeneratedBy4ClassTranspositions  6.2-3LoadDatabaseOfNonbalancedProductsOfClassTranspositions  6.3-2LoadDatabaseOfProductsOf2ClassTranspositions  6.3-1LoadRCWAExamples  6.1-1LoadRCWAExamples  7.LocalizedRcwaMapping, for an rcwa mapping of Z and a prime  2.2-6Loops, of an rcwa mapping  2.8-9MaximalShift, of an rcwa mapping of Z  2.4MergerExtension, for finite permutation groups  3.1-4Mirrored  3.1-9mKnot, for an odd integer  2.5-3Mod, for an rcwa group  3.1-7Mod, for an rcwa mapping  2.3Modulus, of an rcwa group  3.1-7Modulus, of an rcwa group over Z x Z  5.4Modulus, of an rcwa mapping  2.3Modulus, of an rcwa mapping of Z x Z  5.3Modulus, of an rcwa monoid  4.2ModulusOfRcwaMonoid, for an rcwa group  3.1-7Monoid  4.1MonoidByGenerators  4.1MovedPoints, of an rcwa group  3.3MovedPoints, of an rcwa mapping  2.3MovedPoints, of an rcwa mapping of Z x Z  5.3Mult, for an rcwa group  3.1-7Mult, for an rcwa mapping  2.4Multiplier, of an rcwa group  3.1-7Multiplier, of an rcwa group over Z x Z  5.4Multiplier, of an rcwa mapping  2.4Multiplier, of an rcwa mapping of Z x Z  5.3Multpk, for an rcwa mapping, a prime and an exponent  2.4-3Multpk, for rcwa mapping of Z x Z, prime and exponent  5.3NrClassPairs, m  2.2-3NrConjugacyClassesOfRCWAZOfOrder  3.1-8NrConjugacyClassesOfCTZOfOrder  3.1-9NrElementsOfCTZWithGivenModulus  3.1-9ObjByExtRep  2.10-1One, for an rcwa mapping of Z x Z  5.3Orbit, for an rcwa group and a point  3.3-1Orbit, for an rcwa group and a set  3.3-1OrbitLengthBound  3.2-1OrbitsModulo, for an rcwa group and a modulus  3.3-11OrbitsModulo, for an rcwa mapping and a modulus  2.8-5Order, of an rcwa mapping of Z x Z  5.3Order, of an rcwa permutation  2.3PermutationOpNC, g, P, OnPoints  3.4-1PreImage, of a residue class union under an rcwa mapping  2.3PreImage, of a set of ring elements under an rcwa mapping  2.3PreImageElm, of a ring element under an rcwa mapping  2.3PreImagesElm, of a ring element under an rcwa mapping  2.3PreImagesRepresentative, for an epi. from a free group to an rcwa group  3.2-3PreImagesRepresentatives, for an epi. from a free group to an rcwa group  3.2-3PrimeSet, of an rcwa group  3.1-7PrimeSet, of an rcwa mapping  2.4PrimeSet, of an rcwa mapping of Z x Z  5.3PrimeSet, of an rcwa monoid  4.2PrimeSwitch, p  2.5-2PrimeSwitch, p, k  2.5-2Print, for an rcwa group  3.1-7Print, for an rcwa mapping  2.2-6Print, for an rcwa mapping of Z x Z  5.3Print, for an rcwa monoid  4.1ProjectionsToCoordinates, for an rcwa mapping of Z x Z  5.3-1ProjectionsToInvariantUnionsOfResidueClasses, for rcwa group and modulus  3.3-11Random, CT(R)  3.5Random, RCWA(R)  3.5RankOfKernelOfActionOnRespectedPartition, for a tame rcwa group  3.4-2RCWA, the group formed by all rcwa permutations of Z x Z  5.4RCWA, the group formed by all rcwa permutations of a ring  3.1-8Rcwa, the monoid formed by all rcwa mappings of a ring  4.1-1Rcwa, the monoid formed by all rcwa permutations of Z x Z  5.4rcwa monoids, membership test  4.2RCWABuildManual  9.3-1RCWAInfo  9.5-1RcwaMapping, by arithmetical expression  2.2-5RcwaMapping, by finite field size, modulus and list of coefficients  2.2-5RcwaMapping, by list of coefficients  2.2-5RcwaMapping, by list of coefficients, sparse representation  2.9RcwaMapping, by modulus and list of values  2.2-5RcwaMapping, by permutation and range  2.2-5RcwaMapping, by residue class cycles  2.2-5RcwaMapping, by ring = Z x Z, modulus and coefficients  5.2-1RcwaMapping, by ring and list of coefficients  2.2-5RcwaMapping, by ring, modulus and list of coefficients  2.2-5RcwaMapping, by set of non-invertible primes and list of coefficients  2.2-5RcwaMapping, by two partitions of Z x Z into residue classes  5.2-1RcwaMapping, by two partitions of a ring into residue classes  2.2-5RcwaMapping, of Z x Z, by projections to coordinates  5.2-1RcwaMapping, of Z x Z, by residue class cycles  5.2-1RcwaMappingsFamily, of a ring  2.10-2RCWATestAll  9.4-2RCWATestExamples  9.4-3RCWATestInstall  9.4-1RepresentativeAction, G, source, destination, action  3.3-10RepresentativeAction, for RCWA(R) and 2 partitions of R into residue classes  3.3-12RepresentativeActionPreImage, G, source, destination, action, F  3.3-10RespectedPartition, of a tame rcwa group  3.4-1RespectedPartition, of a tame rcwa permutation  3.4-1RespectsPartition, for an rcwa group  3.4-1RespectsPartition, for an rcwa permutation  3.4-1RestrictedBall, G, g, r, modulusbound  3.3-9RestrictedPerm, for an rcwa permutation and a residue class union  2.3Restriction, for an rcwa monoid, by an injective rcwa mapping  4.1-1Restriction, of an rcwa group, by an injective rcwa mapping  3.1-6Restriction, of an rcwa mapping, by an injective rcwa mapping  3.1-6RightInverse, of an injective rcwa mapping  2.7-1Root, k-th root of an rcwa mapping  2.6-1RotationFactor, of a class rotation  2.2-4RotationFactor, of a class rotation of Z x Z  5.2-3SemilocalizedRcwaMapping, for an rcwa mapping of Z and a set of primes  2.2-6ShiftsDownOn  2.4-3ShiftsUpOn  2.4-3ShortCycles, for rcwa perm. of Z x Z, set of points and max. length  5.3ShortCycles, for rcwa permutation and bound on length  3.3-4ShortCycles, for rcwa permutation, set of points and bound on length  3.3-4ShortCycles, for rcwa permutation, set of points and bounds on length and points  3.3-4ShortOrbits, for rcwa group, set of points and bound on length  3.3-4ShortOrbits, for rcwa group, set of points and bounds on length and points  3.3-4ShortOrbits, for rcwa monoid, set of points and bound on length  4.2-1ShortResidueClassCycles, for rcwa permutation and bounds on modulus and length  3.3-5ShortResidueClassOrbits, for rcwa group and bounds on modulus and length  3.3-5Sign, of an rcwa permutation of Z  2.4-5Sinks, of an rcwa mapping  2.8-8Size, for an rcwa group  3.2-1Size, for an rcwa group over Z x Z  5.4Size, for an rcwa monoid  4.2SmallGeneratingSet  3.1-7Sources, of an rcwa mapping  2.8-8SparseRep, of an rcwa mapping  2.9-1SparseRepresentation, of an rcwa mapping  2.9-1SplittedClassTransposition, for a class transposition and a number of factors  2.2-3SplittedClassTransposition, for a class transposition of Z x Z  5.2-2StandardRep, of an rcwa mapping  2.9-1StandardRepresentation, of an rcwa mapping  2.9-1String, for an rcwa group  3.1-7String, for an rcwa mapping  2.2-6String, for an rcwa mapping of Z x Z  5.3String, for an rcwa monoid  4.1StructureDescription, for an rcwa group  3.2-1Support, of an rcwa group  3.3Support, of an rcwa mapping  2.3Support, of an rcwa mapping of Z x Z  5.3Support, of an rcwa monoid  4.2Trajectory, for rcwa mapping, starting point, length  2.8-1Trajectory, for rcwa mapping, starting point, length, coeff.-spec.  2.8-2Trajectory, for rcwa mapping, starting point, length, modulus  2.8-1Trajectory, for rcwa mapping, starting point, set of end points  2.8-1Trajectory, for rcwa mapping, starting point, set of end points, coeff.-spec.  2.8-2Trajectory, for rcwa mapping, starting point, set of end points, modulus  2.8-1Trajectory, for rcwa mappings of Z x Z  5.3TransitionGraph, for an rcwa mapping and a modulus  2.8-4TransitionMatrix, for an rcwa mapping and a modulus  2.8-7TransitivityCertificate, for an rcwa group over Z and a search limit  3.3TransposedClasses, of a class transposition  2.2-3TransposedClasses, of a class transposition of Z x Z  5.2-2TryIsTransitiveOnNonnegativeIntegersInSupport, for an rcwa group over Z and a search limit  3.3TryToComputeTransitivityCertificate, for an rcwa group over Z and a search limit  3.3View, for an rcwa group  3.1-7View, for an rcwa mapping  2.2-6View, for an rcwa mapping of Z x Z  5.3View, for an rcwa monoid  4.1WreathProduct, for an rcwa group over Z and a permutation group  3.1-3WreathProduct, for an rcwa group over Z and the infinite cyclic group  3.1-3Zero, for an rcwa mapping of Z x Z  5.3
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