`ActionOnRespectedPartition`

, for a tame rcwa group 3.4-2`AllElementsOfCTZWithGivenModulus`

3.1-9`AssignGlobals`

7.balanced, definition 2.4

`Ball`

, for group, element and radius 3.3-9`Ball`

, for group, point and radius 3.3-9`Ball`

, for group, point, radius and action 3.3-9`Ball`

, for monoid, element and radius 4.2-2`Ball`

, for monoid, point, radius and action 4.2-2class-wise translating, definition 2.4

class-wise translating, definition 5.1

`ClassPairs`

, m 2.2-3`ClassReflection`

, cl 2.2-2`ClassReflection`

, r, m 2.2-2`ClassRotation`

, cl, u 2.2-4`ClassRotation`

, cl, u; for Z x Z 5.2-3`ClassRotation`

, r, L, u; for Z x Z 5.2-3`ClassRotation`

, r, m, u 2.2-4`ClassShift`

, cl 2.2-1`ClassShift`

, cl, k; for Z x Z 5.2-4`ClassShift`

, r, L, k; for Z x Z 5.2-4`ClassShift`

, r, m 2.2-1`ClassTransposition`

, cl1, cl2 2.2-3`ClassTransposition`

, cl1, cl2 (for Z x Z) 5.2-2`ClassTransposition`

, r1, L1, r2, L2 (for Z x Z) 5.2-2`ClassTransposition`

, r1, m1, r2, m2 2.2-3`ClassWiseConstantOn`

2.4-3`ClassWiseConstantOn`

, for rcwa mappings of Z x Z 5.3`ClassWiseOrderPreservingOn`

2.4-3`ClassWiseOrderPreservingOn`

, for rcwa mappings of Z x Z 5.3`ClassWiseOrderReversingOn`

2.4-3`ClassWiseOrderReversingOn`

, for rcwa mappings of Z x Z 5.3`Coefficients`

, of an rcwa mapping 2.3`Coefficients`

, of an rcwa mapping of Z x Z 5.3Collatz conjecture 1.

Collatz mapping 1.

`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`CT`

, the group generated by all class transpositions of a ring 3.1-9`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`Display`

, for an rcwa mapping 2.2-6`Display`

, for an rcwa mapping of Z x Z 5.3`Display`

, for an rcwa monoid 4.1`DistanceToNextSmallerPointInOrbit`

3.3-2`Div`

, for an rcwa group 3.1-7`Div`

, for an rcwa mapping 2.4divisor, definition 2.1

`Divisor`

, of an rcwa group 3.1-7`Divisor`

, of an rcwa group over Z x Z 5.4`Divisor`

, of an rcwa mapping 2.4`Divisor`

, of an rcwa mapping of Z x Z 5.3`DrawGrid`

, P, yrange, xrange, filename 5.4-2`DrawGrid`

, U, yrange, xrange, filename 5.4-2`DrawOrbitPicture`

, G, p0, bound, h, w, colored, palette, filename 3.3-3`DrawOrbitPicture`

, for rcwa groups over Z x Z 5.4-1`EpimorphismFromFpGroup`

, for an rcwa group and a search radius 3.2-2`EpimorphismFromFpGroup`

, for rcwa group, search radius and bound on number of affine parts 3.2-2`Exponent`

, of an rcwa group 3.2-1`ExtRepOfObj`

2.10-1`ExtRepOfObj`

, for a class transposition 2.2-3`Factorization`

, for an rcwa permutation of Z 2.5-1`FactorizationIntoCSCRCT`

, for an rcwa permutation of Z 2.5-1`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`FixedResidueClasses`

, for rcwa mapping 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`GrowthFunctionOfOrbit`

, for an rcwa group, a point 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`Induction`

, of an rcwa mapping, by an injective rcwa mapping 3.1-7`InfoRCWA`

9.5-1`InjectiveAsMappingFrom`

, for an rcwa mapping 2.7-3integral, definition 2.4

`IntegralConjugate`

, of a tame rcwa group 3.4-2`IntegralConjugate`

, of a tame rcwa permutation 3.4-2`IntegralizingConjugator`

, of a tame rcwa group 3.4-2`IntegralizingConjugator`

, of a tame rcwa permutation 3.4-2`IsBalanced`

, for an rcwa mapping 2.4`IsBalanced`

, for an rcwa mapping of Z x Z 5.3`IsBijective`

, for an rcwa mapping 2.3`IsBijective`

, for an rcwa mapping of Z x Z 5.3`IsClassReflection`

, for an rcwa mapping 2.2-4`IsClassRotation`

, for an rcwa mapping 2.2-4`IsClassRotation`

, for an rcwa mapping of Z x Z 5.2-4`IsClassShift`

, for an rcwa mapping 2.2-4`IsClassShift`

, for an rcwa mapping of Z x Z 5.2-4`IsClassTransposition`

, for an rcwa mapping 2.2-4`IsClassTransposition`

, for an rcwa mapping of Z x Z 5.2-4`IsClassWiseOrderPreserving`

, for an rcwa group 3.1-7`IsClassWiseOrderPreserving`

, for an rcwa mapping 2.4`IsClassWiseOrderPreserving`

, for an rcwa mapping of Z x Z 5.3`IsClassWiseOrderPreserving`

, for an rcwa monoid 4.2`IsClassWiseTranslating`

, for an rcwa group 3.1-7`IsClassWiseTranslating`

, for an rcwa group over Z x Z 5.4`IsClassWiseTranslating`

, for an rcwa mapping 2.4`IsConjugate`

, for elements of CT(R) 3.2-1`IsConjugate`

, for elements of RCWA(R) 3.2-1`IsGeneralizedClassTransposition`

, for an rcwa mapping 2.2-4`IsInjective`

, for an rcwa mapping 2.3`IsInjective`

, for an rcwa mapping of Z x Z 5.3`IsIntegral`

, for an rcwa group 3.1-7`IsIntegral`

, for an rcwa group over Z x Z 5.4`IsIntegral`

, for an rcwa mapping 2.4`IsIntegral`

, for an rcwa mapping of Z x Z 5.3`IsIntegral`

, for an rcwa monoid 4.2`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 GL(2,Z) and a residue class 5.4-1`IsomorphismRcwaGroup`

, for SL(2,Z) and a residue class 5.4-1`IsomorphismRcwaGroup`

, for a group 3.1-1`IsomorphismRcwaGroup`

, for a group, over a given ring 3.1-1`IsOne`

, for an rcwa mapping of Z x Z 5.3`IsPerfect`

, for an rcwa group 3.2-1`IsPrimeSwitch`

, for an rcwa mapping 2.5-2`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`IsSignPreserving`

, for an rcwa mapping 2.4`IsSignPreserving`

, for an rcwa monoid 4.2`IsSolvable`

, for an rcwa group 3.2-1`IsSubset`

, for two rcwa monoids 4.2`IsSurjective`

, for an rcwa mapping 2.3`IsSurjective`

, for an rcwa mapping of Z x Z 5.3`IsTame`

, for an rcwa group 3.2-1`IsTame`

, for an rcwa group over Z x Z 5.4`IsTame`

, for an rcwa mapping 2.3`IsTame`

, for an rcwa mapping of Z x Z 5.3`IsTame`

, for an rcwa monoid 4.2`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`LaTeXAndXDVI`

, for an rcwa mapping of Z x Z 5.3`LaTeXStringRcwaMapping`

, for an rcwa mapping 2.2-6`LaTeXStringRcwaMapping`

, for an rcwa mapping of Z x Z 5.3`LikelyContractionCentre`

, of an rcwa mapping 2.8-11`LoadDatabaseOfGroupsGeneratedBy3ClassTranspositions`

, both databases 6.2-2`LoadDatabaseOfGroupsGeneratedBy3ClassTranspositions`

, small database 6.2-1`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 2.8-9maximal shift, definition 2.4

`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 2.5-3`Mod`

, for an rcwa group 3.1-7`Mod`

, for an rcwa mapping 2.3modulus, definition 2.1

`Modulus`

, of an rcwa group 3.1-7`Modulus`

, of an rcwa group over Z x Z 5.4`Modulus`

, of an rcwa mapping 2.3`Modulus`

, of an rcwa mapping of Z x Z 5.3`Modulus`

, of an rcwa monoid 4.2`ModulusOfRcwaMonoid`

, for an rcwa group 3.1-7`Monoid`

4.1`MonoidByGenerators`

4.1`MovedPoints`

, of an rcwa group 3.3`MovedPoints`

, of an rcwa mapping 2.3`MovedPoints`

, of an rcwa mapping of Z x Z 5.3`Mult`

, for an rcwa group 3.1-7`Mult`

, for an rcwa mapping 2.4multiplier, definition 2.1

`Multiplier`

, of an rcwa group 3.1-7`Multiplier`

, of an rcwa group over Z x Z 5.4`Multiplier`

, of an rcwa mapping 2.4`Multiplier`

, of an rcwa mapping of Z x Z 5.3`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`Orbit`

, for an rcwa group and a set 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`Order`

, of an rcwa permutation 2.3`PermutationOpNC`

, g, P, OnPoints 3.4-1`PreImage`

, of a residue class union under an rcwa mapping 2.3`PreImage`

, of a set of ring elements 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 3.2-3prime set, definition 5.1

`PrimeSet`

, of an rcwa group 3.1-7`PrimeSet`

, of an rcwa mapping 2.4`PrimeSet`

, of an rcwa mapping of Z x Z 5.3`PrimeSet`

, of an rcwa monoid 4.2`PrimeSwitch`

, p 2.5-2`PrimeSwitch`

, p, cl 2.5-2`PrimeSwitch`

, p, k 2.5-2`PrimeSwitch`

, p, r, m 2.5-2`Print`

, for an rcwa group 3.1-7`Print`

, for an rcwa mapping 2.2-6`Print`

, for an rcwa mapping of Z x Z 5.3`Print`

, for an rcwa monoid 4.1`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`Random`

, RCWA(R) 3.5`RankOfKernelOfActionOnRespectedPartition`

, for a tame rcwa group 3.4-2`RCWA`

, the group formed by all rcwa permutations of Z x Z 5.4`RCWA`

, the group formed by all rcwa permutations of a ring 3.1-8`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 5.4rcwa group, class-wise order-preserving 3.1-7

rcwa group, class-wise translating 3.1-7

rcwa group, coercion 2.3

rcwa group, conjugacy problem 3.2-1

rcwa group, definition 2.1

rcwa group, divisor 3.1-7

rcwa group, integral 3.1-7

rcwa group, membership test 3.2-1

rcwa group, modulus 3.1-7

rcwa group, multiplier 3.1-7

rcwa group, prime set 3.1-7

rcwa group, sign-preserving 3.1-7

rcwa group, tame 2.1

rcwa group, wild 2.1

rcwa mapping, arithmetic operations 2.3

rcwa mapping, balanced 2.4

rcwa mapping, class-wise order-preserving 2.4

rcwa mapping, class-wise translating 2.4

rcwa mapping, class-wise translating 5.1

rcwa mapping, coercion 2.3

rcwa mapping, definition 2.1

rcwa mapping, divisor 2.1

rcwa mapping, images under 2.3

rcwa mapping, integral 2.4

rcwa mapping, maximal shift 2.4

rcwa mapping, modulus 2.1

rcwa mapping, modulus 5.1

rcwa mapping, multiplier 2.1

rcwa mapping, of Z x Z, definition 5.1

rcwa mapping, prime set 2.4

rcwa mapping, sign-preserving 2.4

rcwa mapping, sparse representation 2.9

rcwa mapping, tame 2.1

rcwa mapping, transition graph 2.8-4

rcwa mapping, wild 2.1

rcwa monoid, class-wise order-preserving 4.2

rcwa monoid, definition 4.

rcwa monoid, integral 4.2

rcwa monoid, modulus 4.2

rcwa monoid, prime set 4.2

rcwa monoid, sign-preserving 4.2

rcwa monoid, tame 4.2

rcwa monoid, wild 4.2

`rcwa monoids`

, membership test 4.2`RCWABuildManual`

9.3-1`RCWAInfo`

9.5-1`RcwaMapping`

, by arithmetical expression 2.2-5`RcwaMapping`

, by finite field size, modulus and list of coefficients 2.2-5`RcwaMapping`

, by list of coefficients 2.2-5`RcwaMapping`

, by list of coefficients, sparse representation 2.9`RcwaMapping`

, by modulus and list of values 2.2-5`RcwaMapping`

, by permutation and range 2.2-5`RcwaMapping`

, by residue class cycles 2.2-5`RcwaMapping`

, by ring = Z x Z, modulus and coefficients 5.2-1`RcwaMapping`

, by ring and list of coefficients 2.2-5`RcwaMapping`

, by ring, modulus and list of coefficients 2.2-5`RcwaMapping`

, by set of non-invertible primes and list of coefficients 2.2-5`RcwaMapping`

, by two partitions of Z x Z into residue classes 5.2-1`RcwaMapping`

, by two partitions of a ring into residue classes 2.2-5`RcwaMapping`

, of Z x Z, by projections to coordinates 5.2-1`RcwaMapping`

, of Z x Z, by residue class cycles 5.2-1`RcwaMappingsFamily`

, of a ring 2.10-2`RCWATestAll`

9.4-2`RCWATestExamples`

9.4-3`RCWATestInstall`

9.4-1`RepresentativeAction`

, G, source, destination, action 3.3-10`RepresentativeAction`

, for RCWA(R) and 2 partitions of R into residue classes 3.3-12`RepresentativeActionPreImage`

, G, source, destination, action, F 3.3-10`RespectedPartition`

, of a tame rcwa group 3.4-1`RespectedPartition`

, of a tame rcwa permutation 3.4-1`RespectsPartition`

, for an rcwa group 3.4-1`RespectsPartition`

, for an rcwa permutation 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`Restriction`

, of an rcwa mapping, 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`RotationFactor`

, of a class rotation of Z x Z 5.2-3`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`ShortCycles`

, for rcwa permutation, set of points and bound on length 3.3-4`ShortCycles`

, for rcwa permutation, set of points and bounds on length and points 3.3-4`ShortOrbits`

, for rcwa group, set of points and bound on length 3.3-4`ShortOrbits`

, for rcwa group, set of points and bounds on length and points 3.3-4`ShortOrbits`

, for rcwa monoid, set of points and bound on length 4.2-1`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 2.4-5sign-preserving, definition 2.4

`Sinks`

, of an rcwa mapping 2.8-8`Size`

, for an rcwa group 3.2-1`Size`

, for an rcwa group over Z x Z 5.4`Size`

, for an rcwa monoid 4.2`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`SplittedClassTransposition`

, for a class transposition of Z x Z 5.2-2`StandardRep`

, of an rcwa mapping 2.9-1`StandardRepresentation`

, of an rcwa mapping 2.9-1`String`

, for an rcwa group 3.1-7`String`

, for an rcwa mapping 2.2-6`String`

, for an rcwa mapping of Z x Z 5.3`String`

, for an rcwa monoid 4.1`StructureDescription`

, for an rcwa group 3.2-1`Support`

, of an rcwa group 3.3`Support`

, of an rcwa mapping 2.3`Support`

, of an rcwa mapping of Z x Z 5.3`Support`

, of an rcwa monoid 4.2tame, rcwa group 2.1

tame, rcwa mapping 2.1

`Trajectory`

, for rcwa mapping, starting point, length 2.8-1`Trajectory`

, for rcwa mapping, starting point, length, coeff.-spec. 2.8-2`Trajectory`

, for rcwa mapping, starting point, length, modulus 2.8-1`Trajectory`

, for rcwa mapping, starting point, set of end points 2.8-1`Trajectory`

, for rcwa mapping, starting point, set of end points, coeff.-spec. 2.8-2`Trajectory`

, for rcwa mapping, starting point, set of end points, modulus 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`TransposedClasses`

, of a class transposition of Z x Z 5.2-2`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`View`

, for an rcwa mapping 2.2-6`View`

, for an rcwa mapping of Z x Z 5.3`View`

, for an rcwa monoid 4.1wild, rcwa group 2.1

wild, rcwa mapping 2.1

`WreathProduct`

, for an rcwa group over Z and a permutation group 3.1-3`WreathProduct`

, for an rcwa group over Z and the infinite cyclic group 3.1-3`Zero`

, for an rcwa mapping of Z x Z 5.3

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