GAP (RCWA) - Index

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### Index

`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
for group, point and radius 3.3-9
for group, point, radius and action 3.3-9
for monoid, element and radius 4.2-2
for monoid, point, radius and action 4.2-2
class-wise translating, definition 2.4 5.1
`ClassPairs`, m 2.2-3
`ClassReflection`, cl 2.2-2
r, m 2.2-2
`ClassRotation`, cl, u 2.2-4
cl, u; for Z x Z 5.2-3
r, L, u; for Z x Z 5.2-3
r, m, u 2.2-4
`ClassShift`, cl 2.2-1
cl, k; for Z x Z 5.2-4
r, L, k; for Z x Z 5.2-4
r, m 2.2-1
`ClassTransposition`, cl1, cl2 2.2-3
cl1, cl2 (for Z x Z) 5.2-2
r1, L1, r2, L2 (for Z x Z) 5.2-2
r1, m1, r2, m2 2.2-3
`ClassWiseConstantOn` 2.4-3
for rcwa mappings of Z x Z 5.3
`ClassWiseOrderPreservingOn` 2.4-3
for rcwa mappings of Z x Z 5.3
`ClassWiseOrderReversingOn` 2.4-3
for rcwa mappings of Z x Z 5.3
`Coefficients`, of an rcwa mapping 2.3
of an rcwa mapping of Z x Z 5.3
Collatz 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
the group generated by all class transpositions of a ring 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
for an rcwa mapping 2.2-6
for an rcwa mapping of Z x Z 5.3
for an rcwa monoid 4.1
`DistanceToNextSmallerPointInOrbit` 3.3-2
`Div`, for an rcwa group 3.1-7
for an rcwa mapping 2.4
divisor, definition 2.1
`Divisor`, of an rcwa group 3.1-7
of an rcwa group over Z x Z 5.4
of an rcwa mapping 2.4
of an rcwa mapping of Z x Z 5.3
`DrawGrid`, P, yrange, xrange, filename 5.4-2
U, 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
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
for a class transposition 2.2-3
`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
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
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
of an rcwa mapping, by an injective rcwa mapping 3.1-7
`InfoRCWA` 9.4-1
`InjectiveAsMappingFrom`, for an rcwa mapping 2.7-3
integral, definition 2.4
`IntegralConjugate`, of a tame rcwa group 3.4-2
of a tame rcwa permutation 3.4-2
`IntegralizingConjugator`, of a tame rcwa group 3.4-2
of a tame rcwa permutation 3.4-2
`IsBalanced`, for an rcwa mapping 2.4
for an rcwa mapping of Z x Z 5.3
`IsBijective`, for an rcwa mapping 2.3
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
for an rcwa mapping of Z x Z 5.2-4
`IsClassShift`, for an rcwa mapping 2.2-4
for an rcwa mapping of Z x Z 5.2-4
`IsClassTransposition`, for an rcwa mapping 2.2-4
for an rcwa mapping of Z x Z 5.2-4
`IsClassWiseOrderPreserving`, for an rcwa group 3.1-7
for an rcwa mapping 2.4
for an rcwa mapping of Z x Z 5.3
for an rcwa monoid 4.2
`IsClassWiseTranslating`, for an rcwa group 3.1-7
for an rcwa group over Z x Z 5.4
for an rcwa mapping 2.4
`IsConjugate`, for elements of CT(R) 3.2-1
for elements of RCWA(R) 3.2-1
`IsGeneralizedClassTransposition`, for an rcwa mapping 2.2-4
`IsInjective`, for an rcwa mapping 2.3
for an rcwa mapping of Z x Z 5.3
`IsIntegral`, for an rcwa group 3.1-7
for an rcwa group over Z x Z 5.4
for an rcwa mapping 2.4
for an rcwa mapping of Z x Z 5.3
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 a group 3.1-1
for a group, over a given ring 3.1-1
for GL(2,Z) and a residue class 5.4-1
for SL(2,Z) and a residue class 5.4-1
`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
for an rcwa mapping 2.4
for an rcwa monoid 4.2
`IsSolvableGroup`, for an rcwa group 3.2-1
`IsSubset`, for two rcwa monoids 4.2
`IsSurjective`, for an rcwa mapping 2.3
for an rcwa mapping of Z x Z 5.3
`IsTame`, for an rcwa group 3.2-1
for an rcwa group over Z x Z 5.4
for an rcwa mapping 2.3
for an rcwa mapping of Z x Z 5.3
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
for an rcwa mapping of Z x Z 5.3
`LaTeXStringRcwaMapping`, for an rcwa mapping 2.2-6
for an rcwa mapping of Z x Z 5.3
`LikelyContractionCentre`, of an rcwa mapping 2.8-11
`LoadDatabaseOfGroupsGeneratedBy3ClassTranspositions`, both databases 6.2-2
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 2.8-9
maximal 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 2.5-4
`Mod`, for an rcwa group 3.1-7
for an rcwa mapping 2.3
modulus, definition 2.1
`Modulus`, of an rcwa group 3.1-7
of an rcwa group over Z x Z 5.4
of an rcwa mapping 2.3
of an rcwa mapping of Z x Z 5.3
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
of an rcwa mapping 2.3
of an rcwa mapping of Z x Z 5.3
`Mult`, for an rcwa group 3.1-7
for an rcwa mapping 2.4
multiplier, definition 2.1
`Multiplier`, of an rcwa group 3.1-7
of an rcwa group over Z x Z 5.4
of an rcwa mapping 2.4
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
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
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
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 3.2-3
prime set, definition 5.1
`PrimeSet`, of an rcwa group 3.1-7
of an rcwa mapping 2.4
of an rcwa mapping of Z x Z 5.3
of an rcwa monoid 4.2
`PrimeSwitch`, p 2.5-3
p, cl 2.5-3
p, k 2.5-3
p, r, m 2.5-3
`Print`, for an rcwa group 3.1-7
for an rcwa mapping 2.2-6
for an rcwa mapping of Z x Z 5.3
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
RCWA(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 group, class-wise order-preserving 3.1-7
class-wise translating 3.1-7
coercion 2.3
conjugacy problem 3.2-1
definition 2.1
divisor 3.1-7
integral 3.1-7
membership test 3.2-1
modulus 3.1-7
multiplier 3.1-7
prime set 3.1-7
sign-preserving 3.1-7
tame 2.1
wild 2.1
rcwa mapping, arithmetic operations 2.3
balanced 2.4
class-wise order-preserving 2.4
class-wise translating 2.4 5.1
coercion 2.3
definition 2.1
divisor 2.1
images under 2.3
integral 2.4
maximal shift 2.4
modulus 2.1 5.1
multiplier 2.1
of Z x Z, definition 5.1
prime set 2.4
sign-preserving 2.4
sparse representation 2.9
tame 2.1
transition graph 2.8-4
wild 2.1
rcwa monoid, class-wise order-preserving 4.2
definition 4.
integral 4.2
modulus 4.2
prime set 4.2
sign-preserving 4.2
tame 4.2
wild 4.2
`rcwa monoids`, membership test 4.2
`RCWAInfo` 9.4-1
`RcwaMapping`, by arithmetical expression 2.2-5
by finite field size, modulus and list of coefficients 2.2-5
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
by permutation and range 2.2-5
by residue class cycles 2.2-5
by ring = Z x Z, modulus and coefficients 5.2-1
by ring and list of coefficients 2.2-5
by ring, modulus and list of coefficients 2.2-5
by set of non-invertible primes and list of coefficients 2.2-5
by two partitions of a ring into residue classes 2.2-5
by two partitions of Z x Z into residue classes 5.2-1
of Z x Z, by projections to coordinates 5.2-1
of Z x Z, by residue class cycles 5.2-1
`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
G, source, destination, action 3.3-10
`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
of a tame rcwa permutation 3.4-1
`RespectsPartition`, for an rcwa group 3.4-1
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
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
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
for rcwa permutation, set of points and bound on length 3.3-4
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
for rcwa group, set of points and bounds on length and points 3.3-4
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 2.4-5
sign-preserving, definition 2.4
`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
for an rcwa group over Z x Z 5.4
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
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
for an rcwa mapping 2.2-6
for an rcwa mapping of Z x Z 5.3
for an rcwa monoid 4.1
`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
of an rcwa mapping 2.3
of an rcwa mapping of Z x Z 5.3
of an rcwa monoid 4.2
tame, rcwa group 2.1
rcwa mapping 2.1
`Trajectory`, for rcwa mapping, starting point, length 2.8-1
for rcwa mapping, starting point, length, coeff.-spec. 2.8-2
for rcwa mapping, starting point, length, modulus 2.8-1
for rcwa mapping, starting point, set of end points 2.8-1
for rcwa mapping, starting point, set of end points, coeff.-spec. 2.8-2
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
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
for an rcwa mapping 2.2-6
for an rcwa mapping of Z x Z 5.3
for an rcwa monoid 4.1
wild, rcwa group 2.1
rcwa mapping 2.1
`WreathProduct`, for an rcwa group over Z and a permutation group 3.1-3
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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