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 mapping 1.
Collatz conjecture 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
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 2.5-1
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
    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 9.5-1
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
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
    for an rcwa mapping 2.4
    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
    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 2.5-3
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 2.5-2
    p, cl 2.5-2
    p, k 2.5-2
    p, r, m 2.5-2
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
RCWABuildManual 9.3-1
RCWAInfo 9.5-1
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 9.4-2
RCWATestExamples 9.4-3
RCWATestInstall 9.4-1
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
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
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