Dictionary from GAP3/Chevie
The dictionary from GAP3/Chevie is as follows:
AbelianGenerators abelian_gens
AbelianInvariants abelian_invariants
Affine affine
AlgebraicCentre algebraic_center
AlmostCharacter AlmostChar
Arrangements arrangements
AsFraction fraction
AsReflection reflection
AsRootOfUnity Root1
AssociatedPartition conjugate_partition
AsWord word
AsymptoticAlgebra AsymptoticAlgebra
BadPrimes badprimes
BaseIntMat baseInt
Basis basis
BetaSet βset
BigCellDecomposition bigcell_decomposition
Binomial binomial
BipartiteDecomposition bipartite_decomposition
BlocksMat blocks
Braid BraidMonoid
BraidMonoid BraidMonoid
BraidRelations braid_relations
BrieskornNormalForm Brieskorn_normal_form
Bruhat bruhatless
BruhatPoset Poset
BruhatSmaller bruhatless
CartanMat("A",5) cartan(:A,5)
CartanMatFromCoxeterMatrix cartan
CartanMatrix cartan
Cartesian cartesian
CartesianAt lin2cart
Catalan catalan
CentralIdempotents centralidempotents
Centralizer centralizer
CentralizerGenerators centralizer_gens
CharFFE char
CharNames charnames
CharParams(W) charinfo(W).charparams
CharRepresentationWords traces_words_mats
CharTable CharTable
CheckHeckeDefiningRelations isrepresentation
ChevieCharInfo charinfo
ChevieClassInfo classinfo
ClassName see ClassNames
ClassTypes ClassTypes
Coefficient(p,i) p[i]
CollectBy(l,f) collectby(f,l)
Collected tally
Combinations combinations
Comm comm or commutator
ComplementIntMat complementInt
ComplexConjugate conj
ComplexReflectionGroup complex_reflection_group or crg
Compositions compositions
Concatenation(s::Vector) vcat(s...)
ConcatenationString(s...) prod([s...])
ConjugacyClasses conjugacy_classes
ConjugacySet(b[,F][,type]) conjcat(b[,F],ss=type).obj
ConjugatePartition conjugate_partition
CoxeterCoset spets
CoxeterElements(W[,l]) elements(W[,l])
CoxeterGroup("A",5) coxeter_group(:A,5) or coxgroup
CoxeterGroupByCartanMatrix(C) coxeter_group(C) or coxgroup
CoxeterGroupByCoxeterMatrix(C) coxeter_group(cartan(C)) or coxgroup
CoxeterGroupHyperoctaedralGroup(n) coxeter_hyperoctaedral_group(n) or coxhyp
CoxeterGroupSymmetricGroup(n) coxeter_symmetric_group(n) or coxsym
CoxeterLength(W,w) length(W,w)
CoxeterMatrix coxmat or coxeter_matrix
CoxeterMatrixFromCartanMat coxmat or coxeter_matrix
CoxeterNumber coxnum or coxeter_number
CoxeterSubCoset subspets
CoxeterWord(W,w) word(W,w)
CoxeterWords(W[,l]) word.(Ref(W),elements(W[,l]))
CuspidalPairs cuspidal_data
CuspidalUnipotentCharacters(W[,d]) cuspidal(UnipotentCharacters(W)[,d])
Cycle orbit
Cycles orbits
CyclotomicModP(c,p) FFE{p}(c)
CyclotomicPolynomial(R,i) cyclotomic_polynomial(i)
CycPol CycPol
CycPolFakeDegreeSymbol fegsymbol
CycPolGenericDegreeSymbol gendeg_symbol
CycPolUnipotentDegrees CycPolUnipotentDegrees
DecomposedMat diagblocks
DefectSymbol defectsymbol
Degree(p) degree(p)
DegreeFFE degree
DeligneLusztigCharacter DLChar
DeligneLusztigLefschetz DLLeftschetz
DescribeInvolution describe_involution
DetPerm(W) vec(detPerm(W))
DiaconisGraham diaconis_graham
DiagonalMat Diagonal or cat
DiagonalOfMat diag
Digits digits
Dimension dim or dimension
DistinguishedParabolicSubgroups distinguished_parabolics
Dominates dominates
DrinfeldDouble drinfeld_double
Drop deleteat!
DualBraid DualBraidMonoid
DualBraidMonoid DualBraidMonoid
EigenspaceProjector eigenspace_projector
EigenvaluesMat eigmat
Elements elements
ElementWithInversions(W,l) with_inversions(W,l)
EltBraid image
EltWord(W,w) W(w...)
ER root
ExteriorPower exterior_power
FactorizedSchurElement FactorizedSchurElement
FactorizedSchurElements FactorizedSchurElements
FakeDegree fakedegree
FakeDegrees fakedegrees
FamiliesClassical FamiliesClassical
Family Family
FamilyImprimitive family_imprimitive
FiniteCoxeterTypeFromCartanMat(m) type_cartan(m)
FirstLeftDescending(W,w) firstleftdescent(W,w)
ForEachCoxeterWord(W,f) for w in W f(word(W,w)) end
ForEachElement(W,f) for w in W f(w) end
FormatTable showtable
Frobenius Frobenius
FullSymbol fullsymbol
FundamentalGroup fundamental_group
FusionAlgebra fusion_algebra
FusionConjugacyClasses fusion_conjugacy_classes
GaloisCyc galois
GarsideAlpha α
GarsideWords elements
GcdPartitions gcd_partitions
GcdRepresentation(x,y) gcdx(x,y)[2:3]
GenericOrder generic_order
GenericSign generic_sign
GetRoot root
GraphAutomorphisms graph_automorphisms
Hasse hasse
Hecke hecke
HeckeCentralMonomials central_monomials
HeckeCharValues char_values
HeckeClassPolynomials class_polynomials
HeckeReflectionRepresentation reflection_representation or reflrep
HermiteNormalFormIntegerMat hermite
HermiteNormalFormIntegerMatTransforms(m) hermite_transforms(m)
HighestPowerFakeDegrees(W) charinfo(W).B
HighestPowerFakeDegreeSymbol degree_fegsymbol
HighestPowerGenericDegrees(W) charinfo(W).A
HighestPowerGenericDegreeSymbol degree_gendeg_symbol
HighestShortRoot highest_short_root
HyperplaneOrbits hyperplane_orbits
ICCTable ICCTable
Idempotents idempotents
Incidence incidence
IndependentLines independent_lines
IndependentRoots independent_roots
InducedLinearForm induced_linear_form
InductionTable induction_table
Inherit look at merge for hashes
IntermediateGroup intermediate_group
Intersection intersect
IntFFE Int
IntListToString joindigits
InvariantForm invariant_form
Invariants invariants
Inversions inversions
IsAbelian isabelian
IsAssociative isassociative
IsCyclic iscyclic
IsCycPol(p) p isa CycPol
IsFamily(f) f isa Family
IsFFE(x) x isa FFE
IsIsolated isisolated
IsJoinLattice isjoin_lattice
IsLeftDescending(W,w,i) isleftdescent(W,w,i)
IsMeetLattice ismeet_lattice
IsomorphismType isomorphism_type
IsParabolic isparabolic
IsSubset(a,b) issubset(b,a)
IsUnipotentElement(x) x isa UnipotentElement
JInductionTable J_induction_table
jInductionTable j_induction_table
Join join
KazhdanLusztigPolynomial KLPol
KroneckerProduct kron
LargestMovedPoint largest_moved_point
last ans
LcmPartitions lcm_partitions
LeadingCoefficient(p) p[end]
LeftCell LeftCell
LeftCells left_cells
LeftDescentSet(W,w) leftdescents(W,w)
LeftDivisorsSimple left_divisors
LeftGcd leftgcd
LeftLcm leftlcm
Length(W.generators) ngens(W) or number_of_generators(W)
LinearExtension linear_extension
List(ConjugacyClasses(G),Representative) classreps(G) or class_representatives(G)
ListBlist(a,b) a[b]
ListPerm(p) vec(p)
LoewyLength loewylength
LogFFE log
LongestCoxeterElement(W) longest(W)
LongestCoxeterWord(W) word(W,longest(W))
LowestPowerFakeDegrees(W) charinfo(W).b
LowestPowerFakeDegreeSymbol valuation_fegsymbol
LowestPowerGenericDegrees(W) charinfo(W).a
LowestPowerGenericDegreeSymbol valuation_gendeg_symbol
Lusztigaw Lusztigaw
LusztigAw LusztigAw
LusztigInduction lusztig_induce
LusztigInductionTable lusztig_induction_table
LusztigRestriction lusztig_restrict
M.LeftLcmSimples(x...) leftlcm(M,...)
M.RightLcmSimples(x...) rightlcm(M,...)
M.ToOrdinary(i) B(M,i)
MappingPermListList mappingPerm
MatStab stab_onmats
MatXPerm(W,p) reflection_representation(W,p) or reflrep
MatYPerm YMatrix
Mod1 modZ
MovedPoints support
Mvp("x") Mvp(:x)
NrArrangements narrangements
NrCombinations ncombinations
NrConjugacyClasses nconjugacy_classes
NrDrinfeldDouble ndrinfeld_double
NrPartitions npartitions
NrPartitionsSet npartitions
NrPartitionTuples npartition_tuples
NrRestrictedPartitions npartitions
NullMat(m[,n]) zeros(Int,m,m) resp. zeros(Int,m,n)
NullspaceIntMat lnullspaceInt
OnFamily(f,p::Int) galois(f,p)
OnFamily(f,p::Perm) f^p
OnMatrices onmats
OnPolynomials(m,p) p^m
OnSets onsets
OnTuples ontuples
OrderedPartitions compositions
OrderFFE order
OrderMod(n,m) order(Mod{m}(n))
ParabolicClosure parabolic_closure
ParabolicRepresentatives parabolic_reps
PartBeta partβ
Partition partition
Partitions partitions
PartitionsSet partitions
PartitionTuples partition_tuples
PermCosetsSubgroup(H,W) D=vcat(reduced(H,W)...);map(s->Perm(reduced.(Ref(H),D.*s),D),gens(W))
PermList(v) Perm(v)
PermListList(l1,l2) Perm(l1,l2)
PermMatMat(m,n) Perm(m,n;dims=(1,2))
PermMatX PermX
PermMatY PermY
PermutationMat(p,dim) Matrix(p,dim)
PermutationOnCharacters on_chars
PermutationOnClasses on_classes
PermutationOnUnipotents on_unipotents
Permuted(v,p) invpermute(v,p)
PermutedByCols(m,p) invpermute(m,p;dims=2)
Poset Poset
Position(l,x) findfirst(==(x),l)
PositionCartesian cart2lin
PositionCartesian(a,b) LinearIndices(reverse(Tuple(a)))[CartesianIndices(Tuple(b))]
PositionClass position_class
PositionDet charinfo(W).positionDet
PositionId charinfo(W).positionId
PositionProperty(l,f) findfirst(f,l)
PositionRegularClass position_regular_class
Positions(l,x) findall(==(x),l)
PositionsProperty(l,f) findall(f,l)
PowerRoot(x,y) (Root1(;r=x)^y).r
Presentation Presentation
PrintDiagram(W) diagram(W)
Product prod
ProportionalityCoefficient(v,w) ratio(v,w)
QuasiIsolatedRepresentatives quasi_isolated_reps
QuoInt div
Radical radical
RadicalPower radicalpower
Rank rank
RankSymbol ranksymbol
ReducedCoxeterWord(W,w) word(W,W(w...))
ReducedExpressions(W,w) words(W,w)
ReducedInRightCoset(W,w) reduced(W,w)
ReducedRightCosetRepresentatives(W,H) reduced(H,W)
Reflection refls(W,i) or reflectionMatrix(root,coroot)
ReflectionCharacter reflection_character or reflchar
ReflectionCharValue tr(reflrep(W,w))
ReflectionCoDegrees(W) codegrees(W)
ReflectionDegrees(W) degrees(W)
ReflectionEigenvalues refleigen
ReflectionGroup reflection_group
ReflectionLength(W,w) reflength(W,w)
ReflectionName(W) repr(W;context=:limit=>true)
Reflections Perm.(reflections(W)[1:nhyp(W)])
ReflectionSubgroup reflection_subgroup
ReflectionType refltype
RegularEigenvalues regular_eigenvalues
RelativeDegrees relative_degrees
RelativeGroup relative_group
Replace replace
Representations representations
RepresentativeConjugation(b,b'[,F][,type]) conjugating_elt(b,b'[,F],ss=type)
RepresentativeDiagonalConjugation diagconj_elt
RepresentativeOperation transporting_elt or transporting_element
RepresentativeRowColPermutation Perm_rowcol
Restricted restricted
RestrictedPartitions partitions
RestrictedPerm(p,d) restricted(p,d)
Reversed reverse
ReversedWord reverse
RightDescentSet(W,w) rightdescents(W,w)
RightGcd rightgcd
RightLcm rightlcm
RootDatum rootdatum
RootsCartan(m) roots(m)
Rotation(v,i) circshift(v,-i)
Rotations(v) circshift.(Ref(v),length(v):-1:1)
ScalarProduct Chars.scalarproduct
ScalMvp scalar
SchurElements schur_elements
SchurFunctor schur_functor
SemisimpleCentralizerRepresentatives semisimple_centralizer_representatives or sscentralizer_reps
SemisimpleElement ss
SemisimpleRank semisimplerank
SemisimpleSubgroup torsion_subgroup
ShiftBeta shiftβ
ShrinkGarsideGeneratingSet shrink
SignedMatStab sstab_onmats
SignedPerm SPerm
SignedPermListList SPerm
SignedPermMatMat(M,N) SPerm(M,N;dims=(1,2))
Size(W) length(W)
SmallestMovedPoint smallest_moved_point
SmithNormalFormIntegerMat smith
SmithNormalFormIntegerMatTransforms(m) smith_transforms(m)
SolutionIntMat solutionmatInt
SolutionMat solutionmat
SortingPerm(a) inv(sortPerm(a))
SortParallel(a,b) b=b[sortperm(a)];sort!(a)
SpecialPieces special_pieces
Spets spets
SplitLevis split_levis
Stabilizer stabilizer
StandardParabolic standard_parabolic
StandardParabolicClass standard_parabolic_class
StructureRationalPointsConnectedCentre structure_rational_points_connected_centre
SubSpets subspets
SubTorus SubTorus
Sum sum
SumIntersectionMat(m,n) (rowspace(vcat(m,n)),intersect_rowspace(m,n))
Symbols HasType.BDSymbols
SymbolsDefect(e,r,def,ct) symbols(e,r,ct,def)
SymmetricDifference symdiff
SymmetricPower symmetric_power
Tableaux tableaux
Tensored(c,d) vec([i.*j for i in c,j ind])
Torus torus
TorusOrder torus_order
TraceMat tr
TransitiveClosure transitive_closure
Transporter transporter
TransposedMat transpose or permutedims
Transversals related to transversal and orbits
TriangulizeMat echelon!
Twistings twistings
TwoTree(m) twotree(m)
UnipotentAbelianPart abelianpart
UnipotentCharacter UniChar
UnipotentCharacters UnipotentCharacters
UnipotentClasses UnipotentClasses
UnipotentDecompose decompose
UnipotentDegrees(W,q) degrees(UnipotentCharacters(W),q)
UnipotentGroup UnipotentGroup
UnorderedTuples multisets
Valuation(p) valuation(p)
Value(p,x) p(x)
W.generators gens(W) or generators(W)
W.matgens reflection_representation(W) or reflrep
W.matgens[i] reflection_representation(W,i) or reflrep
W.N nref(W) or number_of_reflections(W)
W.Nhyp number_of_hyperplanes(W) or nyp(W)
W.orbitRepresentative simple_reps(W)
W.orbitRepresentativeElements[i] simple_conjugating(W,i)
W.OrdersGeneratingReflections ordergens(W) or orders_of_generators(W)
W.rootInclusion inclusion(W)
W.rootLengths rootlengths(W)
W.rootRestriction restriction(W)
W.roots W.rootdec
W.simpleCoroots simplecoroots(W)
W.simpleRoots simpleroots(W)
WeightInfo weightinfo
WGraph Wgraph
WGraphToRepresentation WGraphToRepresentation