Dictionary from GAP3/Chevie
The dictionary from GAP3/Chevie is as follows:
AbelianGenerators abelian_gens
AbelianInvariants abelian_invariants
Add push!
Affine affine
AlgebraicCentre algebraic_center
AlmostCharacter almost_character or almostchar
Append append!
ApplyFunc(f,l) f(l...)
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 bruhatPoset
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(W) CycPoldegrees(UnipotentCharacters(W))
DecomposedMat diagblocks
DefectSymbol defectsymbol
Degree(p) degree(p)
DegreeFFE degree
DeligneLusztigCharacter deligne_lusztig_character or dlchar
DeligneLusztigLefschetz deligne_lusztig_leftschetz or dlleftschetz
DescribeInvolution describe_involution
DetPerm(W) perm(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
Filtered(l,f) filter(f,l)
FiniteCoxeterTypeFromCartanMat(m) type_cartan(m)
FirstLeftDescending(W,w) firstleftdescent(W,w)
ForAll(l::list,f::function) all(f,l)
ForAny(l::list,f::function) any(f,l)
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 Zbasedring
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_rows
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 is_join_semilattice
IsLeftDescending(W,w,i) isleftdescent(W,w,i)
IsMeetLattice is_meet_semilattice
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 last_moved
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)
List(l,f) map(f,l)
List(l::list,f::function) map(f,l)
ListBlist(a,b) a[b]
ListPerm(p) perm(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)
M::GarsideMonoid.delta M.δ
MappingPermListList mappingPerm
MatStab stab_onmats
MatXPerm(W,p) reflection_representation(W,p) or reflrep
MatYPerm YMatrix
Maximum max or maximum
Minimum min or minimum
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
Number(l,f) count(f,l)
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
PartitionTupleToString string_partition_tuple
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(a,b) cart2lin(a,b)=LinearIndices(reverse(Tuple(a)))[reverse(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
RecFields propertynames
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 first_moved
SmithNormalFormIntegerMat smith
SmithNormalFormIntegerMatTransforms(m) smith_transforms(m)
SolutionIntMat solutionmatInt
SolutionMat solutionmat
Sort sort!
SortBy(l,f) sort!(l,by=f)
SortingPerm(a) inv(sortPerm(a))
SortParallel(a,b) b=b[sortperm(a)];sort!(a)
SpecialPieces special_pieces
Spets spets
Split split
SplitLevis split_levis
Sprint string
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 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 unipotent_character or 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)
ValuePol evalpoly
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
Zip(a1,..,an,f) map(f,a1,...,an)