Constructing Coxeter Groups
CoxeterGroup(GrpFPCox, M) : Cat, AlgMatElt -> GrpFPCox
Example GrpFPCox_ContructFromMatrix (H86E1)
CoxeterGroup(GrpFPCox, N) : Cat, MonStgElt -> GrpFPCox
IrreducibleCoxeterGroup(GrpFPCox, X, n) : Cat, MonStgElt, RngIntElt -> GrpFPCox
Example GrpFPCox_ConstructByName (H86E2)
CoxeterGroup(GrpFPCox, R) : Cat, RootSys -> GrpFPCox
CoxeterGroup(GrpFPCox, W) : Cat, GrpPermCox -> GrpFPCox, Map
CoxeterGroup(GrpFPCox, W) : Cat, GrpMat -> GrpFPCox
Operations on Coxeter Groups
IsCoxeterIsomorphic(W1, W2) : GrpFPCox, GrpFPCox -> BoolElt
Example GrpFPCox_CoxeterIsomorphism (H86E3)
CartanName(W) : GrpFPCox -> List
CoxeterDiagram(W) : GrpFPCox ->
Example GrpFPCox_NamesAndDiagrams (H86E4)
CoxeterMatrix(W) : GrpFPCox -> AlgMatElt
CoxeterGraph(W) : GrpFPCox -> GrphUnd
Rank(W) : GrpFPCox -> RngIntElt
NumberOfPositiveRoots(W) : GrpFPCox -> RngIntElt
BasicDegrees(W) : GrpPermCox -> RngIntElt
Example GrpFPCox_BasicDegrees (H86E5)
Properties of Coxeter Groups
IsFinite(W) : GrpFPCox -> BoolElt
IsAffine(W) : GrpFPCox -> BoolElt
IsHyperbolic(W) : GrpFPCox -> BoolElt
IsCompactHyperbolic(W) : GrpFPCox -> BoolElt
IsIrreducible(W) : GrpFPCox -> BoolElt
IsSimplyLaced(W) : GrpFPCox -> BoolElt
Example GrpFPCox_Properties (H86E6)
Operations on Words
W ! [i_1,...,i_m] : GrpFPCox, SeqEnum[RngIntElt] -> GrpFPCoxElt
Identity(W) : GrpFPCox -> GrpFPCoxElt
w1 eq w2 : GrpFPElt, GrpFPElt -> BoolElt
w1 * w2 : GrpFPCoxElt, GrpFPCoxElt -> GrpFPCoxElt
w ^ n : GrpFPCoxElt, RngIntElt -> GrpFPCoxElt
# w : GrpFPCoxElt -> RngIntElt
Example GrpFPCox_WordArithmetic (H86E7)
LongestElement(W) : GrpFPCox -> SeqEnum
CoxeterElement(W) : GrpFPCox -> SeqEnum
CoxeterNumber(W) : GrpFPCox -> SeqEnum
Example GrpFPCox_SpecialWords (H86E8)
LeftDescentSet(W, w) : GrpFPCox, GrpFPCoxElt -> {}
RightDescentSet(W, w) : GrpFPCox, GrpFPCoxElt -> {}
Example GrpFPCox_DescentSets (H86E9)
Reflections
IsReflection(w) : GrpCoxElt -> BoolElt, ., ., RngInt
Reflections(W) : GrpFPCox -> GrpFPCoxElt
Example GrpFPCox_Reflections (H86E10)
Constructing Coxeter Groups from Existing Coxeter Groups
DirectSum(W1, W2) : GrpPermCox, GrpPermCox -> GrpPermCox
Example GrpFPCox_SumDual (H86E11)
Braid Groups
BraidGroup(W) : GrpFPCox -> GrpFP, Map
PureBraidGroup(W) : GrpFPCox -> GrpFP, Map
Example GrpFPCox_BraidGroups (H86E12)
Related Structures
CoxeterGroup(GrpPermCox, W) : Cat, GrpFPCox -> GrpPermCox
CoxeterGroup(W) : Cat, GrpFPCox -> GrpPermCox