Constructing Coxeter Groups
CoxeterGroup( GrpFPCox, M ) : Cat, AlgMatElt -> GrpFPCox
Example GrpFPCox_ContructFromMatrix (H83E1)
CoxeterGroup( GrpFPCox, N ) : Cat, MonStgElt -> GrpFPCox
Example GrpFPCox_ConstructByName (H83E2)
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 (H83E3)
CartanName( W ) : GrpFPCox -> List
CoxeterDiagram( W ) : GrpFPCox ->
Example GrpFPCox_NamesAndDiagrams (H83E4)
CoxeterMatrix( W ) : GrpFPCox -> AlgMatElt
CoxeterGraph( W ) : GrpFPCox -> GrphUnd
Rank( W ) : GrpFPCox -> RngIntElt
NumberOfPositiveRoots( W ) : GrpFPCox -> RngIntElt
BasicDegrees( W ) : GrpPermCox -> RngIntElt
Example GrpFPCox_BasicDegrees (H83E5)
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 (H83E6)
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 (H83E7)
LongestElement( W ) : GrpFPCox -> SeqEnum
CoxeterElement( W ) : GrpFPCox -> SeqEnum
CoxeterNumber( W ) : GrpFPCox -> SeqEnum
Example GrpFPCox_SpecialWords (H83E8)
LeftDescentSet( W, w ) : GrpFPCox, GrpFPCoxElt -> {}
RightDescentSet( W, w ) : GrpFPCox, GrpFPCoxElt -> {}
Example GrpFPCox_DescentSets (H83E9)
Reflections
IsReflection( w ) : GrpCoxElt -> BoolElt, ., ., RngInt
Reflections( W ) : GrpFPCox -> GrpFPCoxElt
Example GrpFPCox_Reflections (H83E10)
Braid Groups
BraidGroup( W ) : GrpFPCox -> GrpFP, Map
PureBraidGroup( W ) : GrpFPCox -> GrpFP, Map
Example GrpFPCox_BraidGroups (H83E11)
Related Structures
CoxeterGroup( GrpPermCox, W ) : Cat, GrpFPCox -> GrpPermCox
CoxeterGroup( W ) : Cat, GrpFPCox -> GrpPermCox