- Introduction
- Constructing Coxeter Groups
- CoxeterGroup(GrpFPCox, N) : Cat, MonStgElt -> GrpFPCox
- IrreducibleCoxeterGroup(GrpFPCox, X, n) : Cat, MonStgElt, RngIntElt -> GrpFPCox
- Example GrpCox_ConstructByName (H105E1)
- CoxeterGroup(GrpFPCox, M) : Cat, AlgMatElt -> GrpFPCox
- CoxeterGroup(GrpFPCox, G) : Cat, GrphUnd -> GrpFPCox
- CoxeterGroup(GrpFPCox, C) : Cat, AlgMatElt -> GrpFPCox
- CoxeterGroup(GrpFPCox, D) : Cat, GrphDir -> GrpFPCox
- Example GrpCox_ConstructFromMatrix (H105E2)
- CoxeterGroup(GrpFPCox, R) : Cat, RootSys -> GrpFPCox
- CoxeterGroup(A, B) : Mtrx, Mtrx -> GrpPermCox
- Example GrpCox_ConstructByRoot (H105E3)
- Converting Between Types of Coxeter Group
- CoxeterGroup(GrpFPCox, W) : Cat, GrpPermCox -> GrpFPCox, Map
- CoxeterGroup(GrpFPCox, W) : Cat, GrpMat -> GrpFPCox
- CoxeterGroup(GrpPermCox, W) : Cat, GrpFPCox -> GrpPermCox, Map
- CoxeterGroup(GrpPermCox, W) : Cat, GrpMat -> GrpPermCox, Map
- Example GrpCox_ConstructByGroup (H105E4)
- ReflectionGroup(W) : GrpFPCox -> GrpMat, Map
- ReflectionGroup(W) : GrpPermCox -> GrpMat, Map
- Example GrpCox_ReflectionGroupConversion (H105E5)
- CoxeterGroup(GrpFP, W) : Cat, GrpFPCox -> GrpFP, Map
- CoxeterGroup(GrpFP, W) : Cat, GrpPermCox -> GrpFP, Map
- CoxeterGroup(GrpFP, W) : Cat, GrpMat -> GrpPermCox, Map
- CoxeterGroup(GrpPerm, W) : Cat, GrpFPCox -> GrpPerm, Map
- CoxeterGroup(GrpPerm, W) : Cat, GrpPermCox -> GrpPerm, Map
- CoxeterGroup(GrpPerm, W) : Cat, GrpMat -> GrpPermCox, Map
- Operations on Coxeter Groups
- Properties of Coxeter Groups
- Operations on Elements
- Roots, Coroots and Reflections
- Accessing Roots and Coroots
- Operations and Properties for Root and Coroot Indices
- Sum(W, r, s) : GrpPermCox, RngIntElt, RngIntElt -> RngIntElt
- IsPositive(W, r) : GrpPermCox, RngIntElt -> BoolElt
- IsNegative(W, r) : GrpPermCox, RngIntElt -> BoolElt
- Negative(W, r) : GrpPermCox, RngIntElt -> RngIntElt
- LeftString(W, r, s) : GrpPermCox, RngIntElt, RngIntElt -> RngIntElt
- RightString(W, r, s) : GrpPermCox, RngIntElt, RngIntElt -> RngIntElt
- LeftStringLength(W, r, s) : GrpPermCox, RngIntElt, RngIntElt -> RngIntElt
- RightStringLength(W, r, s) : GrpPermCox, RngIntElt, RngIntElt -> RngIntElt
- Example GrpCox_RootArithmetic (H105E19)
- RootHeight(W, r) : GrpPermCox, RngIntElt -> RngIntElt
- RootNorms(W) : GrpPermCox -> [RngIntElt]
- RootNorm(W, r) : GrpPermCox, RngIntElt -> RngIntElt
- IsLongRoot(W, r) : GrpPermCox, RngIntElt -> BoolElt
- IsShortRoot(W, r) : GrpPermCox, RngIntElt -> BoolElt
- Example GrpCox_RootOperations (H105E20)
- Weights
- Reflections
- Reflection Subgroups
- ReflectionSubgroup(W, a) : GrpPermCox, () -> GrpPermCox
- ReflectionSubgroup(W, s) : GrpPermCox, [] -> GrpPermCox
- StandardParabolicSubgroup(W, J) : GrpPermCox, () -> GrpPermCox
- IsReflectionSubgroup(W, H) : GrpPermCox, GrpPermCox -> BoolElt
- IsParabolicSubgroup(W, H) : GrpPermCox, GrpPermCox -> BoolElt
- IsStandardParabolicSubgroup(W, H) : GrpPermCox, GrpPermCox -> BoolElt
- Overgroup(H) : GrpPermCox -> GrpPermCox
- Overdatum(H) : GrpPermCox -> RootDtm
- LocalCoxeterGroup(H) : GrpPermCox -> GrpPermCox, Map
- Example GrpCox_ReflectionSubgroups (H105E24)
- Transversal(W, H) : GrpPermCox, GrpPermCox -> @ @
- TransversalWords(W, H) : GrpPermCox, GrpPermCox -> @ @
- TransversalElt(W, H, x) : GrpPermCox, GrpPermCox, GrpPermElt -> GrpPermElt
- Example GrpCox_Transversals (H105E25)
- TransversalElt(W, x, H) : GrpPermCox, GrpPermElt, GrpPermCox -> GrpPermElt
- TransversalElt(W, H, x, J) : GrpPermCox, GrpPermCox, GrpPermElt, GrpPermCox -> GrpPermElt
- Transversal(W, J) : GrpFPCox, (RngIntElt} -> (@ GrpFPCoxElt @)
- Transversal(W, J, K) : GrpFPCox, (RngIntElt}, (RngIntElt} -> [ GrpFPCoxElt ], [ ]
- DirectProduct(W1, W2) : GrpPermCox, GrpPermCox -> GrpPermCox
- Dual(W) : GrpPermCox -> GrpPermCox
- Example GrpCox_SumDual (H105E26)
- Root Actions
- Standard Action
- Braid Groups
- W-graphs
- SetVerbose("WGraph", v) : MonStgElt, RngIntElt ->
- Mij2EltRootTable(seq) : SeqEnum -> SeqEnum[SeqEnum[RngIntElt]]
- Name2Mij(name) : MonStgElt -> SeqEnum
- Example GrpCox_mijseq (H105E32)
- Partition2WGtable(pi) : SeqEnum -> SeqEnum, GrpFPCox
- WGtable2WG(table) : SeqEnum -> GrphUnd
- TestWG(W,wg) : GrpFPCox, GrphUnd -> .
- Example GrpCox_SpechtWgraph (H105E33)
- WGelement2WGtable(g,K) : GrpFPCoxElt, SetEnum -> SeqEnum, SeqEnum
- Example GrpCox_B5Wgraph (H105E34)
- GetCells(wg) : GrphUnd -> SeqEnum
- InduceWG(W,wg,seq) : GrpFPCox, GrphUnd, SeqEnum -> GrphUnd
- InduceWGtable(J, table, W) : SeqEnum, SeqEnum, GrpFPCox -> SeqEnum[SeqEnum[RngIntElt]]
- IsWGsymmetric(dwg) : GrphDir -> BoolElt, GrphDir
- MakeDirected(uwg) : GrphUnd -> GrphDir
- TestHeckeRep(W,r) : GrpFPCox, SeqEnum -> .
- WG2GroupRep(wg) : GrphUnd -> SeqEnum
- WG2HeckeRep(W,wg) : GrpFPCox, GrphUnd -> SeqEnum
- WGidealgens2WGtable(dgens,K) : SeqEnum, SetEnum -> SeqEnum[SeqEnum[RngIntElt]], SetIndx
- Example GrpCox_WgraphIdeal (H105E35)
- WriteWG(file,uwg) : MonStgElt, GrphUnd -> .
- Related Structures
- Bibliography
V2.28, 13 July 2023