- Introduction
- Coxeter Matrices
- Coxeter Graphs
- Cartan Matrices
- Dynkin Digraphs
- Finite and Affine Coxeter Groups
- IsCoxeterFinite(M) : AlgMatElt -> BoolElt
- IsCoxeterAffine(M) : AlgMatElt -> BoolElt
- Example Cartan_Testing (H102E11)
- CoxeterMatrix(N) : MonStgElt -> AlgMatElt
- CoxeterGraph(N) : MonStgElt -> GrpUnd
- CartanMatrix(N) : MonStgElt -> AlgMatElt
- DynkinDigraph(N) : MonStgElt -> GrphDir
- Example Cartan_MatricesAndGraphs (H102E12)
- IrreducibleCoxeterMatrix(X, n) : MonStgElt, RngIntElt -> AlgMatElt
- IrreducibleCoxeterGraph(X, n) : MonStgElt, RngIntElt -> GrpUnd
- IrreducibleCartanMatrix(X, n) : MonStgElt, RngIntElt -> AlgMatElt
- IrreducibleDynkinDigraph(X, n) : MonStgElt, RngIntElt -> GrphDir
- Example Cartan_IrreducibleCoxeter (H102E13)
- IsCoxeterIsomorphic(N1, N2) : MonStgElt, MonStgElt -> BoolElt
- IsCartanEquivalent(N1, N2) : MonStgElt, MonStgElt -> BoolElt
- Example Cartan_IsomorphismAndEquivalence (H102E14)
- IsSimplyLaced(N) : MonStgElt -> BoolElt
- CoxeterGroupOrder(N) : MonStgElt -> .
- NumberOfPositiveRoots(N) : MonStgElt -> .
- FundamentalGroup(N) : MonStgElt -> GrpAb
- Example Cartan_GroupOrders (H102E15)
- CartanName(M) : AlgMatElt -> MonStgElt
- Example Cartan_CartanName (H102E16)
- DynkinDiagram(M) : AlgMatElt ->
- Example Cartan_DynkinDiagram (H102E17)
- CoxeterDiagram(M) : AlgMatElt ->
- Example Cartan_CoxeterDiagram (H102E18)
- Hyperbolic Groups
- Related Structures
- RootSystem(M) : AlgMatElt -> RootSys
- RootDatum(C) : AlgMatElt -> RootDtm
- CoxeterGroup(GrpFPCox, M) : Cat, AlgMatElt -> GrpFPCox
- CoxeterGroup(GrpPermCox, M) : Cat, AlgMatElt -> GrpPermCox
- CoxeterGroup(M) : AlgMatElt -> GrpPermCox
- ReflectionGroup(M) : AlgMatElt -> GrpMat
- LieAlgebra(C, k) : AlgMatElt, Rng -> AlgLie
- MatrixLieAlgebra(C, k) : AlgMatElt, Rng -> AlgLie
- GroupOfLieType(C, k) : AlgMatElt, Rng -> GrpLie
- Bibliography
V2.28, 13 July 2023