Introduction
Terminology
The Category of Rewrite Groups
The Construction of a Rewrite Group
Constructing Confluent Presentations
The Knuth-Bendix Procedure RWSGroup(F: parameters) : MonFP -> MonRWS Example GrpRWS_RWSGroup (H65E1)
Defining Orderings RWSGroup(F: parameters) : MonFP -> MonRWS Example GrpRWS_RWSGroup-2 (H65E2) Example GrpRWS_RWSGroup-3 (H65E3)
Setting Limits RWSMonoid(F: parameters) : MonFP -> MonRWS SetVerbose("KBMAG", v) : MonStgElt, RngIntElt ->
Accessing Group Information G . i : GrpRWS, RngIntElt -> GrpRWSElt Generators(G) : GrpRWS -> [GrpRWSElt] NumberOfGenerators(G) : GrpRWS -> RngIntElt Relations(G) : GrpRWS -> [GrpFPRel] NumberOfRelations(G) : GrpRWS -> RngIntElt Ordering(G) : GrpRWS -> String Example GrpRWS_BasicAccess (H65E4)
Properties of a Rewrite Group IsConfluent(G) : GrpRWS -> BoolElt IsFinite(G) : GrpRWS -> BoolElt, RngIntElt Order(G) : GrpRWS -> RngIntElt Example GrpRWS_IsConfluent (H65E5) Example GrpRWS_Order (H65E6)
Arithmetic with Words
Construction of a Word Identity(G) : GrpRWS -> GrpRWSElt G ! [ i1, ..., is ] : GrpRWS, [ RngIntElt ] -> GrpRWSElt Parent(w) : GrpRWSElt -> GrpRWS Example GrpRWS_Words (H65E7)
Element Operations u * v : GrpRWSElt, GrpRWSElt -> GrpRWSElt u / v : GrpRWSElt, GrpRWSElt -> GrpRWSElt u ^ n : GrpRWSElt, RngIntElt -> GrpRWSElt u ^ v : GrpRWSElt, GrpRWSElt -> GrpRWSElt Inverse(w) : GrpRWSElt -> GrpRWSElt (u, v) : GrpRWSElt, GrpRWSElt -> GrpRWSElt (u1, ..., ur) : GrpRWSElt, ..., GrpRWSElt -> GrpRWSElt u eq v : GrpRWSElt, GrpRWSElt -> BoolElt u ne v : GrpRWSElt, GrpRWSElt -> BoolElt IsId(w) : GrpRWSElt -> BoolElt # u : GrpRWSElt -> RngIntElt ElementToSequence(u) : GrpRWSElt -> [ RngIntElt ] Example GrpRWS_Arithmetic (H65E8)
Operations on the Set of Group Elements Random(G, n) : GrpRWS, RngIntElt -> GrpRWSElt Random(G) : GrpRWS -> GrpRWSElt Representative(G) : GrpRWS -> GrpRWSElt Set(G, a, b) : GrpRWS, RngIntElt, RngIntElt -> SetEnum Set(G) : GrpRWS -> SetEnum Seq(G, a, b) : GrpRWS, RngIntElt, RngIntElt -> SeqEnum Example GrpRWS_Set (H65E9)
Homomorphisms
General Remarks
Construction of Homomorphisms hom< R -> G | S > : Struct , Struct -> Map
Conversion to a Finitely Presented Group
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