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 (H74E1)
Defining Orderings
RWSGroup(F: parameters) : MonFP -> MonRWS
Example GrpRWS_RWSGroup-2 (H74E2)
Example GrpRWS_RWSGroup-3 (H74E3)
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 (H74E4)
Properties of a Rewrite Group
IsConfluent(G) : GrpRWS -> BoolElt
IsFinite(G) : GrpRWS -> BoolElt, RngIntElt
Order(G) : GrpRWS -> RngIntElt
Example GrpRWS_IsConfluent (H74E5)
Example GrpRWS_Order (H74E6)
Construction of a Word
Identity(G) : GrpRWS -> GrpRWSElt
G ! [ i1, ..., is ] : GrpRWS, [ RngIntElt ] -> GrpRWSElt
Parent(w) : GrpRWSElt -> GrpRWS
Example GrpRWS_Words (H74E7)
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 (H74E8)
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
Seq(G) : GrpRWS -> SeqEnum
Example GrpRWS_Set (H74E9)
Construction of Homomorphisms
hom< R -> G | S > : Struct , Struct -> Map
Conversion to a Finitely Presented Group
Example GrpRWS_Conversion (H74E10)
Bibliography
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Version: V2.19 of
Wed Apr 24 15:09:57 EST 2013