Introduction
Terminology
The Category of Rewrite Monoids
The Construction of a Rewrite Monoid
Construction of a Rewrite Monoid RWSMonoid(Q: parameters) : MonFP -> MonRWS SetVerbose("KBMAG", v) : MonStgElt, RngIntElt -> Example MonRWS_RWSMonoid (H69E1) Example MonRWS_RWSMonoid-2 (H69E2) Example MonRWS_RWSMonoid-4 (H69E3) Example MonRWS_RWSMonoid-5 (H69E4)
Basic Operations
Accessing Monoid Information M . i : MonRWS, RngIntElt -> MonRWSElt Generators(M) : MonRWS -> [ MonRWSElt] NumberOfGenerators(M) : MonRWS -> RngIntElt Relations(M) : MonRWS -> [MonFPRel] NumberOfRelations(M) : MonRWS -> RngIntElt Ordering(M) : MonRWS -> String Parent(w) : MonRWSElt -> MonRWS Example MonRWS_BasicAccess (H69E5)
Properties of a Rewrite Monoid IsConfluent(M) : MonRWS -> BoolElt IsFinite(M) : MonRWS -> BoolElt, RngIntElt Order(M) : MonRWS -> RngIntElt Example MonRWS_order-finite (H69E6) Example MonRWS_order-infinite (H69E7) Example MonRWS_order (H69E8)
Construction of a Word Identity(M) : MonRWS -> MonRWSElt M ! [ i1, ..., is ] : MonRWS, [ RngIntElt ] -> MonRWSElt Example MonRWS_Words (H69E9)
Arithmetic with Words u * v : MonRWSElt, MonRWSElt -> MonRWSElt u ^ n : MonRWSElt, RngIntElt -> MonRWSElt u eq v : MonRWSElt, MonRWSElt -> BoolElt u ne v : MonRWSElt, MonRWSElt -> BoolElt IsId(w) : MonRWSElt -> BoolElt # u : MonRWSElt -> RngIntElt ElementToSequence(u) : MonRWSElt -> [ RngIntElt ] Example MonRWS_Arithmetic (H69E10)
Homomorphisms
General remarks
Construction of Homomorphisms hom< M -> N | S > : Struct , Struct -> Map
Set Operations Random(M, n) : MonRWS, RngIntElt -> MonRWSElt Random(M) : MonRWS -> MonRWSElt Representative(M) : MonRWS -> MonRWSElt Set(M, a, b) : MonRWS, RngIntElt, RngIntElt -> SetEnum Set(M) : MonRWS -> SetEnum Seq(M, a, b) : MonRWS, RngIntElt, RngIntElt -> SeqEnum Seq(M) : MonRWS -> SeqEnum Example MonRWS_Set (H69E11)
Conversion to a Finitely Presented Monoid
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