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 (H87E1)
      Example MonRWS_RWSMonoid-2 (H87E2)
      Example MonRWS_RWSMonoid-4 (H87E3)
      Example MonRWS_RWSMonoid-5 (H87E4)

 
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 (H87E5)

      Properties of a Rewrite Monoid
            IsConfluent(M) : MonRWS -> BoolElt
            IsFinite(M) : MonRWS -> BoolElt, RngIntElt
            Order(M) : MonRWS -> RngIntElt
            Example MonRWS_order-finite (H87E6)
            Example MonRWS_order-infinite (H87E7)
            Example MonRWS_order (H87E8)

      Construction of a Word
            Identity(M) : MonRWS -> MonRWSElt
            M ! [ i₁, ..., i_s ] : MonRWS, [ RngIntElt ] -> MonRWSElt
            Example MonRWS_Words (H87E9)

      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 (H87E10)

 
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 (H87E11)

 
Conversion to a Finitely Presented Monoid
      Example MonRWS_Conversion (H87E12)

 
Bibliography

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