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MONOIDS GIVEN BY REWRITE SYSTEMS

 
Introduction
      Terminology
      The Category of Rewrite Monoids
      The Construction of a Rewrite Monoid
 
Construction of a Rewrite Monoid
      Construction of a Word
 
Arithmetic with Words
 
Basic Operations
      Accessing Monoid Information
 
Homomorphisms
      General remarks
      Construction of Homomorphisms
 
Operations on the Set of Elements
      Order Functions
      Set Operations
      Membership and Equality
 
Properties of a Rewrite Monoid
      Rewrite Monoid Predicates
 
Conversion to a Finitely Presented Monoid
 
Bibliography







DETAILS

 
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 (H18E1)

      Construction of a Word
            Identity(M) : MonRWS -> MonRWSElt
            M ! [ i_1, ..., i_s ] : MonRWS, [ RngIntElt ] -> MonRWSElt
            Example MonRWS_Words (H18E2)

 
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 (H18E3)

 
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 (H18E4)

 
Homomorphisms

      General remarks

      Construction of Homomorphisms
            hom< M -> N | S > : Struct , Struct -> Map

 
Operations on the Set of Elements

      Order Functions
            Order(M) : MonRWS -> RngIntElt
            IsFinite(M) : MonRWS -> BoolElt, RngIntElt
            Example MonRWS_Order (H18E5)

      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 (H18E6)

      Membership and Equality
            w in M : MonRWSElt, MonRWS -> BoolElt
            w notin M : MonRWSElt, MonRWS -> BoolElt
            S subset M : { MonRWSElt }, MonRWS -> BoolElt
            S notsubset M : { MonRWSElt }, MonRWS -> BoolElt

 
Properties of a Rewrite Monoid

      Rewrite Monoid Predicates
            IsConfluent(M) : MonRWS -> BoolElt
            Example MonRWS_IsConfluent (H18E7)

 
Conversion to a Finitely Presented Monoid

 
Bibliography