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GROUPS OF STRAIGHT-LINE PROGRAMS

 
Acknowledgements
 
Introduction
 
Construction of an SLP-Group and its Elements
      Structure Constructors
      Construction of an Element
 
Arithmetic with Elements
      Accessing the Defining Generators and Relations
 
Addition of Extra Generators
 
Creating Homomorphisms
 
Operations on Elements
      Equality and Comparison
 
Set-Theoretic Operations
      Membership and Equality
      Set Operations
      Coercions Between Related Groups
 
Bibliography







DETAILS

 
Introduction

 
Construction of an SLP-Group and its Elements

      Structure Constructors
            SLPGroup(n) : RngIntElt -> GrpSLP
            Example GrpSLP_SLPGroup (H76E1)

      Construction of an Element
            Identity(G) : GrpSLP -> GrpSLPElt

 
Arithmetic with Elements
      u * v : GrpSLPElt, GrpSLPElt -> GrpSLPElt
      u ^ m : GrpSLPElt, RngIntElt -> GrpSLPElt
      u ^ v : GrpSLPElt, GrpSLPElt -> GrpSLPElt
      # u : GrpSLPElt -> RngIntElt

      Accessing the Defining Generators and Relations
            G . i : GrpSLP, RngIntElt -> GrpSLPElt
            Generators(G) : GrpSLP -> { GrpSLPElt }
            NumberOfGenerators(G) : GrpSLP -> RngIntElt
            Parent(u) : GrpSLPElt -> GrpSLP

 
Addition of Extra Generators
      AddRedundantGenerators(G, Q) : GrpSLP, [ GrpSLPElt ] -> GrpSLP

 
Creating Homomorphisms
      hom< G -> H | L: parameters> : GrpSLP, Grp -> Map
      Evaluate(u, Q) : GrpSLPElt, [ GrpElt ] -> GrpElt
      Example GrpSLP_ConstructingHomomorphisms (H76E2)

 
Operations on Elements

      Equality and Comparison
            u eq v : GrpSLPElt, GrpSLPElt -> BoolElt
            u ne v : GrpSLPElt, GrpSLPElt -> BoolElt

 
Set-Theoretic Operations

      Membership and Equality
            g in G : GrpSLPElt, GrpSLP -> BoolElt
            g notin G : GrpSLPElt, GrpSLP -> BoolElt
            S subset G : { GrpSLPElt } , GrpSLP -> BoolElt
            S notsubset G : { GrpSLPElt } , GrpSLP -> BoolElt

      Set Operations
            RandomProcess(G) : GrpSLP -> Process
            Random(P) : Process -> GrpSLPElt
            Rep(G) : GrpSLP -> GrpSLPElt
            Example GrpSLP_HomomorphismSpeed (H76E3)

      Coercions Between Related Groups
            G ! g : GrpSLP, GrpSLPElt -> GrpSLPElt

 
Bibliography

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