Introduction

 
Construction of an SLP-Group and its Elements

      Structure Constructors
            SLPGroup(n) : RngIntElt -> GrpSLP
            Example GrpSLP_SLPGroup (H85E1)

      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 (H85E2)

 
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 (H85E3)

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

 
Bibliography

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