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BLACK-BOX GROUPS

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







DETAILS

 
Introduction

 
Construction of an SLP-Group and its Elements

      Structure Constructors
            NaturalBlackBoxGroup(H) : Grp -> GrpBB

      Construction of an Element
            Identity(G) : GrpBB -> GrpBBElt

 
Arithmetic with Elements
      u * v : GrpBBElt, GrpBBElt -> GrpBBElt
      u ^ m : GrpBBElt, RngIntElt -> GrpBBElt
      u ^ v : GrpBBElt, GrpBBElt -> GrpBBElt
      (u, v) : GrpBBElt, GrpBBElt -> GrpBBElt

      Accessing the Defining Generators
            G . i : GrpBB, RngIntElt -> GrpBBElt
            Generators(G) : GrpBB -> { GrpBBElt }
            NumberOfGenerators(G) : GrpBB -> RngIntElt

 
Operations on Elements

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

      Attributes of Elements
            Parent(u) : GrpBBElt -> GrpBB
            UnderlyingElement(u) : GrpBBElt -> GrpElt
            Order(u) : GrpBBElt -> RngIntElt
            Example GrpBB_standard-gens (H64E1)

 
Set-Theoretic Operations

      Membership and Equality
            g in G : GrpBBElt, GrpBB -> BoolElt

      Set Operations
            PseudoRandom(G) : GrpBB -> GrpBBElt
            Rep(G) : GrpBB -> GrpBBElt

      Coercions Between Related Groups
            G ! g : GrpBB, GrpBBElt -> GrpBBElt

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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013