MAPPINGS

DETAILS

 
Introduction

      The Map Constructors

      The Graph of a Map

      Rules for Maps

      Homomorphisms

      Checking of Maps

 
Creation Functions

      Creation of Maps
            map< A -> B | G > : Struct, Struct -> Map
            map< A -> B | x : -> e(x) > : Struct, Struct -> Map
            map< A -> B | x : -> e(x), y : -> i(y) > : Struct, Struct -> Map

      Creation of Partial Maps
            pmap< A -> B | G > : Struct, Struct -> Map
            pmap< A -> B | x : -> e(x) > : Struct, Struct -> Map
            pmap< A -> B | x : -> e(x), y : -> i(y) > : Struct, Struct -> Map

      Creation of Homomorphisms
            hom< A -> B | G > : Struct, Struct -> Map
            hom< A -> B | y_1, ..., y_n > : Struct, Struct -> Map
            hom< A -> B | x : -> e(x) > : Struct, Struct -> Map
            pmap< A -> B | x : -> e(x), y : -> i(y) > : Struct, Struct -> Map

      Coercion Maps
            Coercion(D, C) : Struct, Struct -> Map

 
Operations on Mappings

      Composition
            f * g : Map, Map -> Map

      (Co)Domain and (Co)Kernel
            Domain(f) : Map -> Struct
            Codomain(f) : Map -> Struct
            Image(f) : Map -> Elt
            Kernel(f) : Map -> Struct

      Function
            Function(f) : Map -> UserProgram

 
Images and Preimages
      a @ f : Elt, Map -> Elt
      S @ f : SetEnum, Map -> SetEnum
      C @ f : Struct, Map -> Struct
      y @@ f : Elt, Map -> Elt
      R @@ f : SetEnum, Map -> SetEnum
      D @@ f : Struct, Map -> Struct