Mappings

• 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 >: Str, Str → Map
    • map< A -> B | x :-> e(x) >: Str, Str → Map
    • map< A -> B | x :-> e(x), y :-> i(y) >: Str, Str → Map
  • Creation of Partial Maps
    • pmap< A -> B | G >: Str, Str → Map
    • pmap< A -> B | x :-> e(x) >: Str, Str → Map
    • pmap< A -> B | x :-> e(x), y :-> i(y) >: Str, Str → Map
  • Creation of Homomorphisms
    • hom< A -> B | G >: Str, Str → Map
    • hom< A -> B | y₁, ..., yₙ >: Str, Str → Map
    • hom< A -> B | x₁ -> y₁, ..., xₙ -> yₙ >: Str, Str → Map
    • hom< A -> B | x :-> e(x) >: Str, Str → Map
    • hom< A -> B | x :-> e(x), y :-> i(y) >: Str, Str → Map
  • Coercion Maps
    • Coercion(D, C): Str, Str → Map
    • Bang(D, C): Str, Str → Map
• Operations on Mappings
  • Composition
    • f * g: Map, Map → Map
    • Components(f): Map → [ Map ]
  • (Co)Domain and (Co)Kernel
    • Domain(f): Map → Str
    • Codomain(f): Map → Str
    • Image(f): Map → Elt
    • Kernel(f): Map → Str
  • Inverse
    • Inverse(m): Map → Map
  • Function
    • Function(f): Map → UserProgram
• Images and Preimages
  • a @ f: Elt, Map → Elt
  • f(a): Map, Elt → Elt
  • S @ f: SetEnum, Map → SetEnum
  • S @ f: SetIndx, Map → SetIndx
  • S @ f: SeqEnum, Map → Seq
  • f(S): SetEnum, Map → SetEnum
  • f(S): SetIndx, Map → SetIndx
  • f(S): SeqEnum, Map → Seq
  • C @ f: Str, Map → Str
  • f(C): Map, Str → Str
  • y @@ f: Elt, Map → Elt
  • R @@ f: SetEnum, Map → SetEnum
  • R @@ f: SetIndx, Map → SetIndx
  • R @@ f: SeqEnum, Map → Seq
  • D @@ f: Str, Map → Str
  • HasPreimage(x, f): Any, Map → BoolElt, Any
• Parents of Maps
  • Parent(m): Map → PowMap
  • Domain(P): PowMap → Str
  • Codomain(P): PowMap → Str
  • Maps(D, C): Str, Str → PowMap
  • Iso(D, C): Str, Str → PowMap
  • Aut(S): Str → PowMapAut