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Magma
Computer • algebra
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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 | y
1
, ..., y
n
> : 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
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
S @ f : SetEnum, Map -> SetEnum
C @ f : Str, Map -> Str
y @@ f : Elt, Map -> Elt
R @@ f : SetEnum, Map -> SetEnum
D @@ f : Str, Map -> Str
HasPreimage(x, f) : Any, Map -> BoolElt, Any
Parents of Maps
Parent(m) : Map -> PowMap
Domain(P) : PowMap -> Str
Maps(D, C) : Str, Str -> PowMap
Aut(S) : Str -> PowMapAut
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V2.28, 28 February 2025