map -- make a map

Usage:

map(Y,X,d) or map(Y,X)
Inputs:
- Y, an object, such as a ring, module, or chain complex
- X, another object of the same type
- d, a specification, such as a function, list, or matrix, or if omitted, understood to specify the identity map
Optional inputs:
- Degree => ..., default value null, specify the degree of a map
- DegreeLift => ..., default value null, make a ring map
- DegreeMap => ..., default value null, make a ring map
Outputs:
- a map to Y from X defined by data d.

Description

The function map provides a general mechanism for constructing a map (homomorphism) between rings (a ring map), modules (a matrix), or between objects in other categories.

See also the function matrix, which focuses on creating new matrices from rectangular arrays of ring elements or matrices.

map(Module,Module,Function) -- create a matrix by specifying a function that gives each entry
map(Module,Module,List) -- create a matrix by giving a sparse or dense list of entries
map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
map(Module,Module,Matrix) -- create the matrix induced on generators by a given matrix

Creating a map between modules, where the source module is computed

map(Module,ZZ,Function) -- create a matrix from a free module by specifying a function that gives each entry
map(Module,Nothing,List) -- create a matrix by giving a doubly nested list of ring elements
map(Module,ZZ,List) -- create a matrix by giving a sparse or dense list of entries
map(Module,Nothing,Matrix) -- recast a matrix to have a new target, and a free module as source

Creating a map with a different degree

map(Matrix) -- make a matrix with a different degree

Creating a map between modules over different rings

map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings

Creating a map between rings

map(Ring,Ring) -- make a ring map, using the names of the variables
map(Ring,Ring,List) -- make a ring map
map(Ring,Ring,Matrix) -- make a ring map

The Hom and End modules

Hom -- module of homomorphisms
End -- module of endomorphisms

Ways to use map:

map(GaloisField,GaloisField) (missing documentation)
map(Matrix) -- make a matrix with a different degree
map(Module) -- identity map
map(Module,Module,Function) -- create a matrix by specifying a function that gives each entry
map(Module,Module,List) -- create a matrix by giving a sparse or dense list of entries
map(Module,Module,Matrix) -- create the matrix induced on generators by a given matrix
map(Module,Module,Number) -- see map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
map(Module,Module,ZZ) -- see map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
map(Module,ZZ,ZZ) -- see map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
map(Module,Module,RingMap,List) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,Nothing,RingMap,List) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,Nothing,RingMap,Matrix) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,RingMap) -- see map(Module,Module,RingMap,Matrix) -- homomorphism of modules over different rings
map(Module,Nothing,List) -- create a matrix by giving a doubly nested list of ring elements
map(Module,Nothing,Matrix) -- recast a matrix to have a new target, and a free module as source
map(Module,ZZ,Function) -- create a matrix from a free module by specifying a function that gives each entry
map(Module,ZZ,List) -- create a matrix by giving a sparse or dense list of entries
map(Ring,Matrix) -- make a ring map
map(Ring,Ring) -- make a ring map, using the names of the variables
map(Ring,Ring,List) -- make a ring map
map(Ring,Ring,Matrix) -- make a ring map
map(Ring,Ring,RingMap) -- see map(Ring,Ring,Matrix) -- make a ring map

For the programmer

The object map is a method function with options.

The source of this document is in Macaulay2Doc/functions/map-doc.m2:65:0.