Space of morphisms between Ore modules

AUTHOR:

• Xavier Caruso (2024-10)

class sage.modules.ore_module_homspace.OreModule_homspace(domain, codomain, category=None)

Bases: UniqueRepresentation, HomsetWithBase

Class for hom spaces between Ore modules.

Element

alias of OreModuleMorphism

identity()

Return the identity morphism in this homspace.

EXAMPLES:

sage: K.<z> = GF(7^2)
sage: S.<X> = OrePolynomialRing(K, K.frobenius_endomorphism())
sage: M = S.quotient_module(X^3 + z*X + 1)
sage: End(M).identity()
Ore module endomorphism of Ore module of rank 3 over Finite Field in z of size 7^2 twisted by z |--> z^7

matrix_space()

Return the matrix space used to represent the morphisms in this homspace.

EXAMPLES:

sage: K.<z> = GF(7^2)
sage: S.<X> = OrePolynomialRing(K, K.frobenius_endomorphism())
sage: M = S.quotient_module(X^3 + z*X + 1)
sage: End(M).matrix_space()
Full MatrixSpace of 3 by 3 dense matrices over Finite Field in z of size 7^2

sage: N = S.quotient_module(X^2 + z)
sage: Hom(M, N).matrix_space()
Full MatrixSpace of 3 by 2 dense matrices over Finite Field in z of size 7^2

zero()

Return the zero morphism in this homspace.

EXAMPLES:

sage: K.<z> = GF(7^2)
sage: S.<X> = OrePolynomialRing(K, K.frobenius_endomorphism())
sage: M = S.quotient_module(X^3 + z*X + 1)
sage: End(M).zero()
Ore module endomorphism of Ore module of rank 3 over Finite Field in z of size 7^2 twisted by z |--> z^7