Hom spaces between Hecke modules

class sage.modular.hecke.homspace.HeckeModuleHomspace(X, Y)

A space of homomorphisms between two objects in the category of Hecke modules over a given base ring.

__call__(A, name='')

Create an element of this space from A, which should be an element of a Hecke algebra, a Hecke module morphism, or a matrix.

EXAMPLES:

sage: M = ModularForms(Gamma0(7), 4)
sage: H = M.Hom(M)
sage: H(M.hecke_operator(7))
Hecke module morphism T_7 defined by the matrix                                       
[ -7   0   0]                                                                         
[  0   1 240]                                                                         
[  0   0 343]                                                                         
Domain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...      
Codomain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...    
sage: H(H(M.hecke_operator(7)))
Hecke module morphism T_7 defined by the matrix
[ -7   0   0]
[  0   1 240]
[  0   0 343]
Domain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...
Codomain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...
sage: H(matrix(QQ, 3, srange(9)))
Hecke module morphism defined by the matrix
[0 1 2]
[3 4 5]
[6 7 8]
Domain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...
Codomain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...
__init__(X, Y)

Create the space of homomorphisms between X and Y, which must have the same base ring.

EXAMPLE:

sage: M = ModularForms(Gamma0(7), 4)
sage: M.Hom(M)
Set of Morphisms from ... to ... in Category of Hecke modules over Rational Field
sage: sage.modular.hecke.homspace.HeckeModuleHomspace(M, M.base_extend(Qp(13)))
...
TypeError: X and Y must have the same base ring
sage: M.Hom(M) == loads(dumps(M.Hom(M)))
True
sage.modular.hecke.homspace.is_HeckeModuleHomspace(x)

Return True if x is a space of homomorphisms in the category of Hecke modules.

EXAMPLES:

sage: M = ModularForms(Gamma0(7), 4)
sage: sage.modular.hecke.homspace.is_HeckeModuleHomspace(Hom(M, M))
True
sage: sage.modular.hecke.homspace.is_HeckeModuleHomspace(Hom(M, QQ))
False

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