def __call__(self, A, name=''):
r"""
Create an element of the homspace ``self`` from `A`.
INPUT:
- ``A`` -- one of the following:
- an element of a Hecke algebra
- a Hecke module morphism
- a matrix
- a list of elements of the codomain specifying the images
of the basis elements of the domain.
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) ...
"""
try:
if A.parent() == self:
A._set_parent(self)
return A
A = A.hecke_module_morphism()
if A.parent() == self:
A._set_parent(self)
return A
else:
raise TypeError("unable to coerce A to self")
except AttributeError:
pass
if isinstance(A, (list, tuple)):
from sage.matrix.constructor import matrix
A = matrix([f.element() for f in A])
return morphism.HeckeModuleMorphism_matrix(self, A, name)
def __call__(self, A, name=''):
r"""
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) ...
"""
try:
if A.parent() == self:
A._set_parent(self)
return A
A = A.hecke_module_morphism()
if A.parent() == self:
A._set_parent(self)
return A
else:
raise TypeError("unable to coerce A to self")
except AttributeError:
pass
return morphism.HeckeModuleMorphism_matrix(self, A, name)
def hecke_module_morphism(self):
"""
Return the endomorphism of Hecke modules defined by the matrix
attached to this Hecke operator.
EXAMPLES::
sage: M = ModularSymbols(Gamma1(13))
sage: t = M.hecke_operator(2)
sage: t
Hecke operator T_2 on Modular Symbols space of dimension 15 for Gamma_1(13) of weight 2 with sign 0 and over Rational Field
sage: t.hecke_module_morphism()
Hecke module morphism T_2 defined by the matrix
[ 2 1 0 0 0 0 0 0 0 0 0 0 0 0 -1]
[ 0 2 0 1 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 0 2 0 0 1 -1 1 0 -1 0 1 -1 0 0]
[ 0 0 0 2 1 0 1 0 0 0 1 -1 0 0 0]
[ 0 0 1 0 2 0 0 0 0 1 -1 0 0 0 1]
[ 1 0 0 0 0 2 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 1 -1 1 -1 0 -1 1 1]
[ 0 0 0 0 0 0 0 -1 1 1 0 0 -1 1 0]
[ 0 0 0 0 0 0 -1 -1 0 1 -1 -1 1 0 -1]
[ 0 0 0 0 0 0 -2 0 2 -2 0 2 -2 1 -1]
[ 0 0 0 0 0 0 0 0 2 -1 1 0 0 1 -1]
[ 0 0 0 0 0 0 -1 1 2 -1 1 0 -2 2 0]
[ 0 0 0 0 0 0 0 0 1 1 0 -1 0 0 0]
[ 0 0 0 0 0 0 -1 1 1 0 1 1 -1 0 0]
[ 0 0 0 0 0 0 2 0 0 0 2 -1 0 1 -1]
Domain: Modular Symbols space of dimension 15 for Gamma_1(13) of weight ...
Codomain: Modular Symbols space of dimension 15 for Gamma_1(13) of weight ...
"""
try:
return self.__hecke_module_morphism
except AttributeError:
T = self.matrix()
M = self.domain()
H = End(M)
if isinstance(self, HeckeOperator):
name = "T_%s" % self.index()
else:
name = ""
self.__hecke_module_morphism = morphism.HeckeModuleMorphism_matrix(
H, T, name)
return self.__hecke_module_morphism
