def __init__(self, X, Y, category=None):
r"""
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)))
Traceback (most recent call last):
...
TypeError: X and Y must have the same base ring
sage: M.Hom(M) == loads(dumps(M.Hom(M)))
True
"""
if not module.is_HeckeModule(X) or not module.is_HeckeModule(Y):
raise TypeError, "X and Y must be Hecke modules"
if X.base_ring() != Y.base_ring():
raise TypeError, "X and Y must have the same base ring"
if category is None:
category = X.category()
sage.categories.homset.HomsetWithBase.__init__(self,
X,
Y,
category=category)
def __init__(self, X, Y, category = None):
r"""
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)))
Traceback (most recent call last):
...
TypeError: X and Y must have the same base ring
sage: M.Hom(M) == loads(dumps(M.Hom(M)))
True
"""
if not module.is_HeckeModule(X) or not module.is_HeckeModule(Y):
raise TypeError("X and Y must be Hecke modules")
if X.base_ring() != Y.base_ring():
raise TypeError("X and Y must have the same base ring")
if category is None:
category = X.category()
sage.categories.homset.HomsetWithBase.__init__(self, X, Y, category = category)
def __init__(self, M):
"""
INPUT:
- ``M`` - a Hecke module
EXAMPLE::
sage: CuspForms(1, 12).hecke_algebra() # indirect doctest
Full Hecke algebra acting on Cuspidal subspace of dimension 1 of Modular Forms space of dimension 2 for Modular Group SL(2,Z) of weight 12 over Rational Field
"""
if not module.is_HeckeModule(M):
raise TypeError("M (=%s) must be a HeckeModule"%M)
self.__M = M
sage.rings.commutative_algebra.CommutativeAlgebra.__init__(self, M.base_ring())
