def __init__(self, X, Y, category=None):
r"""
Create the space of homomorphisms between X and Y, which must have the
same base ring.
EXAMPLES::
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
TESTS::
sage: M = ModularForms(Gamma0(7), 4)
sage: H = M.Hom(M)
sage: TestSuite(H).run(skip='_test_elements')
"""
if not is_HeckeModule(X) or not 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()
HomsetWithBase.__init__(self, X, Y, category=category)
def __init__(self, G, H):
r"""
Return the homset of two matrix groups.
INPUT:
- ``G`` -- a matrix group.
- ``H`` -- a matrix group.
OUTPUT:
The homset of two matrix groups.
EXAMPLES::
sage: F = GF(5)
sage: gens = [matrix(F,2,[1,2, -1, 1]), matrix(F,2, [1,1, 0,1])]
sage: G = MatrixGroup(gens)
sage: from sage.groups.matrix_gps.homset import MatrixGroupHomset
sage: MatrixGroupHomset(G, G)
Set of Homomorphisms from
Matrix group over Finite Field of size 5 with 2 generators (
[1 2] [1 1]
[4 1], [0 1]
) to Matrix group over Finite Field of size 5 with 2 generators (
[1 2] [1 1]
[4 1], [0 1]
)
"""
from sage.categories.groups import Groups
from sage.categories.homset import HomsetWithBase
HomsetWithBase.__init__(self, G, H, Groups(), G.base_ring())
def __init__(self, domain, codomain, cat):
"""
Create a homspace.
INPUT:
- ``domain, codomain`` - modular abelian varieties
- ``cat`` - category
EXAMPLES::
sage: H = Hom(J0(11), J0(22)); H
Space of homomorphisms from Abelian variety J0(11) of dimension 1 to Abelian variety J0(22) of dimension 2
sage: Hom(J0(11), J0(11))
Endomorphism ring of Abelian variety J0(11) of dimension 1
sage: type(H)
<class 'sage.modular.abvar.homspace.Homspace_with_category'>
sage: H.homset_category()
Category of modular abelian varieties over Rational Field
"""
from .abvar import is_ModularAbelianVariety
if not is_ModularAbelianVariety(domain):
raise TypeError("domain must be a modular abelian variety")
if not is_ModularAbelianVariety(codomain):
raise TypeError("codomain must be a modular abelian variety")
self._gens = None
HomsetWithBase.__init__(self, domain, codomain, category=cat)
def __init__(self, G, H):
r"""
Return the homset of two matrix groups.
INPUT:
- ``G`` -- a matrix group.
- ``H`` -- a matrix group.
OUTPUT:
The homset of two matrix groups.
EXAMPLES::
sage: F = GF(5)
sage: gens = [matrix(F,2,[1,2, -1, 1]), matrix(F,2, [1,1, 0,1])]
sage: G = MatrixGroup(gens)
sage: from sage.groups.matrix_gps.homset import MatrixGroupHomset
sage: MatrixGroupHomset(G, G)
Set of Homomorphisms from
Matrix group over Finite Field of size 5 with 2 generators (
[1 2] [1 1]
[4 1], [0 1]
) to Matrix group over Finite Field of size 5 with 2 generators (
[1 2] [1 1]
[4 1], [0 1]
)
"""
from sage.categories.groups import Groups
from sage.categories.homset import HomsetWithBase
HomsetWithBase.__init__(self, G, H, Groups(), G.base_ring())
def __init__(self, X, Y, category=None, check=True, base=ZZ):
HomsetWithBase.__init__(self,
X,
Y,
category=category,
check=check,
base=base)
def __init__(self, X, S, category=None, check=True):
r"""
EXAMPLES: The bug reported at trac #1785 is fixed::
sage: K.<a> = NumberField(x^2 + x - (3^3-3))
sage: E = EllipticCurve('37a')
sage: X = E(K)
sage: X
Abelian group of points on Elliptic Curve defined by y^2 + y = x^3 + (-1)*x over Number Field in a with defining polynomial x^2 + x - 24
sage: P = X([3,a])
sage: P
(3 : a : 1)
sage: P in E
False
sage: P in E.base_extend(K)
True
"""
R = X.base_ring()
if R != S:
X = X.base_extend(S)
Y = spec.Spec(S, R)
HomsetWithBase.__init__(self,
Y,
X,
category=category,
check=check,
base=ZZ)
def __init__(self, R, S, category=None):
"""
Initialize ``self``.
EXAMPLES::
sage: Hom(ZZ, QQ)
Set of Homomorphisms from Integer Ring to Rational Field
"""
if category is None:
category = _Rings
HomsetWithBase.__init__(self, R, S, category)
def __init__(self, R, S, category = None):
"""
Initialize ``self``.
EXAMPLES::
sage: Hom(ZZ, QQ)
Set of Homomorphisms from Integer Ring to Rational Field
"""
if category is None:
category = _Rings
HomsetWithBase.__init__(self, R, S, category)
def __init__(self, G, H):
r"""
See ``MatrixGroupHomset`` for full documentation.
EXAMPLES::
sage: F = GF(5)
sage: gens = [matrix(F,2,[1,2, -1, 1]), matrix(F,2, [1,1, 0,1])]
sage: G = MatrixGroup(gens)
sage: from sage.groups.matrix_gps.homset import MatrixGroupHomset
sage: MatrixGroupHomset(G, G)
Set of Homomorphisms from Matrix group over Finite Field of size 5 with 2 generators:
[[[1, 2], [4, 1]], [[1, 1], [0, 1]]] to Matrix group over Finite Field of size 5 with 2 generators:
[[[1, 2], [4, 1]], [[1, 1], [0, 1]]]
"""
HomsetWithBase.__init__(self, G, H, GROUPS, G.base_ring())
def __init__(self, G, H):
r"""
See ``MatrixGroupHomset`` for full documentation.
EXAMPLES::
sage: F = GF(5)
sage: gens = [matrix(F,2,[1,2, -1, 1]), matrix(F,2, [1,1, 0,1])]
sage: G = MatrixGroup(gens)
sage: from sage.groups.matrix_gps.homset import MatrixGroupHomset
sage: MatrixGroupHomset(G, G)
Set of Homomorphisms from Matrix group over Finite Field of size 5 with 2 generators:
[[[1, 2], [4, 1]], [[1, 1], [0, 1]]] to Matrix group over Finite Field of size 5 with 2 generators:
[[[1, 2], [4, 1]], [[1, 1], [0, 1]]]
"""
HomsetWithBase.__init__(self, G, H, GROUPS, G.base_ring())
def __init__(self, G, H, category=None, check=True):
r"""
Return the homset of two libgap groups.
TESTS::
sage: from sage.groups.abelian_gps.abelian_group_gap import AbelianGroupGap
sage: A = AbelianGroupGap([2,4])
sage: H = A.Hom(A)
sage: TestSuite(H).run()
"""
if check:
from sage.groups.perm_gps.permgroup import PermutationGroup_generic
if not isinstance(G, (ParentLibGAP, PermutationGroup_generic)):
raise TypeError("G (={}) must be a ParentLibGAP or a permutation group".format(G))
if not isinstance(H, (ParentLibGAP, PermutationGroup_generic)):
raise TypeError("H (={}) must be a ParentLibGAP or a permutation group".format(H))
HomsetWithBase.__init__(self, G, H, category, check=check, base=ZZ)
def _coerce_impl(self, x):
"""
Coerce x into self, if possible.
EXAMPLES::
sage: J = J0(37) ; J.Hom(J)._coerce_impl(matrix(ZZ,4,[5..20]))
Abelian variety endomorphism of Abelian variety J0(37) of dimension 2
sage: K = J0(11) * J0(11) ; J.Hom(K)._coerce_impl(matrix(ZZ,4,[5..20]))
Abelian variety morphism:
From: Abelian variety J0(37) of dimension 2
To: Abelian variety J0(11) x J0(11) of dimension 2
"""
if self.matrix_space().has_coerce_map_from(parent(x)):
return self(x)
else:
return HomsetWithBase._coerce_impl(self, x)
def __init__(self, R, S, category = None):
if category is None:
category = _Rings
HomsetWithBase.__init__(self, R, S, category)
def __init__(self, R, S, category=None):
if category is None:
category = _Rings
HomsetWithBase.__init__(self, R, S, category)
