def __init__(self, A, gens=None, category=None):
"""
A subring of the endomorphism ring.
INPUT:
- ``A`` - an abelian variety
- ``gens`` - (default: None); optional; if given
should be a tuple of the generators as matrices
EXAMPLES::
sage: J0(23).endomorphism_ring()
Endomorphism ring of Abelian variety J0(23) of dimension 2
sage: sage.modular.abvar.homspace.EndomorphismSubring(J0(25))
Endomorphism ring of Abelian variety J0(25) of dimension 0
sage: E = J0(11).endomorphism_ring()
sage: type(E)
<class 'sage.modular.abvar.homspace.EndomorphismSubring_with_category'>
sage: E.category()
Join of Category of rings and Category of hom sets in Category of sets
sage: E.homset_category()
Category of modular abelian varieties over Rational Field
sage: TestSuite(E).run(skip=["_test_prod"])
TESTS:
The following tests against a problem on 32 bit machines that
occured while working on trac ticket #9944::
sage: sage.modular.abvar.homspace.EndomorphismSubring(J1(12345))
Endomorphism ring of Abelian variety J1(12345) of dimension 5405473
"""
self._J = A.ambient_variety()
self._A = A
# Initialise self with the correct category.
# TODO: a category should be able to specify the appropriate
# category for its endomorphism sets
# We need to initialise it as a ring first
if category is None:
homset_cat = A.category()
else:
homset_cat = category
# Remark: Ring.__init__ will automatically form the join
# of the category of rings and of homset_cat
Ring.__init__(self, A.base_ring(), category=homset_cat)
Homspace.__init__(self, A, A, cat=homset_cat)
self._refine_category_(Rings())
if gens is None:
self._gens = None
else:
self._gens = tuple([ self._get_matrix(g) for g in gens ])
self._is_full_ring = gens is None
def __init__(self, A, gens=None, category=None):
"""
A subring of the endomorphism ring.
INPUT:
- ``A`` - an abelian variety
- ``gens`` - (default: None); optional; if given
should be a tuple of the generators as matrices
EXAMPLES::
sage: J0(23).endomorphism_ring()
Endomorphism ring of Abelian variety J0(23) of dimension 2
sage: sage.modular.abvar.homspace.EndomorphismSubring(J0(25))
Endomorphism ring of Abelian variety J0(25) of dimension 0
sage: E = J0(11).endomorphism_ring()
sage: type(E)
<class 'sage.modular.abvar.homspace.EndomorphismSubring_with_category'>
sage: E.category()
Join of Category of rings and Category of hom sets in Category of sets
sage: E.homset_category()
Category of modular abelian varieties over Rational Field
sage: TestSuite(E).run(skip=["_test_prod"])
TESTS:
The following tests against a problem on 32 bit machines that
occured while working on trac ticket #9944::
sage: sage.modular.abvar.homspace.EndomorphismSubring(J1(12345))
Endomorphism ring of Abelian variety J1(12345) of dimension 5405473
"""
self._J = A.ambient_variety()
self._A = A
# Initialise self with the correct category.
# TODO: a category should be able to specify the appropriate
# category for its endomorphism sets
# We need to initialise it as a ring first
if category is None:
homset_cat = A.category()
else:
homset_cat = category
# Remark: Ring.__init__ will automatically form the join
# of the category of rings and of homset_cat
Ring.__init__(self, A.base_ring(), category=homset_cat)
Homspace.__init__(self, A, A, cat=homset_cat)
self._refine_category_(Rings())
if gens is None:
self._gens = None
else:
self._gens = tuple([self._get_matrix(g) for g in gens])
self._is_full_ring = gens is None
def __init__(self):
"""
Initialize ``self``.
TESTS::
sage: sage.rings.infinity.InfinityRing_class() is sage.rings.infinity.InfinityRing_class() is InfinityRing
True
Comparison tests::
sage: InfinityRing == InfinityRing
True
sage: InfinityRing == UnsignedInfinityRing
False
"""
Ring.__init__(self, self, names=('oo',), normalize=False)
def __init__(self, A, gens=None):
"""
A subring of the endomorphism ring.
INPUT:
- ``A`` - an abelian variety
- ``gens`` - (default: None); optional; if given
should be a tuple of the generators as matrices
EXAMPLES::
sage: J0(23).endomorphism_ring()
Endomorphism ring of Abelian variety J0(23) of dimension 2
sage: sage.modular.abvar.homspace.EndomorphismSubring(J0(25))
Endomorphism ring of Abelian variety J0(25) of dimension 0
sage: type(J0(11).endomorphism_ring())
<class 'sage.modular.abvar.homspace.EndomorphismSubring_with_category'>
TESTS:
The following tests against a problem on 32 bit machines that
occured while working on trac ticket #9944::
sage: sage.modular.abvar.homspace.EndomorphismSubring(J1(12345))
Endomorphism ring of Abelian variety J1(12345) of dimension 5405473
"""
self._J = A.ambient_variety()
self._A = A
# Initialise self with the correct category.
# We need to initialise it as a ring first
cat = A.category()
cat = cat.join([cat.hom_category(),Rings()])
Ring.__init__(self, A.base_ring(), category=cat)
Homspace.__init__(self, A, A, cat=cat)
if gens is None:
self._gens = None
else:
self._gens = tuple([ self._get_matrix(g) for g in gens ])
self._is_full_ring = gens is None
def __init__(self, A, gens=None):
"""
A subring of the endomorphism ring.
INPUT:
- ``A`` - an abelian variety
- ``gens`` - (default: None); optional; if given
should be a tuple of the generators as matrices
EXAMPLES::
sage: J0(23).endomorphism_ring()
Endomorphism ring of Abelian variety J0(23) of dimension 2
sage: sage.modular.abvar.homspace.EndomorphismSubring(J0(25))
Endomorphism ring of Abelian variety J0(25) of dimension 0
sage: type(J0(11).endomorphism_ring())
<class 'sage.modular.abvar.homspace.EndomorphismSubring_with_category'>
TESTS:
The following tests against a problem on 32 bit machines that
occured while working on trac ticket #9944::
sage: sage.modular.abvar.homspace.EndomorphismSubring(J1(12345))
Endomorphism ring of Abelian variety J1(12345) of dimension 5405473
"""
self._J = A.ambient_variety()
self._A = A
# Initialise self with the correct category.
# We need to initialise it as a ring first
cat = A.category()
cat = cat.join([cat.hom_category(), Rings()])
Ring.__init__(self, A.base_ring(), category=cat)
Homspace.__init__(self, A, A, cat=cat)
if gens is None:
self._gens = None
else:
self._gens = tuple([self._get_matrix(g) for g in gens])
self._is_full_ring = gens is None
def __init__(self):
"""
Initialize ``self``.
TESTS::
sage: sage.rings.infinity.UnsignedInfinityRing_class() is sage.rings.infinity.UnsignedInfinityRing_class() is UnsignedInfinityRing
True
Sage can understand SymPy's complex infinity (:trac:`17493`)::
sage: import sympy
sage: SR(sympy.zoo)
Infinity
Some equality checks::
sage: infinity == UnsignedInfinityRing.gen()
True
sage: UnsignedInfinityRing(3) == UnsignedInfinityRing(-19.5)
True
"""
Ring.__init__(self, self, names=('oo',), normalize=False)
def __init__(self, A, gens=None, category=None):
"""
A subring of the endomorphism ring.
INPUT:
- ``A`` - an abelian variety
- ``gens`` - (default: None); optional; if given
should be a tuple of the generators as matrices
EXAMPLES::
sage: J0(23).endomorphism_ring()
Endomorphism ring of Abelian variety J0(23) of dimension 2
sage: sage.modular.abvar.homspace.EndomorphismSubring(J0(25))
Endomorphism ring of Abelian variety J0(25) of dimension 0
sage: E = J0(11).endomorphism_ring()
sage: type(E)
<class 'sage.modular.abvar.homspace.EndomorphismSubring_with_category'>
sage: E.homset_category()
Category of modular abelian varieties over Rational Field
sage: E.category()
Category of endsets of modular abelian varieties over Rational Field
sage: E in Rings()
True
sage: TestSuite(E).run(skip=["_test_prod"])
TESTS:
The following tests against a problem on 32 bit machines that
occured while working on :trac:`9944`::
sage: sage.modular.abvar.homspace.EndomorphismSubring(J1(12345))
Endomorphism ring of Abelian variety J1(12345) of dimension 5405473
:trac:`16275` removed the custom ``__reduce__`` method, since
:meth:`Homset.__reduce__` already implements appropriate
unpickling by construction::
sage: E.__reduce__.__module__
'sage.categories.homset'
sage: E.__reduce__()
(<function Hom at ...>,
(Abelian variety J0(11) of dimension 1,
Abelian variety J0(11) of dimension 1,
Category of modular abelian varieties over Rational Field,
False))
"""
self._J = A.ambient_variety()
self._A = A
# Initialise self with the correct category.
# We need to initialise it as a ring first
if category is None:
homset_cat = A.category()
else:
homset_cat = category
# Remark: Ring.__init__ will automatically form the join
# of the category of rings and of homset_cat
Ring.__init__(self, A.base_ring(), category=homset_cat.Endsets())
Homspace.__init__(self, A, A, cat=homset_cat)
if gens is None:
self._gens = None
else:
self._gens = tuple([ self._get_matrix(g) for g in gens ])
self._is_full_ring = gens is None
