def __new__(cls, X, Y, category):
"""
sage: Hom(QQ, QQ, category = Rings()).__class__ # indirect doctest
<class 'sage.rings.homset.RingHomset_generic_with_category'>
sage: Hom(CyclotomicField(3), QQ, category = Rings()).__class__ # indirect doctest
<class 'sage.rings.number_field.morphism.CyclotomicFieldHomset_with_category'>
"""
from sage.rings.homset import RingHomset
return RingHomset(X, Y, category=category)
def _Hom_(self, Y, category):
r"""
Returns the homset from ``self`` to ``Y`` in the category ``category``
INPUT:
- ``Y`` -- a ring
- ``category`` -- a subcategory of :class:`Rings`() or None
The sole purpose of this method is to construct the homset
as a :class:`~sage.rings.homset.RingHomset`. If
``category`` is specified and is not a subcategory of
:class:`Rings`, a ``TypeError`` is raised instead
This method is not meant to be called directly. Please use
:func:`sage.categories.homset.Hom` instead.
EXAMPLES::
sage: H = QQ._Hom_(QQ, category = Rings()); H
Set of Homomorphisms from Rational Field to Rational Field
sage: H.__class__
<class 'sage.rings.homset.RingHomset_generic_with_category'>
TESTS::
sage: Hom(QQ, QQ, category = Rings()).__class__
<class 'sage.rings.homset.RingHomset_generic_with_category'>
sage: Hom(CyclotomicField(3), QQ, category = Rings()).__class__
<class 'sage.rings.number_field.morphism.CyclotomicFieldHomset_with_category'>
sage: TestSuite(Hom(QQ, QQ, category = Rings())).run() # indirect doctest
"""
if category is not None and not category.is_subcategory(Rings()):
raise TypeError("%s is not a subcategory of Rings()" %
category)
if Y not in Rings():
raise TypeError("%s is not a ring" % Y)
from sage.rings.homset import RingHomset
return RingHomset(self, Y, category=category)