def __init__(self, R):
"""
TESTS::
sage: PolyhedralSets(AA)
Category of polyhedral sets over Algebraic Real Field
"""
Category_over_base_ring.__init__(self, R)
def __init__(self, R):
"""
TESTS::
sage: PolyhedralSets(AA)
Category of polyhedral sets over Algebraic Real Field
"""
Category_over_base_ring.__init__(self, R)
def __init__(self, R):
"""
TESTS::
sage: PolyhedralSets((1,2,3))
Traceback (most recent call last):
...
TypeError: base ring R (=(1, 2, 3)) must be ZZ, QQ, or RDF.
"""
from sage.rings.all import ZZ, QQ, RDF
if R not in [ZZ, QQ, RDF]:
raise TypeError('base ring R (='+str(R)+') must be ZZ, QQ, or RDF.')
Category_over_base_ring.__init__(self, R, 'Polyhedra')
def __init__(self, base, name=None):
r"""
Initialize ``self``.
EXAMPLES::
sage: from sage.categories.manifolds import Manifolds
sage: C = Manifolds(RR)
sage: TestSuite(C).run(skip="_test_category_over_bases")
"""
if base not in Fields().Topological():
raise ValueError("base must be a topological field")
Category_over_base_ring.__init__(self, base, name)
def __init__(self, base, name=None):
r"""
Initialize ``self``.
EXAMPLES::
sage: from sage.categories.manifolds import Manifolds
sage: C = Manifolds(RR)
sage: TestSuite(C).run(skip="_test_category_over_bases")
"""
if base not in Fields().Topological():
raise ValueError("base must be a topological field")
Category_over_base_ring.__init__(self, base, name)
def __init__(self, base_space, base_field, name=None):
r"""
Initialize ``self``.
EXAMPLES::
sage: M = Manifold(2, 'M')
sage: from sage.categories.vector_bundles import VectorBundles
sage: C = VectorBundles(M, RR)
sage: TestSuite(C).run(skip="_test_category_over_bases")
"""
if base_field not in Fields().Topological():
raise ValueError("base field must be a topological field")
self._base_space = base_space
Category_over_base_ring.__init__(self, base_field, name)
def __init__(self, base_category, base_ring):
"""
EXAMPLES::
sage: C = Semigroups().Algebras(QQ)
sage: C
Category of semigroup algebras over Rational Field
sage: C.base_category()
Category of semigroups
sage: C.super_categories()
[Category of algebras with basis over Rational Field, Category of set algebras over Rational Field]
TESTS::
sage: C._short_name()
'Algebras'
sage: latex(C) # todo: improve that
\mathbf{Algebras}(\mathbf{Semigroups})
"""
CovariantConstructionCategory.__init__(self, base_category, base_ring)
Category_over_base_ring.__init__(self, base_ring)
def _repr_object_names(self):
r"""
Return the name of the objects of this category.
.. SEEALSO:: :meth:`Category._repr_object_names`
EXAMPLES::
sage: M = Manifold(2, 'M')
sage: from sage.categories.vector_bundles import VectorBundles
sage: VectorBundles(M, RR)._repr_object_names()
'vector bundles over Real Field with 53 bits of precision with base
space 2-dimensional differentiable manifold M'
"""
base_space = self._base_space
return Category_over_base_ring._repr_object_names(self) + \
" with base space %s"%base_space
def __init__(self, R):
Category_over_base_ring.__init__(self, R)
