def __init__(self, sets, category, order=None, **kwargs):
r"""
See :class:`CartesianProductPoset` for details.
TESTS::
sage: P = Poset((srange(3), lambda left, right: left <= right))
sage: C = cartesian_product((P, P), order='notexisting')
Traceback (most recent call last):
...
ValueError: No order 'notexisting' known.
sage: C = cartesian_product((P, P), category=(Groups(),))
sage: C.category()
Join of Category of groups and Category of posets
"""
if order is None:
self._le_ = self.le_product
elif isinstance(order, str):
try:
self._le_ = getattr(self, 'le_' + order)
except AttributeError:
raise ValueError("No order '%s' known." % (order, ))
else:
self._le_ = order
from sage.categories.category import Category
from sage.categories.posets import Posets
if not isinstance(category, tuple):
category = (category, )
category = Category.join(category + (Posets(), ))
super(CartesianProductPoset, self).__init__(sets, category, **kwargs)
def __init__(self, **keywords):
DisjointUnionEnumeratedSets.__init__(
self,
Family(NonNegativeIntegers(),
lambda i: Relations_size(i, **keywords)),
facade=True,
keepkey=False,
category=(Posets(), EnumeratedSets()))
self._sign = None
self._initialise_properties(keywords)
def super_categories(self):
r"""
Returns a list of the (immediate) super categories of
``self``, as per :meth:`Category.super_categories`.
EXAMPLES::
sage: FinitePosets().super_categories()
[Category of posets, Category of finite enumerated sets]
"""
return [Posets(), FiniteEnumeratedSets()]
def super_categories(self):
r"""
Returns a list of the (immediate) super categories of
``self``, as per :meth:`Category.super_categories`.
EXAMPLES::
sage: LatticePosets().super_categories()
[Category of posets]
"""
return [Posets()]
def __init__(self, elements, facade=True):
"""
Initialize ``self``.
TESTS::
sage: TestSuite(TotallyOrderedFiniteSet([1,2,3])).run()
sage: TestSuite(TotallyOrderedFiniteSet([1,2,3],facade=False)).run()
sage: TestSuite(TotallyOrderedFiniteSet([1,3,2],facade=False)).run()
sage: TestSuite(TotallyOrderedFiniteSet([])).run()
"""
Parent.__init__(self, facade = facade, category = (Posets(),FiniteEnumeratedSets()))
self._elements = elements
if facade:
self._facade_elements = None
else:
self._facade_elements = self._elements
self._elements = [self.element_class(self,x) for x in elements]