Coverage for local/lib/python2.7/site-packages/sage/categories/facade_sets.py : 90%
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r""" Facade Sets
For background, see :ref:`What is a facade set? <facade-sets>`. """ #***************************************************************************** # Copyright (C) 2010-2011 Nicolas M. Thiery <nthiery at users.sf.net> # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #******************************************************************************
r""" Returns an example of facade set, as per :meth:`Category.example() <sage.categories.category.Category.example>`.
INPUT:
- ``choice`` -- 'union' or 'subset' (default: 'subset').
EXAMPLES::
sage: Sets().Facade().example() An example of facade set: the monoid of positive integers sage: Sets().Facade().example(choice='union') An example of a facade set: the integers completed by +-infinity sage: Sets().Facade().example(choice='subset') An example of facade set: the monoid of positive integers """ else: raise TypeError("choice should be 'union' or 'subset'")
""" Coerce ``element`` into ``self``
INPUT:
- ``element`` -- any object
This default implementation returns ``element`` if ``self`` is a facade for ``parent(element)`. Otherwise it attempts in turn to coerce ``element`` into each parent ``self`` is a facade for.
This implementation is only valid for a facade parent which models the full union of the parents it is a facade for. Other facade parents should redefine :meth:`element_constructor` appropriately.
EXAMPLES::
sage: S = Sets().Facade().example("union"); S An example of a facade set: the integers completed by +-infinity sage: S(1) 1 sage: S(1/2) Traceback (most recent call last): ... ValueError: Can't coerce `1/2` in any parent `An example of a facade set: the integers completed by +-infinity` is a facade for sage: S(2/1) 2 sage: S(2/1).parent() Integer Ring sage: S(int(1)) 1 sage: S(int(1)).parent() Integer Ring
Facade parents that model strict subsets should redefine :meth:`element_constructor`::
sage: S = Sets().Facade().example(); S An example of facade set: the monoid of positive integers sage: S(-1) Traceback (most recent call last): ... ValueError: %s should be positive """ else: raise NotImplementedError
""" Returns the parents this set is a facade for
This default implementation assumes that ``self`` has an attribute ``_facade_for``, typically initialized by :meth:`Parent.__init__`. If the attribute is not present, the method raises a NotImplementedError.
EXAMPLES::
sage: S = Sets().Facade().example(); S An example of facade set: the monoid of positive integers sage: S.facade_for() (Integer Ring,)
Check that :trac:`13801` is corrected::
sage: class A(Parent): ....: def __init__(self): ....: Parent.__init__(self, category=Sets(), facade=True) sage: a = A() sage: a.facade_for() Traceback (most recent call last): ... NotImplementedError: this parent did not specify which parents it is a facade for """
""" Returns whether ``self`` is the parent of ``element``
INPUT:
- ``element`` -- any object
Since ``self`` is a facade domain, this actually tests whether the parent of ``element`` is any of the parent ``self`` is a facade for.
EXAMPLES::
sage: S = Sets().Facade().example(); S An example of facade set: the monoid of positive integers sage: S.is_parent_of(1) True sage: S.is_parent_of(1/2) False
This method differs from :meth:`__contains__` in two ways. First, this does not take into account the fact that ``self`` may be a strict subset of the parent(s) it is a facade for::
sage: -1 in S, S.is_parent_of(-1) (False, True)
Furthermore, there is no coercion attempted::
sage: int(1) in S, S.is_parent_of(int(1)) (True, False)
.. warning::
this implementation does not handle facade parents of facade parents. Is this a feature we want generically? """
""" Membership testing
Returns whether ``element`` is in one of the parents ``self`` is a facade for.
.. warning:: this default implementation is currently overriden by :meth:`Parent.__contains__`.
EXAMPLES::
sage: S = Sets().Facade().example("union"); S An example of a facade set: the integers completed by +-infinity sage: 1 in S, -5 in S, oo in S, -oo in S, int(1) in S, 2/1 in S (True, True, True, True, True, True) sage: 1/2 in S, "bla" in S (False, False) """ return any(element in parent for parent in self.facade_for())
""" Try to return an element of ``self``, as per :meth:`Sets.ParentMethods.an_element`.
For each parent ``self`` is a facade for, this default implementation tries the method ``an_element`` until it finds an element in ``self``. If none is found raise a ``NotImplementedError``.
EXAMPLES::
sage: S = Sets().Facade().example(); S An example of facade set: the monoid of positive integers sage: S.an_element() 1 """ raise NotImplementedError |