Coverage for local/lib/python2.7/site-packages/sage/categories/infinite_enumerated_sets.py : 46%
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r""" Infinite Enumerated Sets
AUTHORS:
- Florent Hivert (2009-11): initial revision.
""" #***************************************************************************** # Copyright (C) 2009 Florent Hivert <Florent.Hivert@univ-rouen.fr> # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #******************************************************************************
from sage.categories.category_with_axiom import CategoryWithAxiom
class InfiniteEnumeratedSets(CategoryWithAxiom): """ The category of infinite enumerated sets
An infinite enumerated sets is a countable set together with a canonical enumeration of its elements.
EXAMPLES::
sage: InfiniteEnumeratedSets() Category of infinite enumerated sets sage: InfiniteEnumeratedSets().super_categories() [Category of enumerated sets, Category of infinite sets] sage: InfiniteEnumeratedSets().all_super_categories() [Category of infinite enumerated sets, Category of enumerated sets, Category of infinite sets, Category of sets, Category of sets with partial maps, Category of objects]
TESTS::
sage: C = InfiniteEnumeratedSets() sage: TestSuite(C).run() """
class ParentMethods:
def random_element(self): """ Returns an error since self is an infinite enumerated set.
EXAMPLES::
sage: NN = InfiniteEnumeratedSets().example() sage: NN.random_element() Traceback (most recent call last): ... NotImplementedError: infinite set
TODO: should this be an optional abstract_method instead? """
def list(self): """ Returns an error since self is an infinite enumerated set.
EXAMPLES::
sage: NN = InfiniteEnumeratedSets().example() sage: NN.list() Traceback (most recent call last): ... NotImplementedError: cannot list an infinite set """ _list_default = list # needed by the check system.
def _test_enumerated_set_iter_cardinality(self, **options): """ Check that the methods :meth:`.cardinality` and :meth:`.__iter__` are consistent.
See also :class:`TestSuite`.
For infinite enumerated sets:
* :meth:`.cardinality` is supposed to return `infinity`
* :meth:`.list` is supposed to raise a ``NotImplementedError``.
EXAMPLES::
sage: NN = InfiniteEnumeratedSets().example() sage: NN._test_enumerated_set_iter_cardinality() """ |