AUTHORS:
- Florent Hivert (2009-11): initial revision.
Bases: sage.categories.category_with_axiom.CategoryWithAxiom_singleton
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()
Returns an error since self is an infinite enumerated set.
EXAMPLES:
sage: NN = InfiniteEnumeratedSets().example()
sage: NN.list()
Traceback (most recent call last):
...
NotImplementedError: infinite list
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?