Infinite Enumerated Sets

AUTHORS:

• Florent Hivert (2009-11): initial revision.

class sage.categories.infinite_enumerated_sets.InfiniteEnumeratedSets(s=None)

Bases: sage.categories.category.Category

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]
sage: InfiniteEnumeratedSets().all_super_categories()
[Category of infinite enumerated sets,
 Category of enumerated sets,
 Category of sets,
 Category of sets with partial maps, 
 Category of objects]

TESTS:

sage: C = InfiniteEnumeratedSets()
sage: TestSuite(C).run()

class ParentMethods

cardinality()

Counts the elements of the enumerated set.

EXAMPLES:

sage: NN = InfiniteEnumeratedSets().example()
sage: NN.cardinality()
+Infinity

is_finite()

Returns False since self is not finite.

EXAMPLES:

sage: C = InfiniteEnumeratedSets().example()
sage: C.is_finite()
False

list()

Returns an error since self is an infinite enumerated set.

EXAMPLES:

sage: NN = InfiniteEnumeratedSets().example()
sage: NN.list()
...
NotImplementedError: infinite list

random_element()

Returns an error since self is an infinite enumerated set.

EXAMPLES:

sage: NN = InfiniteEnumeratedSets().example()
sage: NN.random_element()
...
NotImplementedError: infinite set

TODO: should this be an optional abstract_method instead?

InfiniteEnumeratedSets.super_categories(*args, **kwds)

EXAMPLES:

sage: InfiniteEnumeratedSets().super_categories()
[Category of enumerated sets]