Infinite Enumerated Sets¶
AUTHORS:
Florent Hivert (2009-11): initial revision.
- class sage.categories.infinite_enumerated_sets.InfiniteEnumeratedSets(base_category)[source]¶
- Bases: - 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] - >>> from sage.all import * >>> InfiniteEnumeratedSets() Category of infinite enumerated sets >>> InfiniteEnumeratedSets().super_categories() [Category of enumerated sets, Category of infinite sets] >>> 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] - class ParentMethods[source]¶
- Bases: - object- list()[source]¶
- Raise an error because - selfis an infinite enumerated set.- EXAMPLES: - sage: NN = InfiniteEnumeratedSets().example() sage: NN.list() Traceback (most recent call last): ... NotImplementedError: cannot list an infinite set - >>> from sage.all import * >>> NN = InfiniteEnumeratedSets().example() >>> NN.list() Traceback (most recent call last): ... NotImplementedError: cannot list an infinite set 
 - random_element()[source]¶
- Raise an error because - selfis an infinite enumerated set.- EXAMPLES: - sage: NN = InfiniteEnumeratedSets().example() sage: NN.random_element() Traceback (most recent call last): ... NotImplementedError: infinite set - >>> from sage.all import * >>> NN = InfiniteEnumeratedSets().example() >>> NN.random_element() Traceback (most recent call last): ... NotImplementedError: infinite set - TODO: should this be an optional abstract_method instead? 
 - tuple()[source]¶
- Raise an error because - selfis an infinite enumerated set.- EXAMPLES: - sage: NN = InfiniteEnumeratedSets().example() sage: NN.tuple() Traceback (most recent call last): ... NotImplementedError: cannot list an infinite set - >>> from sage.all import * >>> NN = InfiniteEnumeratedSets().example() >>> NN.tuple() Traceback (most recent call last): ... NotImplementedError: cannot list an infinite set