Bases: sage.structure.unique_representation.UniqueRepresentation, sage.structure.parent.Parent
An example of a finite enumerated set:
This class provides a minimal implementation of a finite enumerated set.
See FiniteEnumeratedSet for a full featured implementation.
EXAMPLES:
sage: C = FiniteEnumeratedSets().example()
sage: C.cardinality()
3
sage: C.list()
[1, 2, 3]
sage: C.an_element()
1
This checks that the different methods of the enumerated set return consistent results:
sage: TestSuite(C).run(verbose = True)
running ._test_an_element() . . .
The set doesn't seems to implement __call__; skipping test of construction idempotency
pass
running ._test_category() . . . pass
running ._test_elements() . . .
Running the test suite of self.an_element()
running ._test_category() . . . pass
running ._test_eq() . . . pass
running ._test_not_implemented_methods() . . . pass
running ._test_pickling() . . . pass
pass
running ._test_elements_eq() . . . pass
running ._test_enumerated_set_contains() . . . pass
running ._test_enumerated_set_iter_cardinality() . . . pass
running ._test_enumerated_set_iter_list() . . . pass
running ._test_eq() . . . pass
running ._test_not_implemented_methods() . . . pass
running ._test_pickling() . . . pass
running ._test_some_elements() . . . pass
An element in self.
self.an_element() returns a particular element of the set self. This is a generic implementation from the category EnumeratedSets() which can be used when the method __iter__ is provided.
EXAMPLES:
sage: C = FiniteEnumeratedSets().example()
sage: C.an_element() # indirect doctest
1
Bases: sage.structure.unique_representation.UniqueRepresentation, sage.structure.parent.Parent
Returns the ambient space for self, as per Sets.Subquotients.ParentMethods.ambient().
EXAMPLES:
sage: C = FiniteEnumeratedSets().IsomorphicObjects().example(); C
The image by some isomorphism of An example of a finite enumerated set: {1,2,3}
sage: C.ambient()
An example of a finite enumerated set: {1,2,3}
Lifts x to the ambient space for self, as per Sets.Subquotients.ParentMethods.lift().
EXAMPLES:
sage: C = FiniteEnumeratedSets().IsomorphicObjects().example(); C
The image by some isomorphism of An example of a finite enumerated set: {1,2,3}
sage: C.lift(9)
3
Retracts x from the ambient space to self, as per Sets.Subquotients.ParentMethods.retract().
EXAMPLES:
sage: C = FiniteEnumeratedSets().IsomorphicObjects().example(); C
The image by some isomorphism of An example of a finite enumerated set: {1,2,3}
sage: C.retract(3)
9