Examples of finite enumerated sets

class sage.categories.examples.finite_enumerated_sets.Example

Bases: UniqueRepresentation, Parent

An example of a finite enumerated set: \(\{1,2,3\}\)

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 \(C\) return consistent results:

sage: TestSuite(C).run(verbose = True)
running ._test_an_element() . . . pass
running ._test_cardinality() . . . pass
running ._test_category() . . . pass
running ._test_construction() . . . pass
running ._test_elements() . . .
  Running the test suite of self.an_element()
  running ._test_category() . . . pass
  running ._test_eq() . . . pass
  running ._test_new() . . . pass
  running ._test_nonzero_equal() . . . pass
  running ._test_not_implemented_methods() . . . pass
  running ._test_pickling() . . . pass
  pass
running ._test_elements_eq_reflexive() . . . pass
running ._test_elements_eq_symmetric() . . . pass
running ._test_elements_eq_transitive() . . . pass
running ._test_elements_neq() . . . 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_new() . . . pass
running ._test_not_implemented_methods() . . . pass
running ._test_pickling() . . . pass
running ._test_some_elements() . . . pass

class sage.categories.examples.finite_enumerated_sets.IsomorphicObjectOfFiniteEnumeratedSet(ambient=An example of a finite enumerated set: {1, 2, 3})

Bases: UniqueRepresentation, Parent

ambient()

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}

lift(x)

INPUT:

• x – an element of self

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

retract(x)

INPUT:

• x – an element of the ambient space for self

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