Example of facade set¶
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class
sage.categories.examples.facade_sets.
IntegersCompletion
¶ Bases:
sage.structure.unique_representation.UniqueRepresentation
,sage.structure.parent.Parent
An example of a facade parent: the set of integers completed with \(+-\infty\)
This class illustrates a minimal implementation of a facade parent that models the union of several other parents.
EXAMPLES:
sage: S = Sets().Facade().example("union"); S An example of a facade set: the integers completed by +-infinity
TESTS:
sage: TestSuite(S).run(verbose = True) running ._test_an_element() . . . pass running ._test_cardinality() . . . 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_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_eq() . . . pass running ._test_not_implemented_methods() . . . pass running ._test_pickling() . . . pass running ._test_some_elements() . . . pass
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class
sage.categories.examples.facade_sets.
PositiveIntegerMonoid
¶ Bases:
sage.structure.unique_representation.UniqueRepresentation
,sage.structure.parent.Parent
An example of a facade parent: the positive integers viewed as a multiplicative monoid
This class illustrates a minimal implementation of a facade parent which models a subset of a set.
EXAMPLES:
sage: S = Sets().Facade().example(); S An example of facade set: the monoid of positive integers
TESTS:
sage: TestSuite(S).run(verbose = True) running ._test_an_element() . . . pass running ._test_associativity() . . . pass running ._test_cardinality() . . . 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_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_eq() . . . pass running ._test_not_implemented_methods() . . . pass running ._test_one() . . . pass running ._test_pickling() . . . pass running ._test_prod() . . . pass running ._test_some_elements() . . . pass