Examples of posets¶
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sage.categories.examples.posets.
FiniteSetsOrderedByInclusion
¶ An example of a poset: finite sets ordered by inclusion
This class provides a minimal implementation of a poset
EXAMPLES:
sage: P = Posets().example(); P An example of a poset: sets ordered by inclusion
We conclude by running systematic tests on this poset:
sage: TestSuite(P).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_new() . . . 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_new() . . . pass running ._test_not_implemented_methods() . . . pass running ._test_pickling() . . . pass running ._test_some_elements() . . . pass
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sage.categories.examples.posets.
PositiveIntegersOrderedByDivisibilityFacade
¶ An example of a facade poset: the positive integers ordered by divisibility
This class provides a minimal implementation of a facade poset
EXAMPLES:
sage: P = Posets().example("facade"); P An example of a facade poset: the positive integers ordered by divisibility sage: P(5) 5 sage: P(0) Traceback (most recent call last): ... ValueError: Can't coerce `0` in any parent `An example of a facade poset: the positive integers ordered by divisibility` is a facade for sage: 3 in P True sage: 0 in P False