Example of facade set

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_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
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_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

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