Facade Sets¶
For background, see What is a facade set?.
- class sage.categories.facade_sets.FacadeSets(base_category)¶
Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton- class ParentMethods¶
Bases:
object- facade_for()¶
Returns the parents this set is a facade for
This default implementation assumes that
selfhas an attribute_facade_for, typically initialized byParent.__init__(). If the attribute is not present, the method raises a NotImplementedError.EXAMPLES:
sage: S = Sets().Facade().example(); S An example of facade set: the monoid of positive integers sage: S.facade_for() (Integer Ring,)
Check that trac ticket #13801 is corrected:
sage: class A(Parent): ....: def __init__(self): ....: Parent.__init__(self, category=Sets(), facade=True) sage: a = A() sage: a.facade_for() Traceback (most recent call last): ... NotImplementedError: this parent did not specify which parents it is a facade for
- is_parent_of(element)¶
Returns whether
selfis the parent ofelementINPUT:
element– any object
Since
selfis a facade domain, this actually tests whether the parent ofelementis any of the parentselfis a facade for.EXAMPLES:
sage: S = Sets().Facade().example(); S An example of facade set: the monoid of positive integers sage: S.is_parent_of(1) True sage: S.is_parent_of(1/2) False
This method differs from
__contains__()in two ways. First, this does not take into account the fact thatselfmay be a strict subset of the parent(s) it is a facade for:sage: -1 in S, S.is_parent_of(-1) (False, True)
Furthermore, there is no coercion attempted:
sage: int(1) in S, S.is_parent_of(int(1)) (True, False)
Warning
this implementation does not handle facade parents of facade parents. Is this a feature we want generically?
- example(choice='subset')¶
Returns an example of facade set, as per
Category.example().INPUT:
choice– ‘union’ or ‘subset’ (default: ‘subset’).
EXAMPLES:
sage: Sets().Facade().example() An example of facade set: the monoid of positive integers sage: Sets().Facade().example(choice='union') An example of a facade set: the integers completed by +-infinity sage: Sets().Facade().example(choice='subset') An example of facade set: the monoid of positive integers