Unique factorization domains

class sage.categories.unique_factorization_domains.UniqueFactorizationDomains(s=None)

Bases: sage.categories.category_singleton.Category_singleton

The category of unique factorization domains constructive unique factorization domains, i.e. where one can constructively factor members into a product of a finite number of irreducible elements

EXAMPLES:

sage: UniqueFactorizationDomains()
Category of unique factorization domains
sage: UniqueFactorizationDomains().super_categories()
[Category of gcd domains]

TESTS:

sage: TestSuite(UniqueFactorizationDomains()).run()
class ElementMethods
class UniqueFactorizationDomains.ParentMethods
is_unique_factorization_domain()

Return True, since this in an object of the category of unique factorization domains.

EXAMPLES:

sage: Parent(QQ,category=UniqueFactorizationDomains()).is_unique_factorization_domain()
True
UniqueFactorizationDomains.additional_structure()

Return whether self is a structure category.

The category of unique factorization domains does not define additional structure: a ring morphism between unique factorization domains is a unique factorization domain morphism.

EXAMPLES:

sage: UniqueFactorizationDomains().additional_structure()
UniqueFactorizationDomains.super_categories()

EXAMPLES:

sage: UniqueFactorizationDomains().super_categories()
[Category of gcd domains]

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