Unique factorization domains¶
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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()
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class
ElementMethods
¶
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class
UniqueFactorizationDomains.
ParentMethods
¶ -
is_unique_factorization_domain
(proof=True)¶ 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
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UniqueFactorizationDomains.
additional_structure
()¶ Return whether
self
is a structure category.See also
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()
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UniqueFactorizationDomains.
super_categories
()¶ EXAMPLES:
sage: UniqueFactorizationDomains().super_categories() [Category of gcd domains]
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class