Euclidean domains

class sage.categories.euclidean_domains.EuclideanDomains(s=None)

Bases: sage.categories.category_singleton.Category_singleton

The category of euclidean domains constructive euclidean domain, i.e. one can divide producing a quotient and a remainder where the remainder is either zero or is “smaller” than the divisor

EXAMPLES:

sage: EuclideanDomains()
Category of euclidean domains
sage: EuclideanDomains().super_categories()
[Category of principal ideal domains]

TESTS:

sage: TestSuite(EuclideanDomains()).run()
class ElementMethods
class EuclideanDomains.ParentMethods
is_euclidean_domain()

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

EXAMPLES:

sage: Parent(QQ,category=EuclideanDomains()).is_euclidean_domain()
True
EuclideanDomains.super_categories()

EXAMPLES:

sage: EuclideanDomains().super_categories()
[Category of principal ideal domains]

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