UniqueFactorizationDomain Class Reference

#include <Concepts/UniqueFactorizationDomain.h>

Definition

A model of UniqueFactorizationDomain is an IntegralDomain with the additional property that the ring it represents is a unique factorization domain (a.k.a. UFD or factorial ring), meaning that every non-zero non-unit element has a factorization into irreducible elements that is unique up to order and up to multiplication by invertible elements (units). (An irreducible element is a non-unit ring element that cannot be factored further into two non-unit elements. In a UFD, the irreducible elements are precisely the prime elements.)

In a UFD, any two elements, not both zero, possess a greatest common divisor (gcd).

Moreover, CGAL::Algebraic_structure_traits< UniqueFactorizationDomain > is a model of AlgebraicStructureTraits providing:

• CGAL::Algebraic_structure_traits< UniqueFactorizationDomain >::Algebraic_category derived from CGAL::Unique_factorization_domain_tag

• CGAL::Algebraic_structure_traits< UniqueFactorizationDomain >::Gcd which is a model of AlgebraicStructureTraits_::Gcd

  Refines:

  IntegralDomain

See also

IntegralDomainWithoutDivision

IntegralDomain

UniqueFactorizationDomain

EuclideanRing

Field

FieldWithSqrt

FieldWithKthRoot

FieldWithRootOf

AlgebraicStructureTraits