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CGAL 5.0.3 - Algebraic Foundations
UniqueFactorizationDomain Concept Reference
Algebraic Foundations Reference ยป Concepts

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:

Refines:
IntegralDomain
See also
IntegralDomainWithoutDivision
IntegralDomain
UniqueFactorizationDomain
EuclideanRing
Field
FieldWithSqrt
FieldWithKthRoot
FieldWithRootOf
AlgebraicStructureTraits