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A model of EuclideanRing represents an euclidean ring (or Euclidean domain). It is an UniqueFactorizationDomain that affords a suitable notion of minimality of remainders such that given x and y ≠ 0 we obtain an (almost) unique solution to x = qy + r by demanding that a solution (q,r) is chosen to minimize r. In particular, r is chosen to be 0 if possible.
Moreover, CGAL::Algebraic_structure_traits< EuclideanRing > is a model of
AlgebraicStructureTraits providing:
- CGAL::Algebraic_structure_traits< EuclideanRing >::Algebraic_type derived from Unique_factorization_domain_tag
- CGAL::Algebraic_structure_traits< EuclideanRing >::Mod
- CGAL::Algebraic_structure_traits< EuclideanRing >::Div
- CGAL::Algebraic_structure_traits< EuclideanRing >::Div_mod
The most prominent example of a Euclidean ring are the integers. Whenever both x and y are positive, then it is conventional to choose the smallest positive remainder r.
IntegralDomainWithoutDivision
IntegralDomain
UniqueFactorizationDomain
EuclideanRing
Field
FieldWithSqrt
FieldWithKthRoot
FieldWithRootOf
AlgebraicStructureTraits