CGAL 6.0.1 - Algebraic Foundations
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A model of EuclideanRing
represents a Euclidean ring (or Euclidean domain). It is an UniqueFactorizationDomain
that affords a suitable notion of minimality of remainders such that given x and y \neq 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_category
derived from CGAL::Unique_factorization_domain_tag
CGAL::Algebraic_structure_traits< EuclideanRing >::Mod
which is a model of AlgebraicStructureTraits_::Mod
CGAL::Algebraic_structure_traits< EuclideanRing >::Div
which is a model of AlgebraicStructureTraits_::Div
CGAL::Algebraic_structure_traits< EuclideanRing >::Div_mod
which is a model of AlgebraicStructureTraits_::DivMod
Remarks
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.
UniqueFactorizationDomain