Processing math: 100%
 
CGAL 6.0.1 - Algebraic Foundations
All Classes Namespaces Files Functions Variables Typedefs Enumerations Friends Modules Pages
Loading...
Searching...
No Matches
EuclideanRing Concept Reference

Definition

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:

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.

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