CGAL 6.2 - Polynomial: Polynomial_d Concept Reference

CGAL 6.2 - Polynomial

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Polynomial_d Concept Reference
Reference Manual » Concepts

## Definition

A model of `Polynomial_d` is representing a multivariate polynomial in \( d \geq 1\) variables over some basic ring \( R\). This type is denoted as the innermost coefficient. A model of `Polynomial_d` must be accompanied by a traits class `CGAL::Polynomial_traits_d<Polynomial_d>`, which is a model of `PolynomialTraits_d`. Please have a look at the concept `PolynomialTraits_d`, since nearly all functionality related to polynomials is provided by the traits.

Refines
  `IntegralDomainWithoutDivision`

The algebraic structure of `Polynomial_d` depends on the algebraic structure of `PolynomialTraits_d::Innermost_coefficient_type`:

Innermost_coefficient_type | Polynomial_d
--- | ---
IntegralDomainWithoutDivision | IntegralDomainWithoutDivision
IntegralDomain | IntegralDomain
UniqueFactorizationDomain | UniqueFactorizationDomain
EuclideanRing | UniqueFactorizationDomain
Field | UniqueFactorizationDomain

Note
  In case the polynomial is univariate and the innermost coefficient is a `Field` the polynomial is model of `EuclideanRing`.

See also
  `AlgebraicStructureTraits`
  `PolynomialTraits_d`

Has models
  `CGAL::Polynomial<Coeff>`