\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13 - Polynomial
Polynomial_d Concept Reference
Polynomial Reference ยป 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>