\begin{ccRefConcept}{Polynomial_d}

\ccDefinition

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

%The innermost coefficient type of the polynomial is accessible through 
%the traits, that is, the traits provides the public type 
%\ccc{CGAL::Polynomial_traits_d<Polynomial_d>::Innermost_coefficient_type}.

\ccRefines

\ccc{IntegralDomainWithoutDivision} \\

The algebraic structure of \ccc{Polynomial_d} depends on the 
algebraic structure of \ccc{Innermost_coefficient_type}:

\begin{tabular}{|l|l|}
\hline
\ccc{Innermost_coefficient_type}&\ccc{Polynomial_d}\\
\hline
\ccc{IntegralDomainWithoutDivision}&\ccc{IntegralDomainWithoutDivision}\\
\ccc{IntegralDomain}&\ccc{IntegralDomain}\\
\ccc{UniqueFactorizationDomain}&\ccc{UFDomain}\\
\ccc{EuclideanRing}&\ccc{UniqueFactorizationDomain}\\
\ccc{Field}&\ccc{UniqueFactorizationDomain}\\
\hline
\end{tabular}

Note: In case the polynomial is univariate and the innermost coefficient is a \ccc{Field} the polynomial is model of \ccc{EuclideanRing}.

%Note:The concept \ccc{Polynomial_1} refines \ccc{EuclideanRing} in case 
%\ccc{Innermost_coefficient_type} is a \ccc{Field}. 

\ccSeeAlso 

\ccRefIdfierPage{AlgebraicStructureTraits}\\
\ccRefIdfierPage{PolynomialTraits_d}\\

\ccHasModels

\ccRefIdfierPage{CGAL::Polynomial<Coeff>}

\end{ccRefConcept}