mirror of https://github.com/CGAL/cgal
51 lines
1.7 KiB
TeX
51 lines
1.7 KiB
TeX
\begin{ccRefConcept}{Polynomial_d}
|
|
|
|
\ccDefinition
|
|
|
|
A model of \ccRefName\ 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 \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{UniqueFactorizationDomain}\\
|
|
\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} |