mirror of https://github.com/CGAL/cgal
46 lines
1.3 KiB
TeX
46 lines
1.3 KiB
TeX
\begin{ccRefConcept}{PolynomialTraits_d::Canonicalize}
|
|
|
|
\ccDefinition
|
|
|
|
This \ccc{AdaptableUnaryFunction} computes a unique representative from the set:
|
|
$\{ q | \lambda * q = p\ for\ some\ \lambda \in R \}$,
|
|
where $p$ is the given polynomial and $R$ the base of the polynomial ring.
|
|
In particular, the computed polynomial has the same zero set as the given one.
|
|
|
|
In case \ccc{PolynomialTraits::Innermost_coefficient_type} is a model of \ccc{Field},
|
|
the computed polynomial is the {\em monic} polynomial,
|
|
that is the innermost leading coefficient equals one.
|
|
In case \ccc{PolynomialTraits::Innermost_coefficient_type} is a model
|
|
of \ccc{UniqueFactorizationDomain}, the gcd over all innermost coefficients of
|
|
the computed polynomial is one.
|
|
For all other cases the notion of uniqueness is up to the concrete model.
|
|
|
|
|
|
|
|
\ccRefines
|
|
|
|
\ccc{AdaptableUnaryFunction}
|
|
|
|
\ccTypes
|
|
|
|
|
|
\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
|
|
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}\ccGlue
|
|
\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}
|
|
|
|
\ccOperations
|
|
|
|
\ccCreationVariable{fo}
|
|
\ccMethod{result_type operator()(first_argument_type p);}{
|
|
Returns the cononical representative of $p$.}
|
|
|
|
|
|
|
|
%\ccHasModels
|
|
|
|
\ccSeeAlso
|
|
|
|
\ccRefIdfierPage{Polynomial_d}\\
|
|
\ccRefIdfierPage{PolynomialTraits_d}\\
|
|
|
|
\end{ccRefConcept} |