\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.4 - Polynomial
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
PolynomialTraits_d::Canonicalize Concept Reference

Definition

For a given polynomial \( p\) this AdaptableUnaryFunction computes the unique representative of the set

\[ {\cal P} := \{ q\ |\ \lambda * q = p\ for\ some\ \lambda \in R \}, \]

where \( R\) is the base of the polynomial ring.

In case PolynomialTraits::Innermost_coefficient_type is a model of Field, the computed polynomial is the monic polynomial in \( \cal P\), that is, the innermost leading coefficient equals one.

In case PolynomialTraits::Innermost_coefficient_type is a model of UniqueFactorizationDomain, the computed polynomial is the one with a multivariate content of one.

For all other cases the notion of uniqueness is up to the concrete model.

Note that the computed polynomial has the same zero set as the given one.

Refines:

AdaptableUnaryFunction

CopyConstructible

DefaultConstructible

See Also
Polynomial_d
PolynomialTraits_d

Types

typedef
PolynomialTraits_d::Polynomial_d 
result_type
 
typedef
PolynomialTraits_d::Polynomial_d 
argument_type
 

Operations

result_type operator() (first_argument_type p)
 Returns the canonical representative of \( p\).