\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.7 - Polynomial
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PolynomialTraits_d::Canonicalize Concept Reference
Polynomial Reference » Concepts

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 \( p\). More...
 

Member Typedef Documentation

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

Member Function Documentation

result_type PolynomialTraits_d::Canonicalize::operator() ( first_argument_type  p)

Returns the canonical representative of \( p\).