CGAL 4.7 - Polynomial: PolynomialTraits_d::Canonicalize Concept Reference

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - Polynomial

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PolynomialTraits_d::Canonicalize Concept Reference
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 \( p\).