\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11.3 - Polynomial
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PolynomialTraits_d::SquareFreeFactorize Concept Reference

Definition

This Functor computes a square-free factorization of a PolynomialTraits_d::Polynomial_d.

A polynomial \( p\) is factored into square-free and pairwise coprime non-constant factors \( g_i\) with multiplicities \( m_i\) and a constant factor \( a\), such that \( p = a \cdot g_1^{m_1} \cdot ... \cdot g_n^{m_n}\).

The pairs \( (g_i,m_i)\) are written into the given output iterator.

This functor is well defined if PolynomialTraits_d::Polynomial_d is a UniqueFactorizationDomain.

Refines:

Assignable

CopyConstructible

DefaultConstructible

See Also
Polynomial_d
PolynomialTraits_d
PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor
PolynomialTraits_d::MakeSquareFree
PolynomialTraits_d::IsSquareFree

Operations

template<class OutputIterator >
OutputIterator operator() (PolynomialTraits_d::Polynomial_d p, OutputIterator it, PolynomialTraits_d::Innermost_coefficient_type &a)
 Computes the square-free factorization of \( p\) and returns the past-the-end iterator of the written range. More...
 
template<class OutputIterator >
OutputIterator operator() (PolynomialTraits_d::Polynomial_d p, OutputIterator it)
 As the first operator, just not computing the factor \( a\).
 

Member Function Documentation

template<class OutputIterator >
OutputIterator PolynomialTraits_d::SquareFreeFactorize::operator() ( PolynomialTraits_d::Polynomial_d  p,
OutputIterator  it,
PolynomialTraits_d::Innermost_coefficient_type a 
)

Computes the square-free factorization of \( p\) and returns the past-the-end iterator of the written range.

Precondition
std::iterator_traits< OutputIterator >::value_type must be constructible from std::pair<PolynomialTraits_d::Polynomial_d,int>.