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

CGAL 4.8 - Polynomial

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PolynomialTraits_d::SquareFreeFactorize Concept Reference
Concepts

## 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>`.