CGAL 4.7 - Polynomial: PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor Concept Reference

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CGAL 4.7 - Polynomial

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PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor Concept Reference
Concepts

## Definition

This `AdaptableFunctor` computes a square-free factorization up to a constant factor (utcf) of a `PolynomialTraits_d::Polynomial_d`.

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

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

The constant factor \( a\) is not computed.

This functor is well defined even though `PolynomialTraits_d::Innermost_coefficient_type` may not be a `UniqueFactorizationDomain`.

Refines:

  Assignable

  CopyConstructible

  DefaultConstructible

See Also
  `Polynomial_d`
  `PolynomialTraits_d`
  `PolynomialTraits_d::SquareFreeFactorize`

## Operations

template<class OutputIterator >
OutputIterator | operator() (PolynomialTraits_d::Polynomial_d p, OutputIterator it)
| Computes the square-free factorization of \( p\) and returns the past-the-end iterator of the written range. More...

## Member Function Documentation

template<class OutputIterator >

OutputIterator PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor::operator() | ( | PolynomialTraits_d::Polynomial_d | p,
|  | OutputIterator | it
| ) |  |

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>`.