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 \( a\). More...

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>.

template<class OutputIterator >

OutputIterator PolynomialTraits_d::SquareFreeFactorize::operator()	(	PolynomialTraits_d::Polynomial_d	p,
		OutputIterator	it
	)

As the first operator, just not computing the factor \( a\).