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

operator()()

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>.