AlgebraicKernel_d_1::Solve_1 Class Reference

#include <Concepts/AlgebraicKernel_d_1--Solve_1.h>

Definition

Computes the real roots of a univariate polynomial.

Refines:

Assignable

CopyConstructible

Operations
A model of this type must provide:
template<class OutputIterator >
OutputIterator	operator() (AlgebraicKernel_d_1::Polynomial_1 p, OutputIterator res)
	Computes all real solutions of \( p\) with multiplicity, and copies them as objects of type std::pair<AlgebraicKernel_d_1::Algebraic_real_1, AlgebraicKernel_d_1::Multiplicity_type> in res. More...
template<class OutputIterator >
OutputIterator	operator() (AlgebraicKernel_d_1::Polynomial_1 p, bool known_to_be_square_free, OutputIterator res)
	Computes all real solutions of \( p\), and copies them as objects of type AlgebraicKernel_d_1::Algebraic_real_1 in res. More...
template<class OutputIterator >
OutputIterator	operator() (AlgebraicKernel_d_1::Polynomial_1 p, AlgebraicKernel_d_1::Bound l, AlgebraicKernel_d_1::Bound u, OutputIterator res)
	Computes all real solutions of \( p\) in the closed interval \( [l,u]\) with multiplicity, and copies them as objects of type std::pair<AlgebraicKernel_d_1::Algebraic_real_1, AlgebraicKernel_d_1::Multiplicity_type> in res. More...
template<class OutputIterator >
OutputIterator	operator() (AlgebraicKernel_d_1::Polynomial_1 p, bool known_to_be_square_free, AlgebraicKernel_d_1::Bound l, AlgebraicKernel_d_1::Bound u, OutputIterator res)
	Computes all real solutions of \( p\) in the closed interval \( [l,u]\), and copies them as objects of type AlgebraicKernel_d_1::Algebraic_real_1 in res. More...

Member Function Documentation

operator()() [1/4]

template<class OutputIterator >

OutputIterator AlgebraicKernel_d_1::Solve_1::operator()	(	AlgebraicKernel_d_1::Polynomial_1	p,
		AlgebraicKernel_d_1::Bound	l,
		AlgebraicKernel_d_1::Bound	u,
		OutputIterator	res
	)

Computes all real solutions of \( p\) in the closed interval \( [l,u]\) with multiplicity, and copies them as objects of type std::pair<AlgebraicKernel_d_1::Algebraic_real_1, AlgebraicKernel_d_1::Multiplicity_type> in res.

operator()() [2/4]

template<class OutputIterator >

OutputIterator AlgebraicKernel_d_1::Solve_1::operator()	(	AlgebraicKernel_d_1::Polynomial_1	p,
		bool	known_to_be_square_free,
		AlgebraicKernel_d_1::Bound	l,
		AlgebraicKernel_d_1::Bound	u,
		OutputIterator	res
	)

Computes all real solutions of \( p\) in the closed interval \( [l,u]\), and copies them as objects of type AlgebraicKernel_d_1::Algebraic_real_1 in res.

The bool known_to_be_square_free indicates whether \( p\) is known to be square free. Each root, though it might be a multiple root, is reported only once.

operator()() [3/4]

template<class OutputIterator >

OutputIterator AlgebraicKernel_d_1::Solve_1::operator()	(	AlgebraicKernel_d_1::Polynomial_1	p,
		bool	known_to_be_square_free,
		OutputIterator	res
	)

Computes all real solutions of \( p\), and copies them as objects of type AlgebraicKernel_d_1::Algebraic_real_1 in res.

The bool known_to_be_square_free indicates whether \( p\) is known to be square free. Each root, though it might be a multiple root, is reported only once.

operator()() [4/4]

template<class OutputIterator >

OutputIterator AlgebraicKernel_d_1::Solve_1::operator()	(	AlgebraicKernel_d_1::Polynomial_1	p,
		OutputIterator	res
	)

Computes all real solutions of \( p\) with multiplicity, and copies them as objects of type std::pair<AlgebraicKernel_d_1::Algebraic_real_1, AlgebraicKernel_d_1::Multiplicity_type> in res.