AlgebraicKernel_d_2::Solve_2 Concept Reference

Definition

Computes the real zero-dimensional solutions of a bivariate polynomial system. The multiplicity stored in the output iterator is the multiplicity in the system.

Refines:

Assignable

CopyConstructible

Operations
A model of this type must provide:
template<class OutputIterator >
OutputIterator	operator() (AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g, OutputIterator res)
	Computes all common solutions of \( f\) and \( g\) with multiplicity, and copies them as objects of type std::pair<AlgebraicKernel_d_2::Algebraic_real_2, AlgebraicKernel_d_2::Multiplicity_type> in res. More...
template<class OutputIterator >
OutputIterator	operator() (AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g, AlgebraicKernel_d_2::Bound xl, AlgebraicKernel_d_2::Bound xu, AlgebraicKernel_d_2::Bound yl, AlgebraicKernel_d_2::Bound yu, OutputIterator res)
	Computes all common solutions of \( f\) and \( g\) in the closed box \( [xl,xu]\times[yl,yu]\), and copies them as objects of type std::pair<AlgebraicKernel_d_2::Algebraic_real_2, AlgebraicKernel_d_2::Multiplicity_type> in res. More...

Member Function Documentation

operator()() [1/2]

template<class OutputIterator >

OutputIterator AlgebraicKernel_d_2::Solve_2::operator()	(	AlgebraicKernel_d_2::Polynomial_2	f,
		AlgebraicKernel_d_2::Polynomial_2	g,
		OutputIterator	res
	)

Computes all common solutions of \( f\) and \( g\) with multiplicity, and copies them as objects of type std::pair<AlgebraicKernel_d_2::Algebraic_real_2, AlgebraicKernel_d_2::Multiplicity_type> in res.

Precondition

\( f\) is square free.

\( g\) is square free.

\( f\) and \( g\) are coprime.

operator()() [2/2]

template<class OutputIterator >

OutputIterator AlgebraicKernel_d_2::Solve_2::operator()	(	AlgebraicKernel_d_2::Polynomial_2	f,
		AlgebraicKernel_d_2::Polynomial_2	g,
		AlgebraicKernel_d_2::Bound	xl,
		AlgebraicKernel_d_2::Bound	xu,
		AlgebraicKernel_d_2::Bound	yl,
		AlgebraicKernel_d_2::Bound	yu,
		OutputIterator	res
	)

Computes all common solutions of \( f\) and \( g\) in the closed box \( [xl,xu]\times[yl,yu]\), and copies them as objects of type std::pair<AlgebraicKernel_d_2::Algebraic_real_2, AlgebraicKernel_d_2::Multiplicity_type> in res.

Precondition

\( f\) is square free.

\( g\) is square free.

\( f\) and \( g\) are coprime.