synaps/msolve/BSolver.h File Reference

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Detailed Description

Solving bivariate polynomial system of degree up to 2.

Definition in file BSolver.h.

Go to the source code of this file.

Functions
template<class A>
VectDse< A >	make_vector (const A &a, const A &b)
template<typename SOLVER, typename OutputIterator>
OutputIterator	solve_for_circles (const typename SOLVER::MPoly_2_2 &f1, const typename SOLVER::MPoly_2_2 &f2, OutputIterator res, const SOLVER &mth)
template<typename SOLVER, typename OutputIterator>
OutputIterator	fast_solve (const typename SOLVER::MPoly_2_2 &f1, const typename SOLVER::MPoly_2_2 &f2, OutputIterator ii, const SOLVER &mth)
template<typename SOLVER, typename OutputIterator>
OutputIterator	trivial_solve (const typename SOLVER::MPoly_2_2 &f1, const typename SOLVER::MPoly_2_2 &f2, OutputIterator res, const SOLVER &mth)
template<typename RO_t>
int	check_where (const RO_t &y, const RO_t &x, const typename RO_t::POLY &A, const typename RO_t::POLY &B)
template<typename SOLVER, typename OutputIterator>
OutputIterator	solve (const typename SOLVER::MPoly_2_2 &f1, const typename SOLVER::MPoly_2_2 &f2, OutputIterator ii, const SOLVER &mth)
template<typename SOLVER, typename OutputIterator>
OutputIterator	solve_in_range (const typename SOLVER::MPoly_2_2 &f1, const typename SOLVER::MPoly_2_2 &f2, OutputIterator ii, const typename SOLVER::RO_t &start, const typename SOLVER::RO_t &end, const SOLVER &mth)
template<typename SOLVER, typename O, typename R>
Seq< VectDse< typename SOLVER::RO_t > >	Solve_with_sign (const MPol< typename SOLVER::RT, O, R > &s1, const MPol< typename SOLVER::RT, O, R > &s2, const SOLVER &mth)
template<typename SOLVER, typename O, typename R>
Seq< std::pair< typename SOLVER::RO_t, typename SOLVER::RO_t > >	Solve_with_subres (const MPol< typename SOLVER::RT, O, R > &F1, const MPol< typename SOLVER::RT, O, R > &F2, const SOLVER &mth)
template<typename SOLVER>
int	pos_wrt_point (std::pair< typename SOLVER::FT, int > &isol_point, const typename SOLVER::RO_t &r, const typename SOLVER::Poly &A, const typename SOLVER::Poly &B, const SOLVER &)
	--------- NEW SOLVER - Conics --------------------------
template<typename SOLVER>
int	compute_y_in_generic_position (const Seq< typename SOLVER::FT > &IP, const typename SOLVER::RO_t &r, const typename SOLVER::Poly &A, const typename SOLVER::Poly &B, const SOLVER &)
template<typename SOLVER, typename OutputIterator>
OutputIterator	New_solve (const typename SOLVER::MPoly_2_2 &f1, const typename SOLVER::MPoly_2_2 &f2, OutputIterator res, const SOLVER &mth)

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Function Documentation

template<typename SOLVER>

int pos_wrt_point	(	std::pair< typename SOLVER::FT, int > &	isol_point,
		const typename SOLVER::RO_t &	r,
		const typename SOLVER::Poly &	A,
		const typename SOLVER::Poly &	B,
		const SOLVER &
	)

--------- NEW SOLVER - Conics --------------------------

Definition at line 870 of file BSolver.h.

References denominator(), and numerator().

Referenced by compute_y_in_generic_position().

template<typename SOLVER, typename O, typename R>

Seq< VectDse< typename SOLVER::RO_t > > Solve_with_sign	(	const MPol< typename SOLVER::RT, O, R > &	s1,
		const MPol< typename SOLVER::RT, O, R > &	s2,
		const SOLVER &	mth
	)

Solves the system of two bivariate polynomials using sign_at

Parameters:

	f1	Bivariate polynomial
	f2	Bivariate polynomial

Returns:

std::pair<root_of, root_of>

See also:

root_of, MPol, root_of, sign_at

Definition at line 632 of file BSolver.h.

References Seq< C, R >::begin(), Seq< C, R >::end(), make_vector(), Seq< C, R >::size(), SturmSeq< C, UPoly, SEQ >::size(), Solve(), and to_double().

template<typename SOLVER, typename O, typename R>

Seq< std::pair< typename SOLVER::RO_t, typename SOLVER::RO_t > > Solve_with_subres	(	const MPol< typename SOLVER::RT, O, R > &	F1,
		const MPol< typename SOLVER::RT, O, R > &	F2,
		const SOLVER &	mth
	)

Solves the system of two bivariate polynomials using subresultants.

Parameters:

	f1	Bivariate polynomial
	f2	Bivariate polynomial

Returns:

std::pair<root_of, root_of>

See also:

root_of, MPol, root_of, sign_at

Definition at line 697 of file BSolver.h.

References check_where(), UPOLDAR::degree(), UPOLDAR::lcoeff(), make_vector(), Seq< C, R >::push_back(), Resultant(), Seq< C, R >::size(), SturmSeq< C, UPoly, SEQ >::size(), Solve(), and to_double().