AlgebraicKernel_d_2::IsolateY_2 Class Reference

#include <Concepts/AlgebraicKernel_d_2--IsolateY_2.h>

Definition

Computes an isolating interval for the second coordinate of an AlgebraicKernel_d_2::Algebraic_real_2 with respect to the real roots of a univariate polynomial.

Refines

AdaptableBinaryFunction

See also

AlgebraicKernel_d_2::IsolateX_2

AlgebraicKernel_d_2::ComputePolynomialX_2

AlgebraicKernel_d_2::ComputePolynomialY_2

Types
typedef std::pair< AlgebraicKernel_d_2::Bound, AlgebraicKernel_d_2::Bound >	result_type
typedef AlgebraicKernel_d_2::Algebraic_real_2	first_argument_type
typedef AlgebraicKernel_d_2::Polynomial_1	second_argument_type

Operations
result_type	operator() (first_argument_type a, second_argument_type p)
	Computes an open isolating interval \( I=(l,u)\) for the second coordinate \( y\) of \( a\) with respect to the real roots of \( p\).

Member Typedef Documentation

first_argument_type

typedef AlgebraicKernel_d_2::Algebraic_real_2 AlgebraicKernel_d_2::IsolateY_2::first_argument_type

result_type

typedef std::pair<AlgebraicKernel_d_2::Bound,AlgebraicKernel_d_2::Bound> AlgebraicKernel_d_2::IsolateY_2::result_type

second_argument_type

typedef AlgebraicKernel_d_2::Polynomial_1 AlgebraicKernel_d_2::IsolateY_2::second_argument_type

Member Function Documentation

operator()()

result_type AlgebraicKernel_d_2::IsolateY_2::operator()	(	first_argument_type	a,
		second_argument_type	p
	)

Computes an open isolating interval \( I=(l,u)\) for the second coordinate \( y\) of \( a\) with respect to the real roots of \( p\).

It is not required that \( x\) is a root of \( p\).

Postcondition

\( y \in I\).

\( p(\alpha) \neq0 | \forall\alpha\in\overline{I}\backslash y\).