AlgebraicKernel_d_2::Isolate_2 Concept Reference

Definition

Computes an isolating box for a given AlgebraicKernel_d_2::Algebraic_real_2.

Refines

AdaptableFunctor

See also

AlgebraicKernel_d_2::IsolateX_2

AlgebraicKernel_d_2::IsolateY_2

AlgebraicKernel_d_2::ComputePolynomialX_2

AlgebraicKernel_d_2::ComputePolynomialY_2

Types
typedef std::array< AlgebraicKernel_d_1::Bound, 4 >	result_type

Operations
result_type	operator() (AlgebraicKernel_d_2::Algebraic_real_2 a, AlgebraicKernel_d_2::Polynomial_2 f)
	The returned std::array \( [xl,xu,yl,yu]\) represents an open isolating box \( B=(xl,xu)\times(yl,yu)\) for \( a\) with respect to \( f\).
result_type	operator() (AlgebraicKernel_d_2::Algebraic_real_2 a, AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g)
	The returned std::array \( [xl,xu,yl,yu]\) represents an open isolating box \( B=(xl,xu)\times(yl,yu)\) for \( a\) with respect to the common solutions of \( f\) and \( g\).

Member Function Documentation

operator()() [1/2]

result_type AlgebraicKernel_d_2::Isolate_2::operator()	(	AlgebraicKernel_d_2::Algebraic_real_2	a,
		AlgebraicKernel_d_2::Polynomial_2	f
	)

The returned std::array \( [xl,xu,yl,yu]\) represents an open isolating box \( B=(xl,xu)\times(yl,yu)\) for \( a\) with respect to \( f\).

Precondition

\( f(a)\neq0\)

Postcondition

\( a \in B\).

\( \{ r | f(r)=0 \} \cap\overline{B} = \emptyset\).

operator()() [2/2]

result_type AlgebraicKernel_d_2::Isolate_2::operator()	(	AlgebraicKernel_d_2::Algebraic_real_2	a,
		AlgebraicKernel_d_2::Polynomial_2	f,
		AlgebraicKernel_d_2::Polynomial_2	g
	)

The returned std::array \( [xl,xu,yl,yu]\) represents an open isolating box \( B=(xl,xu)\times(yl,yu)\) for \( a\) with respect to the common solutions of \( f\) and \( g\).

It is not necessary that \( a\) is a common solution of \( f\) and \( g\).

Postcondition

\( a \in B\).

\( \{ r | f(r)=g(r)=0 \} \cap\overline{B} \in\{\{a\},\emptyset\}\).