CGAL 5.3 - Algebraic Kernel
AlgebraicKernel_d_2::Isolate_2 Concept Reference

## Definition

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

Refines:
AdaptableFunctor
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 $$f$$. More...

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 $$g$$. More...

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