CGAL 6.0 - Algebraic Kernel
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AlgebraicKernel_d_2::Isolate_2 Concept Reference

Definition

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]

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