\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12.1 - Algebraic Kernel
AlgebraicKernel_d_2::Isolate_2 Concept Reference

Definition

Types

typedef CGAL::cpp11::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 CGAL::cpp11::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 CGAL::cpp11::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...
 

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 CGAL::cpp11::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 CGAL::cpp11::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
\( a \in B\).
\( \{ r | f(r)=g(r)=0 \} \cap\overline{B} \in\{\{a\},\emptyset\}\).