\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12.2 - Algebraic Kernel
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AlgebraicKernel_d_2::IsolateX_2 Concept Reference
Algebraic Kernel Reference » Concepts » Bivariate Algebraic Kernel

Definition

Computes an isolating interval for the first 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::IsolateY_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 first coordinate \( x\) of \( a\) with respect to the real roots of \( p\). More...
 

Member Function Documentation

◆ operator()()

result_type AlgebraicKernel_d_2::IsolateX_2::operator() ( first_argument_type  a,
second_argument_type  p 
)

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

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

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