\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11 - Algebraic Kernel
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AlgebraicKernel_d_1::Isolate_1 Concept Reference
Univariate Algebraic Kernel

Definition

Computes an open isolating interval for an AlgebraicKernel_d_1::Algebraic_real_1 with respect to the real roots of a given univariate polynomial.

Refines:
AdaptableBinaryFunction
See Also
AlgebraicKernel_d_1::ComputePolynomial_1

Types

typedef std::pair
< AlgebraicKernel_d_1::Bound,
AlgebraicKernel_d_1::Bound > 		result_type
 
typedef
AlgebraicKernel_d_1::Algebraic_real_1 		first_argument_type
 
typedef
AlgebraicKernel_d_1::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 \( a\) with respect to the real roots of \( p\). More...
 

Member Function Documentation

result_type AlgebraicKernel_d_1::Isolate_1::operator() ( first_argument_type  a,
second_argument_type  p 
)

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

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

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