\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Algebraic Kernel

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AlgebraicKernel_d_2::IsolateX_2 Concept Reference
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

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