CGAL 6.2 - Algebraic Kernel: AlgebraicKernel_d_1::Isolate_1 Concept Reference

CGAL 6.2 - Algebraic Kernel

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AlgebraicKernel_d_1::Isolate_1 Concept Reference
Reference Manual » Concepts » 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 \( p\).

## Member Function Documentation

## ◆ operator()()

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