CGAL 4.7 - Algebraic Kernel: AlgebraicKernel_d_2::Isolate_2 Concept Reference

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CGAL 4.7 - Algebraic Kernel

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AlgebraicKernel_d_2::Isolate_2 Concept Reference
Bivariate Algebraic Kernel

## Definition

Computes an isolating box for a given `AlgebraicKernel_d_2::Algebraic_real_2`.

Refines:
  `AdaptableFunctor`

See Also
  `AlgebraicKernel_d_2::IsolateX_2`
  `AlgebraicKernel_d_2::IsolateY_2`
  `AlgebraicKernel_d_2::ComputePolynomialX_2`
  `AlgebraicKernel_d_2::ComputePolynomialY_2`

## 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

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
  \( a \in B\).
  \( \{ r | f(r)=0 \} \cap\overline{B} = \emptyset\).

result_type AlgebraicKernel_d_2::Isolate_2::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 \( g\).

It is not necessary that \( a\) is a common solution of \( f\) and \( g\).

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