CGAL 6.1.2 - Algebraic Kernel: AlgebraicKernel_d_2::ApproximateRelativeX_2 Concept Reference

CGAL 6.1.2 - Algebraic Kernel

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AlgebraicKernel_d_2::ApproximateRelativeX_2 Concept Reference
Reference Manual » Concepts » Bivariate Algebraic Kernel

## Definition

A model of `AlgebraicKernel_d_2::ApproximateRelativeX_2` is an `AdaptableBinaryFunction` that computes an approximation of the \( x\)-coordinate of an `AlgebraicKernel_d_2::Algebraic_real_2` value with respect to a given relative precision.

Refines
  `AdaptableBinaryFunction`

See also
  `AlgebraicKernel_d_2::ApproximateAbsoluteY_2`
  `AlgebraicKernel_d_1::ApproximateAbsolute_1`
  `AlgebraicKernel_d_1::ApproximateRelative_1`

## Types
typedef std::pair< AlgebraicKernel_d_1::Bound, AlgebraicKernel_d_1::Bound > | result_type
typedef AlgebraicKernel_d_2::Algebraic_real_2 | first_argument_type
typedef int | second_argument_type

## Operations
result_type | operator() (const first_argument_type &v, const second_argument_type &a)
| The function computes a pair \( p\) of `AlgebraicKernel_d_1::Bound`, where \( p.first\) represents the lower approximation and \( p.second\) represents the upper approximation.

## Member Function Documentation

## ◆ operator()()

result_type AlgebraicKernel_d_2::ApproximateRelativeX_2::operator() | ( | const first_argument_type & | v,
|  | const second_argument_type & | a
| ) |  |

The function computes a pair \( p\) of `AlgebraicKernel_d_1::Bound`, where \( p.first\) represents the lower approximation and \( p.second\) represents the upper approximation.

The pair \( p\) approximates the \( x\)-coordinate \( x\) of the `AlgebraicKernel_d_2::Algebraic_real_2` value \( v\) with respect to the relative precision \( a\).

Postcondition
  \( p.first <= x \)
  \( x <= p.second \)
  \( (x - p.first) <= 2^{-a} |x|\)
  \( (p.second - x) <= 2^{-a} |x|\)