CGAL 6.2 - Algebraic Kernel: AlgebraicKernel_d_1::ApproximateRelative_1 Concept Reference

CGAL 6.2 - Algebraic Kernel

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AlgebraicKernel_d_1::ApproximateRelative_1 Concept Reference
Reference Manual » Concepts » Univariate Algebraic Kernel

## Definition

A model of `AlgebraicKernel_d_1::ApproximateRelative_1` is an `AdaptableBinaryFunction` that computes an approximation of an `AlgebraicKernel_d_1::Algebraic_real_1` value with respect to a given relative precision.

Refines
  `AdaptableBinaryFunction`

See also
  `AlgebraicKernel_d_1::ApproximateAbsolute_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 int | second_argument_type

## Operations
result_type | operator() (const first_argument_type &x, const second_argument_type &r)
| 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_1::ApproximateRelative_1::operator() | ( | const first_argument_type & | x,
|  | const second_argument_type & | r
| ) |  |

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 given value \( x\) with respect to the given relative precision \( r\).

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