CGAL 4.12 - Algebraic Kernel
AlgebraicKernel_d_2::ApproximateRelativeY_2 Concept Reference

## Definition

A model of AlgebraicKernel_d_2::ApproximateRelativeY_2 is an AdaptableBinaryFunction that computes an approximation of the $$y$$-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::Boundresult_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. More...

## ◆ operator()()

 result_type AlgebraicKernel_d_2::ApproximateRelativeY_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 $$y$$-coordinate $$y$$ of the AlgebraicKernel_d_2::Algebraic_real_2 value $$v$$ with respect to the relative precision $$a$$.

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