#include <Concepts/AlgebraicKernel_d_2--ApproximateRelativeY_2.h>

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::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. More...

Member Typedef Documentation

◆ first_argument_type

typedef AlgebraicKernel_d_2::Algebraic_real_2 AlgebraicKernel_d_2::ApproximateRelativeY_2::first_argument_type

◆ result_type

typedef std::pair<AlgebraicKernel_d_1::Bound, AlgebraicKernel_d_1::Bound> AlgebraicKernel_d_2::ApproximateRelativeY_2::result_type

◆ second_argument_type

typedef int AlgebraicKernel_d_2::ApproximateRelativeY_2::second_argument_type

Member Function Documentation

◆ 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: \( p.first <= y \); \( y <= p.second \); \( (y - p.first) <= 2^{-a} |y|\); \( (p.second - y) <= 2^{-a} |y|\)