AlgebraicKernel_d_2::ApproximateRelativeX_2 Concept Reference

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. More...

Member Function Documentation

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

\( p.first <= x \)

\( x <= p.second \)

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

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