\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12 - Algebraic Kernel
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AlgebraicKernel_d_2::ApproximateRelativeX_2 Concept Reference
Algebraic Kernel Reference » 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. More...
 

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