\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13.1 - Algebraic Kernel
List of all members
AlgebraicKernel_d_2::Solve_2 Concept Reference
Algebraic Kernel Reference » Concepts » Bivariate Algebraic Kernel

Definition

Computes the real zero-dimensional solutions of a bivariate polynomial system. The multiplicity stored in the output iterator is the multiplicity in the system.

Refines:

Assignable

CopyConstructible

Operations

A model of this type must provide:

template<class OutputIterator >
OutputIterator operator() (AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g, OutputIterator res)
 Computes all common solutions of \( f\) and \( g\) with multiplicity, and copies them as objects of type std::pair<AlgebraicKernel_d_2::Algebraic_real_2, AlgebraicKernel_d_2::Multiplicity_type> in res. More...
 
template<class OutputIterator >
OutputIterator operator() (AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g, AlgebraicKernel_d_2::Bound xl, AlgebraicKernel_d_2::Bound xu, AlgebraicKernel_d_2::Bound yl, AlgebraicKernel_d_2::Bound yu, OutputIterator res)
 Computes all common solutions of \( f\) and \( g\) in the closed box \( [xl,xu]\times[yl,yu]\), and copies them as objects of type std::pair<AlgebraicKernel_d_2::Algebraic_real_2, AlgebraicKernel_d_2::Multiplicity_type> in res. More...
 

Member Function Documentation

◆ operator()() [1/2]

template<class OutputIterator >
OutputIterator AlgebraicKernel_d_2::Solve_2::operator() ( AlgebraicKernel_d_2::Polynomial_2  f,
AlgebraicKernel_d_2::Polynomial_2  g,
OutputIterator  res 
)

Computes all common solutions of \( f\) and \( g\) with multiplicity, and copies them as objects of type std::pair<AlgebraicKernel_d_2::Algebraic_real_2, AlgebraicKernel_d_2::Multiplicity_type> in res.

Precondition
\( f\) is square free.
\( g\) is square free.
\( f\) and \( g\) are coprime.

◆ operator()() [2/2]

template<class OutputIterator >
OutputIterator AlgebraicKernel_d_2::Solve_2::operator() ( AlgebraicKernel_d_2::Polynomial_2  f,
AlgebraicKernel_d_2::Polynomial_2  g,
AlgebraicKernel_d_2::Bound  xl,
AlgebraicKernel_d_2::Bound  xu,
AlgebraicKernel_d_2::Bound  yl,
AlgebraicKernel_d_2::Bound  yu,
OutputIterator  res 
)

Computes all common solutions of \( f\) and \( g\) in the closed box \( [xl,xu]\times[yl,yu]\), and copies them as objects of type std::pair<AlgebraicKernel_d_2::Algebraic_real_2, AlgebraicKernel_d_2::Multiplicity_type> in res.

Precondition
\( f\) is square free.
\( g\) is square free.
\( f\) and \( g\) are coprime.