CGAL 4.7 - Algebraic Kernel: AlgebraicKernel_d_2::Solve_2 Concept Reference

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - Algebraic Kernel

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AlgebraicKernel_d_2::Solve_2 Concept Reference
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

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.

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.