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

CGAL 4.8 - Algebraic Kernel

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
AlgebraicKernel_d_2::MakeCoprime_2 Concept Reference
Bivariate Algebraic Kernel

## Definition

Computes for a given pair of bivariate polynomials \( p_1\), \( p_2\) their common part \( g\) and coprime parts \( q_1\), \( q_2\) respectively.

That is, it computes \( g, q_1, q_2\) such that:

\( c_1 \cdot p_1 = g \cdot q_1\) for some constant \( c_1\) and

\( c_2 \cdot p_2 = g \cdot q_2\) for some constant \( c_2\), such that \( q_1\) and \( q_2\) are coprime.

Refines:
  `AdaptableFunctor` with five arguments

See Also
  `AlgebraicKernel_d_2::IsCoprime_2`

## Types
typedef bool | result_type

## Operations
result_type | operator() (const AlgebraicKernel_d_2::Polynomial_2 &p1, const AlgebraicKernel_d_2::Polynomial_2 &p2, AlgebraicKernel_d_2::Polynomial_2 &g, AlgebraicKernel_d_2::Polynomial_2 &q1, AlgebraicKernel_d_2::Polynomial_2 &q2)
| Computes \( g, q_1, q_2\) as described above. More...

## Member Function Documentation

result_type AlgebraicKernel_d_2::MakeCoprime_2::operator() | ( | const AlgebraicKernel_d_2::Polynomial_2 & | p1,
|  | const AlgebraicKernel_d_2::Polynomial_2 & | p2,
|  | AlgebraicKernel_d_2::Polynomial_2 & | g,
|  | AlgebraicKernel_d_2::Polynomial_2 & | q1,
|  | AlgebraicKernel_d_2::Polynomial_2 & | q2
| ) |  |

Computes \( g, q_1, q_2\) as described above.

Returns whether \( p_1\) and \( p_2\) where already coprime.