CGAL 6.1.2 - Algebraic Kernel: AlgebraicKernel_d_2::MakeCoprime_2 Concept Reference

CGAL 6.1.2 - Algebraic Kernel

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AlgebraicKernel_d_2::MakeCoprime_2 Concept Reference
Reference Manual » Concepts » 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
  `AdaptableQuinaryFunction`

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.

## Member Function Documentation

## ◆ operator()()

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.