CGAL 4.7 - Algebraic Kernel: AlgebraicKernel_d_2::SquareFreeFactorize_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

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
AlgebraicKernel_d_2::SquareFreeFactorize_2 Concept Reference
Bivariate Algebraic Kernel

## Definition

Computes a square free factorization of an `AlgebraicKernel_d_2::Polynomial_2`.

A polynomial \( p\) is factored into square free and pairwise coprime non-constant factors \( q_i\) with multiplicities \( m_i\) and a constant factor \( c\), such that \( p = c \cdot q_1^{m_1} \cdot ... \cdot q_n^{m_n}\).

The factor multiplicity pairs \( <q_i,m_i>\) are written to the given output iterator. The constant factor \( c\) is not computed.

Refines:

  `Assignable`

  `CopyConstructible`

See Also
  `AlgebraicKernel_d_2::IsSquareFree_2`
  `AlgebraicKernel_d_2::MakeSquareFree_2`

## Operations

template<class OutputIterator >
OutputIterator | operator() (const AlgebraicKernel_d_2::Polynomial_2 &p, OutputIterator res)
| Copies in the output iterator the factors of a square free factorization of \( p\), with their multiplicity, as objects of type `std::pair<AlgebraicKernel_d_2::Polynomial_2, AlgebraicKernel_d_2::Multiplicity_type>`.