CGAL 4.7 - Polynomial: PolynomialTraits_d::PolynomialSubresultants 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 - Polynomial

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PolynomialTraits_d::PolynomialSubresultants Concept Reference
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## Definition

Note: This functor is optional!

Computes the polynomial subresultant of two polynomials \( p\) and \( q\) of type `PolynomialTraits_d::Polynomial_d` with respect to outermost variable. Let \( p=\ccSum{i=0,\ldots,n}{} p_i x^i\) and \( q=\ccSum{i=0,\ldots,m}{} q_i x^i\), where \( x\) is the outermost variable. The \( i\)-th subresultant (with \( i=0,\ldots,\min\{n,m\}\)) is defined by

where \( p_i\) and \( q_i\) are set to zero if \( i<0\). In the case that \( n=m\), \( \mathrm{Sres_n}\) is set to \( q\).

The result is written in an output range, starting with the \( 0\)-th subresultant \( \mathrm{Sres}_0(p,q)\) (aka as the resultant of \( p\) and \( q\)).

Refines:

  `AdaptableBinaryFunction`

  `CopyConstructible`

  `DefaultConstructible`

See Also
  `Polynomial_d`
  `PolynomialTraits_d`
  `PolynomialTraits_d::Resultant`
  `PolynomialTraits_d::PrincipalSubresultants`
  `PolynomialTraits_d::PolynomialSubresultantsWithCofactors`
  `PolynomialTraits_d::SturmHabichtSequence`

## Operations

template<typename OutputIterator >
OutputIterator | operator() (Polynomial_d p, Polynomial_d q, OutputIterator out)
| computes the polynomial subresultants of \( p\) and \( q\), with respect to the outermost variable. More...
template<typename OutputIterator >
OutputIterator | operator() (Polynomial_d p, Polynomial_d q, OutputIterator out, int i)
| computes the polynomial subresultants of \( p\) and \( q\), with respect to the variable \( x_i\).

## Member Function Documentation

template<typename OutputIterator >

OutputIterator PolynomialTraits_d::PolynomialSubresultants::operator() | ( | Polynomial_d | p,
|  | Polynomial_d | q,
|  | OutputIterator | out
| ) |  |

computes the polynomial subresultants of \( p\) and \( q\), with respect to the outermost variable.

Each element is of type `PolynomialTraits_d::Polynomial_d`.