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

CGAL 4.8 - Polynomial

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PolynomialTraits_d::PrincipalSubresultants Concept Reference
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## Definition

Note: This functor is optional!

Computes the principal subresultant of two polynomials \( p\) and \( q\) of type `PolynomialTraits_d::Coefficient_type` with respect to the outermost variable. The \( i\)-th principal subresultant, \( \mathrm{sres}_i(p,q)\), is defined as the coefficient at \( t^i\) of the \( i\)-th polynomial subresultant \( \mathrm{Sres}_i(p,q)\). Thus, it is either the leading coefficient of \( \mathrm{Sres}_i\), or zero in the case where its degree is below \( i\).

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

Refines:

  `AdaptableBinaryFunction`

  `CopyConstructible`

  `DefaultConstructible`

See Also
  `Polynomial_d`
  `PolynomialTraits_d`
  `PolynomialTraits_d::Resultant`
  `PolynomialTraits_d::PolynomialSubresultants`
  `PolynomialTraits_d::PrincipalSturmHabichtSequence`

## Operations
template<typename OutputIterator >
OutputIterator | operator() (Polynomial_d p, Polynomial_d q, OutputIterator out)
| computes the principal 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 principal subresultants of \( p\) and \( q\), with respect to the variable \( x_i\).

## Member Function Documentation

template<typename OutputIterator >

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

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

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