\begin{ccRefConcept}{PolynomialTraits_d::Principal_subresultants}
\ccDefinition

Computes the principal subresultant of two polynomials $f$ and $g$ of 
type \ccc{PolynomialTraits_d::Polynomial_d} 
with respect a certain variable $x_i$.
The principal subresultants are also known as {\it scalar} subresultants.

The $j$th such principal subresultant is defined to be the coefficient 
of $x_i^j$ in the $j$-th subresultant polynomial of $f$ and $g$.
Since the degree of the $j$-th subresultant polynomial is at most $j$,
this principal coefficients are sometimes called the 
{\tt formal leading coefficients} (``formal'' because they might vanish).

The result is written in an output range, 
starting with the $0$th principal subresultant
(aka as the resultant of $f$ and $g$).

\ccOperations
\ccMethod{template<typename OutputIterator>
        OutputIterator operator()(Polynomial_d   f,
                                  Polynomial_d   g,
                                  OutputIterator out);}
         { computes the principal subresultants of $f$ and $g$, 
           with respect to the outermost variable. Each element is of type
           \ccc{PolynomialTraits_d::Coefficient_type}.}

\ccMethod{template<typename OutputIterator>
        OutputIterator operator()(Polynomial_d   f,
                                  Polynomial_d   g,
                                  OutputIterator out,
                                  int i);}
         { computes the principal subresultants of $f$ and $g$, 
           with respect to the variable $x_i$.}

%\ccHasModels

\ccSeeAlso

\ccRefIdfierPage{Polynomial_d}\\
\ccRefIdfierPage{PolynomialTraits_d}\\

\end{ccRefConcept}
