% $Date: 2003/09/15 16:37:45 $ $Author: nthiery $ $Revision: 1.1.1.1 $

\begin{Mhelppage}{SpScalarPol}{S. Veigneau}

  \begin{MInfo}
    \eng{scalar product on polynomials}
  \end{MInfo}
  
\begin{MCalls}
 \Mcall{pol1,pol2,n}
\end{MCalls}

%
\begin{MParameters}
  \param{pol1}
  \eng{any polynomial expression}
  \param{pol2}
  \eng{any polynomial expression}
  \param{n}
  \eng{any positive integer denoting the degree of a symmetric group} 
\end{MParameters}
%
\begin{MIntro}
  \eng{
The {\Mthis} function computes the scalar product
\Mmath{\Mex{<pol1, pol2>}}{\langle\Mex{pol1},\Mex{pol2}\rangle}
corresponding to the symmetric group of degree \Mex{n}.
 
\Mmath{\Mex{<pol1, pol2>}}{\langle\Mex{pol1},\Mex{pol2}\rangle}=
\Mmath{\Mex{<pol1 x pol2, 1>}}{\langle\Mex{pol1}\times\Mex{pol2},1\rangle}.
 
\Mmath{\Mex{<pol, 1>}}{\langle\Mex{pol1},1\rangle} is the symmetric function
(in the basis of Schur functions) obtained  by applying the maximal divided
difference of \Mmath{Sn}{S_n} to \Mex{pol}.
}
\end{MIntro}
%
\begin{MExample}{ex1}
%
\begin{Mexin}
muEC::SP::SpScalarPol(x1^6*x2, x2^2*x3, 3);
\end{Mexin}
\begin{Mexout}
                          s[4, 2, 1]
\end{Mexout}
\end{MExample}
%
\MRelatedFunctions{}
\end{Mhelppage}
