% $Date: 2003/09/15 16:37:46 $ $Author: nthiery $ $Revision: 1.1.1.1 $

\begin{Mhelppage}{SfScalar}{V. Prosper}
  
  \begin{MInfo}
    \eng{scalar product of symmetric functions}
  \end{MInfo}
  
  \begin{MCalls}
    \Mcall{sf1,sf2\Mopt{,sfp}}
  \end{MCalls}

  \begin{MParameters}
    \param{sf1, sf2}
    \eng{any symmetric functions}
    \param{sfp}
    \eng{any procedure accepting a partition as input} 
  \end{MParameters}

  \begin{MIntro}
    \eng{The {\Mthis} function computes the scalar product between the
      symmetric functions \Mex{sf1} and {sf2}.
      
      This scalar product is such that Schur functions constitute an
      orthonormal basis.
      
      The \Mex{p}-basis is an orthogonal basis: \Mex{\Mthis(p[part],
        p[part]) = SfZee([part])}.
      
      One can choose another scalar product, for which the
      \Mex{p}-basis will still remain orthogonal by replacing
      \Mex{SfZee} with any procedure \Mex{sfp} accepting partitions.
      }
  \end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::SYMF::SfScalar( p[3,3,1], p[3,3,1] );
\end{Mexin}
\begin{Mexout}
                              18
\end{Mexout}
\begin{Mexin}
muEC::SYMF::SfZee( [3,3,1] );
\end{Mexin}
\begin{Mexout}
                              18
\end{Mexout}
\end{MExample}

\MRelatedFunctions{SfZee}
\end{Mhelppage}
