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

\begin{Mhelppage}{SfDiff}{V. Prosper}%
  \begin{MInfo}
    \eng{differential operator}
  \end{MInfo}
   

\begin{MCalls}
  \Mcall{sf1,sf2}
\end{MCalls}

\begin{MParameters}
  \param{sf1, sf2}
  \eng{any symmetric functions}
\end{MParameters}

\begin{MIntro}
  \eng{
The {\Mthis} function computes 
\Mmath{D\_{\Mex{sf1}}(\Mex{sf2})}{D_{\mathtt{sf1}}(\mathtt{sf2})}
in which \Mmath{D\_{sf1}}{D_{\mathtt{sf1}}} stands for
the differential operator corresponding to the symmetric function \Mex{sf1}.
Both symmetric functions \Mex{sf1} and \Mex{sf2} can be expressed in terms of
any known basis since both expressions are converted in terms of Schur
functions.
One has
\Mmath{D\_{\Mex{s[part1]}}(\Mex{s[part2]})}%
      {D_{\mathtt{s_{part1}}}(\mathtt{s_{part2}})}
=
\Mmath{\Mex{s[part2/part1]}}{\mathtt{s_{part1/part2}}}, and the operation is
extended by linearity to any pair \Mex{sf1}, \Mex{sf2}.
 
The result is a linear combination of Schur functions, and not collected.
}
\end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::SYMF::SfDiff( s[3,1] + q*s[3], 2*e[2]*p[2] );
\end{Mexin}
\begin{Mexout}
                       2 s[] + 2 q s[1]
\end{Mexout}
% \begin{Mexout}[hide]
                       % 2*s[]+2*q*s[1]
% \end{Mexout}
\begin{Mexin}
muEC::SYMF::Tos( 2*e[2]*p[2] );
\end{Mexin}
\begin{Mexout}
            2 s[3, 1] - 2 s[2, 2] - 2 s[1, 1, 1, 1]
\end{Mexout}
% \begin{Mexout}[hide]
             % 2*s[3, 1]-2*s[2, 2]-2*s[1, 1, 1, 1]
% \end{Mexout}
\begin{Mexin}
muEC::SYMF::SfDiff( s[4,3,2,1,1], s[4,3,2,1,1] );
\end{Mexin}
\begin{Mexout}
                              s[]
\end{Mexout}
\end{MExample}

\MRelatedFunctions{Tos}
\end{Mhelppage}
