% $Date: 2003/10/28 21:59:22 $ $Author: nthiery $ $Revision: 1.1.1.2 $

\begin{Mhelppage}{Sf2Table}%
  {V. Prosper}%
  \begin{MInfo}
    \eng{converts a symmetric function into a table}
  \end{MInfo}
  

\begin{MCalls}
  \Mcall{sf,b}
\end{MCalls}

\begin{MParameters}
  \param{sf}
  \eng{any symmetric function}
  \param{b}
  \eng{any name of known basis}
\end{MParameters}

\begin{MIntro}
  \eng{
The {\Mthis} function converts a symmetric function into  a  table.
The table is indexed by partitions (possibly empty) and each  entry that
corresponds  to  a  partition  \Mex{part} is interpreted as the coefficient of
\Mex{b[part]} in the expression of the  symmetric  function  in  the  basis
\Mex{b}.
 
This function can be useful if one wants to act either  on  coefficients
or on partitions.
For instance, one can use the \Mex{map} function to act on coefficients.
}
\end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::SYMF::Sf2Table( q^2*s[3,1,1] + q*s[4,2] + q + s[4,2], s );
\end{Mexin}
\begin{Mexout}
                       table(
                         [] = q,
                                      2
                         [3, 1, 1] = q ,
                         [4, 2] = q + 1
                       )
\end{Mexout}
% \begin{Mexout}[hide]
           % table([]=q,[3, 1, 1]=q^2,[4, 2]=q + 1)
% \end{Mexout}
\begin{Mexin}
map( %, coefficient -> coefficient - 1 );
\end{Mexin}
\begin{Mexout}
                     table(
                       [] = q - 1,
                                    2
                       [3, 1, 1] = q  - 1,
                       [4, 2] = q
                     )
\end{Mexout}
% \begin{Mexout}[hide]
      % table([]=q + (-1),[3, 1, 1]=q^2 + (-1),[4, 2]=q)
% \end{Mexout}
\begin{Mexin}
muEC::SYMF::Table2Sf( %, s );
\end{Mexin}
\begin{Mexout}
           2
         (q  - 1) s[3, 1, 1] + q s[4, 2] + s[] (q - 1)
\end{Mexout}
% \begin{Mexout}[hide]
    % s[]*(q + (-1)) + q*s[4, 2] + (q^2 + (-1))*s[3, 1, 1]
% \end{Mexout}
\end{MExample}

\MRelatedFunctions{Sf2TableVar,Table2Sf}
\end{Mhelppage}
