% $Date: 2004/10/04 17:25:12 $ $Author: nthiery $ $Revision: 1.1.1.3 $

\begin{Mhelppage}{Pol2SfA}{V. Prosper}%
  \begin{MInfo}
    \eng{from the basis of monomials to SFA}
  \end{MInfo}
  

\begin{MCalls}
  \Mcall{pol,vlist}
\end{MCalls}

\begin{MParameters}
  \param{pol}
  \eng{a polynomial symmetric in \Mex{vlist}}
  \param{vlist}
  \eng{a list of variables}
\end{MParameters}

\begin{MIntro}
  \eng{The {\Mthis} function transforms any polynomial symmetric in
    the list of variables \Mex{vlist} into a linear combination of
    monomial symmetric functions of \Mex{SFA}. }
\end{MIntro}

\Mwarning{{\Mthis} does not check that \Mex{pol} is symmetric.  }

\begin{MExample}{ex1}
\begin{Mexin}
muEC::SFA::SfAVars( {{x}, u, v} );
\end{Mexin}
\begin{Mexout}
                          {{x}, u, v}
\end{Mexout}
\begin{Mexin}
tt := muEC::SFA::SfAExpand( m[3,2](x1+u+v) - q*s[2,2](x1+u+v) );
\end{Mexin}
\begin{Mexout}
 3  2    3   2    2  3      2  2      2         2   3
u  v  + u  x1  + u  v  - q u  v  - q u  v x1 + u  x1  -

      2   2        2              2    3   2    2   3
   q u  x1  - q u v  x1 - q u v x1  + v  x1  + v  x1  -

      2   2
   q v  x1
\end{Mexout}
\begin{Mexin}
muEC::SFA::Pol2SfA(tt, [x1,u,v]);
\end{Mexin}
\begin{Mexout}
m[3, 2](u + v + x1) - q m[2, 2](u + v + x1) -

   q m[2, 1, 1](u + v + x1)
\end{Mexout}
\end{MExample}

\MRelatedFunctions{SfAExpand,SfAVars}
\end{Mhelppage}
