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

\begin{Mhelppage}{SfA2Sf}%
  {V. Prosper}%
  \begin{MInfo}
    \eng{from \Mex{SFA} objects to \Mex{SYMF} objects}
  \end{MInfo}
  

  \begin{MCalls}
    \Mcall{sf\Mopt{,alist}}
  \end{MCalls}

  \begin{MParameters}
    \param{sf}
    \eng{any valid expression in \Mex{SYMF}}
    \param{alist}
    \eng{a list of alphabets} 
  \end{MParameters}

  \begin{MIntro}
    \eng{The {\Mthis} function transforms any symmetric function of
      the \Mex{SFA} package into an object of
      \Mup[SYMF,firstpage]{\Mex{SFA}} for a given list of alphabets
      (by default all alphabets).
 
      Valid bases for symmetric functions are \Mex{e, h, p, s, m}.
 
      Allowed alphabet expressions are linear combinations of formal
      alphabets \Mex{A1}, \Mex{A2}, \Mex{A3}, ..., for instance
      \Mex{3/2*A1 - A3 + 3/4} is valid.
 
      The inverse function is \Mex{Sf2SfA}.}
\end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
sfa :=  7/5*s[2,2](2*A3) + s[3,1](A2)*p[2](A2) - q*e[2,1](A2);
\end{Mexin}
\begin{Mexout}
    7 s[2, 2](2 A3)
    --------------- - q e[2, 1](A2) + p[2](A2) s[3, 1](A2)
           5
\end{Mexout}
\begin{Mexin}
muEC::SFA::SfA2Sf( sfa );
\end{Mexin}
\begin{Mexout}
                                        7 s[2, 2]
             p[2] s[3, 1] - q e[2, 1] + ---------
                                            5
\end{Mexout}
\begin{Mexin}
muEC::SFA::SfA2Sf( sfa, [ A2, A3 ] );
\end{Mexin}
\begin{Mexout}
          7 s[2, 2](2 A3)
          --------------- - q e[2, 1] + p[2] s[3, 1]
                 5
\end{Mexout}
% \begin{Mexout}[hide]
      % q*e[2, 1]*(-1) + s[2, 2](A3*2)*7/5 + p[2]*s[3, 1]
% \end{Mexout}
\begin{Mexin}
muEC::SFA::SfA2Sf( sfa, [ A2, 2*A3 ] );
\end{Mexin}
\begin{Mexout}
                                        7 s[2, 2]
             p[2] s[3, 1] - q e[2, 1] + ---------
                                            5
\end{Mexout}
% \begin{Mexout}[hide]
         % s[2, 2]*7/5 + q*e[2, 1]*(-1) + p[2]*s[3, 1]
% \end{Mexout}
\end{MExample}

\MRelatedFunctions{Sf2SfA,TYP::Sf,TYP::SfA}
\end{Mhelppage}
