% $Date: 2004/10/04 17:25:12 $ $Author: nthiery $ $Revision: 1.1.1.2 $

\begin{Mhelppage}{x2X}{S. Veigneau}

  \begin{MInfo}
    \eng{from the basis of monomials to X Schubert basis}
  \end{MInfo}
      
\begin{MCalls}
 \Mcall{pol}
\end{MCalls}
%
\begin{MParameters}
  \param{pol}
  \eng{any expression in the basis of monomials} 
\end{MParameters}
%
\begin{MIntro}
  \eng{
The {\Mthis} function converts  any expression from the basis of monomials to
X Schubert basis. It uses a different algorithm than \Mex{ToX} (taking the
leading monomials successively).

The result is not expanded.
 
One may add \Mex{NoExpand} just after the argument \Mex{pol} to choose not to
expand the expression \Mex{pol} before treating it.

One may add \Mex{Collect} just after the argument \Mex{pol} or just after the
argument \Mex{NoExpand} to collect the result.
}
\end{MIntro}
%
\begin{MExample}{ex1}
%
\begin{Mexin}
muEC::SP::x2X((1+q)^5*x1*x2^2, NoExpand);
\end{Mexin}
\begin{Mexout}
                                                  5
            - (X[3, 2, 1] - X[2, 4, 1, 3]) (q + 1)
\end{Mexout}
% \begin{Mexout}[hide]
         % (q + 1)^5*(X[3, 2, 1]*(-1) + X[2, 4, 1, 3])
% \end{Mexout}
\begin{Mexin}
muEC::SP::x2X((1+q)^5*x1*x2^2, Collect);
\end{Mexin}
\begin{Mexout}
  5      4       3       2
(q  + 5 q  + 10 q  + 10 q  + 5 q + 1) X[2, 4, 1, 3] +

       5      4       3       2
   (- q  - 5 q  - 10 q  - 10 q  - 5 q - 1) X[3, 2, 1]
\end{Mexout}
% \begin{Mexout}[hide]
% X[2, 4, 1, 3]*(q*5 + q^2*10 + q^3*10 + q^4*5 + q^5 + 1) +
% X[3, 2, 1]*(q*(-5) + q^2*(-10) + q^3*(-10) + q^4*(-5) + q^5*(-1) + (-1)
% \end{Mexout}
\end{MExample}
%
\MRelatedFunctions{}
\end{Mhelppage}
