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

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

  \begin{MInfo}
    \eng{converts any expression to the Y Schubert basis}
  \end{MInfo}
      
\begin{MCalls}
 \Mcall{expr}
\end{MCalls}
%
\begin{MParameters}
  \param{expr}
  \eng{any expression}
  \param{b}
  \eng{any name of a known basis} 
\end{MParameters}
%
\begin{MIntro}
  \eng{
The {\Mthis} function  converts  any  expression expr to the Y Schubert basis.
\Mex{expr} may involve some \Mex{x}i's, simple  Schubert  polynomials
(\Mex{X[perm]}, \Mex{Y[code]}), double Schubert polynomials
(\Mex{XX[perm]}, \Mex{YY[code]}), product of elementary functions
(\Mex{Pe[vect]}), other terms being considered as coefficients.

The expression \Mex{expr} is expanded and the result is not collected.

One  may  specify  by  a  second  argument, say  \Mpar{b}, that \Mex{expr} is
solely expressed in terms of the known basis \Mpar{b} (\Mex{x}, \Mex{X},
\Mex{Y}, \Mex{XX}, \Mex{YY}, \Mex{Pe} and even \Mex{y} that is seen as a basis
in the package).

The call \Mex{{\Mthis}(expr, Y)} does not affect the argument \Mex{expr}, but
it simplifies Schubert polynomials indices.

One may add \Mex{NoExpand} just after the argument \Mex{expr} to choose not to
expand the expression expr before treating it.

One may collect the result by adding a third  argument: this is done by 
\Mex{ToY(expr, b, Collect)}.
For instance, \Mex{{\Mthis}(expr, Y, Collect)} may be used to collect the
argument \Mex{expr}.
}
\end{MIntro}
%
\begin{MExample}{ex1}
%
\begin{Mexin}
muEC::SP::ToY((1+q)^5*x3*x4,NoExpand,x);
\end{Mexin}
\begin{Mexout}
(Y[0, 1, 0] - Y[0, 0, 1, 0]) (Y[0, 0, 1, 0] - Y[0, 0, 0, 1, 0])

           5
    (q + 1)
\end{Mexout}

\begin{Mexin}
muEC::SP::ToY(q^2*x3*XX[3,1,2]*Y[0,0,1], Collect);
\end{Mexin}
\begin{Mexout}
  2       2
(q  y1 + q  y2) Y[1, 2, 0, 0] +

     2       2
   (q  y1 + q  y2) Y[3, 0, 0, 0] -

     2       2                         2
   (q  y1 + q  y2) Y[1, 0, 2, 0, 0] - q  Y[2, 2, 0, 0] -

    2                  2
   q  Y[3, 1, 0, 0] + q  Y[2, 0, 2, 0, 0] -

    2                        2
   q  y1 y2 Y[0, 2, 0, 0] + q  y1 y2 Y[0, 0, 2, 0, 0]
\end{Mexout}
\end{MExample}
%
\MRelatedFunctions{Tox,ToX}
\end{Mhelppage}
