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

\begin{Mhelppage}{Sp2TableVar}{S. Veigneau}

  \begin{MInfo}
    \eng{variable set for the SP package}
  \end{MInfo}
      
\begin{MCalls}
 \Mcall{expr}
\end{MCalls}
%
\begin{MParameters}
  \param{expr}
  \eng{any expression} 
\end{MParameters}
%
\begin{MIntro}
  \eng{
The {\Mthis} function returns a table whose entries describe the
set of all Schubert polynomials and variables that appear in a given
expression \Mex{expr}.
The indices of the table are taken into the global variable \Mex{SP::SPBases}.
 

For all bases of type \Mex{\_index} (\Mex{SP::SPBasesIndexed}), the entry
consists of the set of all permutations that index the corresponding Schubert
polynomials in \Mex{expr}.
 

For all bases of type \Mex{DOM\_IDENT} (\Mex{SP::SPBasesString}), the entry
consists of the set of all integers that index the corresponding variable in
\Mex{expr}.
 

An entry equal to an empty set means that the element does not appear in
\Mex{expr}.  

One  can  add  a  second argument to select some elements among those in
\Mex{SP::SPBases}.
If the second argument is a set of names, then the  restriction to this set of
indices of the table is returned.
In case the second argument is a single name, then the corresponding entry in
the table is returned instead of the table.
}
\end{MIntro}
%
\begin{MExample}{ex1}
%
\begin{Mexin}
muEC::SP::Sp2TableVar(x1^3*x4*y4 + q*y6*X[4,1,3,2]*X[2,3,1]);
\end{Mexin}
\begin{Mexout}
               table(
                 Pe = {},
                 YY = {},
                 Y = {},
                 XX = {},
                 X = {[2, 3, 1], [4, 1, 3, 2]},
                 y = {4, 6},
                 x = {1, 4}
               )
\end{Mexout}
% \begin{Mexout}[hide]
% table(x={1, 4},y={4, 6},XX={},YY={},X={[2, 3, 1], [4, 1, 3, 2]},Y={},Pe={})
% \end{Mexout}
%
\begin{Mexin}
muEC::SP::Sp2TableVar(x1^3*x4*y4 + q*y6*X[4,1,3,2]*X[2,3,1], {X, x});
\end{Mexin}
\begin{Mexout}
               table(
                 X = {[2, 3, 1], [4, 1, 3, 2]},
                 x = {1, 4}
               )
\end{Mexout}
% \begin{Mexout}[hide]
         % table(x={1, 4},X={[2, 3, 1], [4, 1, 3, 2]})
% \end{Mexout}
%
\begin{Mexin}
muEC::SP::Sp2TableVar(x1^3*x4*y4 + q*y6*X[4,1,3,2]*X[2,3,1], y);
\end{Mexin}
\begin{Mexout}
                            {4, 6}
\end{Mexout}
\end{MExample}
%
\MRelatedFunctions{}
\end{Mhelppage}
