% $Date: 2003/09/15 16:37:46 $ $Author: nthiery $ $Revision: 1.1.1.1 $

\begin{Mhelppage}{SfJtMat}{V. Prosper}

  \begin{MInfo}
    \eng{computes the Jacobi-Trudi matrix}
  \end{MInfo}

  \begin{MCalls}
    \Mcall{part\Mopt{,b}}
  \end{MCalls}

  \begin{MParameters}
    \param{part}
    \eng{any list denoting a (skew) partition} 
    \param{b}
    \eng{any name} 
  \end{MParameters}

  \begin{MIntro}
    \eng{The {\Mthis} function computes the Jacobi-Trudi matrix
      corresponding to the (skew) partition \Mex{part}.  The
      determinant of this matrix is exactly the Schur function indexed
      by the partition, expressed in the \Mex{h}-basis.
      
      When given a second argument, \Mex{b}, {\Mthis} returns a result
      expressed on the \Mex{b}-basis.  }
  \end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::SYMF::SfJtMat( [3,2,1,1] );
\end{Mexin}
\begin{Mexout}
                 +-                        -+
                 |  h[3], h[4], h[5], h[6]  |
                 |                          |
                 |  h[1], h[2], h[3], h[4]  |
                 |                          |
                 |    0,    1,  h[1], h[2]  |
                 |                          |
                 |    0,    0,    1,  h[1]  |
                 +-                        -+
\end{Mexout}
% \begin{Mexout}[hide]
% array(1..4, 1..4, (1,1) = h[3], (1,2) = h[4], (1,3) = h[5], (1,4) = h[6],
%                   (2,1) = h[1], (2,2) = h[2], (2,3) = h[3], (2,4) = h[4],
%                   (3,1) = 0,    (3,2) = 1,    (3,3) = h[1], (3,4) = h[2],
%                   (4,1) = 0,    (4,2) = 0,    (4,3) = 1,    (4,4) = h[1])
% \end{Mexout}
\begin{Mexin}
muEC::SYMF::SfJtMat( [[2,1], [1]] );
\end{Mexin}
\begin{Mexout}
                       +-            -+
                       |  h[1], h[3]  |
                       |              |
                       |    0,  h[1]  |
                       +-            -+
\end{Mexout}
% \begin{Mexout}[hide]
        % array(1..2, 1..2, (1,1) = h[1], (1,2) = h[3],
        %                   (2,1) = 0,    (2,2) = h[1])
% \end{Mexout}
\begin{Mexin}
muEC::SYMF::SfJtMat( [[2,2,1], [1,1,1]], b );
\end{Mexin}
\begin{Mexout}
                    +-                  -+
                    |  b[1], b[2], b[3]  |
                    |                    |
                    |    1,  b[1], b[2]  |
                    |                    |
                    |    0,    0,    1   |
                    +-                  -+
\end{Mexout}
% \begin{Mexout}[hide]
 % array(1..3, 1..3, (1,1) = b[1], (1,2) = b[2], (1,3) = b[3],
 %                   (2,1) = 1,    (2,2) = b[1], (2,3) = b[2],
 %                   (3,1) = 0,    (3,2) = 0,    (3,3) = 1)
% \end{Mexout}
\end{MExample}

\MRelatedFunctions{Iss}
\end{Mhelppage}
