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

\begin{Mhelppage}{SfMat}%
  {V. Prosper}%
  \begin{MInfo}
    \eng{transition matrix between symmetric functions bases}
  \end{MInfo}
  

\begin{MCalls}
  \Mcall{n,b1,b2}
\end{MCalls}

\begin{MParameters}
  \param{n}
  \eng{any positive integer}
  \param{b1, b2}
  \eng{any names denoting known bases}
\end{MParameters}

\begin{MIntro}
  \eng{
The {\Mthis} function returns the transition matrix from the \Mex{b1} basis
to the \Mex{b2} basis of the homogeneous component of weight n of the space of
symmetric functions.
 

Parameters \Mex{b1} and \Mex{b2} are taken from the \Mex{SYMF::SYMFBases}
global variable.
 

The result is a matrix indexed by partitions of \Mex{n}, each row giving the
expansion of an element of the \Mex{b1} basis in the \Mex{b2} basis.
 
}
\end{MIntro}

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

\MRelatedFunctions{Sf}
\end{Mhelppage}
