%% $OpenXM: OpenXM/doc/Papers/ohp-v-minimal.tex,v 1.1 2000/05/13 08:09:51 takayama Exp $
\documentclass{slides}
\begin{document}
V-minimal free resolution
of the Laplace transform of
the annihilating ideal of $1/(x^3-y^2 z^2)$
with $(-w,w) = (-1,-1,-1,1,1,1)$.

{\footnotesize
\begin{verbatim}
In(3)=a=Sannfs3("x^3-y^2*z^2");
In(4)=b=a[0];
In(5)=sm1_pmat(b);
 [ 
  [ 
    [    y*Dy-z*Dz ] 
    [    -2*x*Dx-3*z*Dz+h^2 ] 
    [    2*x*Dy*Dz^2-3*y*Dx^2*h ] 
    [    2*x*Dy^2*Dz-3*z*Dx^2*h ] 
  ]
  [ 
    [    9*z*Dx^2*h , 2*x*Dy^2*Dz-3*z*Dx^2*h , 
          3*z*Dy , 2*x*Dx ] 
    [    2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0 ] 
    [    -6*x*Dy*Dz^2+9*y*Dx^2*h , 
         2*x*Dy*Dz^2-3*y*Dx^2*h , 2*x*Dx+3*y*Dy , 0 ] 
    [    3*Dx^2*h , 0 , Dy , -Dz ] 
    [    -2*x*Dy*Dz , 0 , -z , y ] 
    [    2*x*Dx*Dz^2+3*z*Dz^3+5*Dz^2*h^2 , 
          y*Dy*Dz^2-z*Dz^3-2*Dz^2*h^2 , 0 , 0 ] 
  ]
  [ 
    [    -y , 2*x*Dy*Dz , z , 0 , 2*x*Dx , 0 ] 
    [    -Dz , 3*Dx^2*h , Dy , -2*x*Dx-3*y*Dy-3*h^2 , 
         -3*Dy*Dz , 0 ] 
  ]
 ]
In(6)=Map(a[3],"Length"):
[    8 , 17 , 13 , 3 ] 
In(7)=Map(a[0],"Length"):
[    4 , 6 , 2 ] 
In(8)=sm1_pmat(a[3,2]);
 [ 
   [    0 , 1 , 0 , 0 , -1 , 0 , 0 , 0 , 3*z , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ] 
   [    -y , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 3*z*Dz+3*h^2 , 0 , -2*x , 0 , 0 , 0 , 0 ] 
   [    z , y , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , -3*z*Dz , 0 , 0 , 2*x , 0 , 0 ] 
   [    0 , y , 0 , 0 , 0 , 0 , -z , 0 , 3*y*z , 0 , 3*z*Dy , 0 , 0 , 0 , 2*x , 0 , 0 ] 
   [    -h^2 , 0 , 2*x , Dy , 0 , -3*y*Dx^2*h , z*Dz+h^2 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ] 
   [    0 , 0 , 3 , 0 , 0 , 0 , 0 , 3*y , 0 , 0 , 0 , 0 , 3*Dy , 0 , 3*Dz , 0 , 0 ] 
   [    Dx , 0 , -3 , 0 , 0 , 0 , Dx , 0 , 0 , 0 , 0 , 0 , 0 , 3*Dy , 0 , 3*z*Dz+6*h^2 , 0 ] 
   [    0 , 0 , -Dy , 0 , 0 , 0 , 0 , z*Dz , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ] 
   [    -1 , 0 , 0 , 0 , 0 , 0 , -1 , 0 , 3*y , 0 , 3*Dy , 3*Dz , 0 , 0 , 0 , 0 , 0 ] 
   [    Dy , 0 , 0 , 0 , Dz , -3*Dx^2*h , 0 , -2*x , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ] 
   [    0 , 0 , 0 , 0 , 0 , 0 , 0 , -1 , -Dx , 0 , 0 , 0 , 0 , 0 , 0 , Dy , Dz ] 
   [    0 , 0 , 0 , 0 , 0 , -Dz^2 , 0 , 0 , 0 , 0 , Dx , 0 , 1 , 1 , 0 , y , 0 ] 
   [    0 , 0 , 0 , 0 , 0 , Dy*Dz , 0 , 0 , 0 , 0 , 0 , Dx , 0 , 0 , 1 , z , y ] 
 ]
\end{verbatim} }




\end{document}

{\footnotesize
\begin{verbatim}



\end{verbatim} }