D.5.4.12 tmatrix
................
Procedure from library gaussman.lib (see gaussman_lib).

Usage:
tmatrix(t); poly t

Assume:
characteristic 0; local degree ordering;

isolated critical point 0 of t

Return:
list l=A0,A1,T,M;
  matrix A0,A1;  t=A0+s*A1+s^2*(d/ds) on H" w.r.t. C[[s]]-basis M*T
  module T;  C-basis of C^mu
  ideal M;  monomial C-basis of H"/sH"

Example:
LIB "gaussman.lib";
ring R=0,(x,y),ds;
poly t=x5+x2y2+y5;
list A=tmatrix(t);
print(A[1]);
==> 0,0,0,0,0,0,0,0,0,0,0,
==> 0,0,0,0,0,0,0,0,0,0,0,
==> 0,0,0,0,0,0,0,0,0,0,0,
==> 0,0,0,0,0,0,0,0,0,0,0,
==> 0,0,0,0,0,0,0,0,0,0,0,
==> 0,0,0,0,0,0,0,0,0,0,0,
==> 0,0,0,0,0,0,0,0,0,0,0,
==> 0,0,0,0,0,0,0,0,0,0,0,
==> 0,0,0,0,0,0,0,0,0,0,0,
==> 0,0,0,0,0,0,0,0,0,0,0,
==> 1,0,0,0,0,0,0,0,0,0,0 
print(A[2]);
==> 1/2,0,   0,   0,   0,   0,0,    0,    0,    0,    0, 
==> 0,  7/10,0,   0,   0,   0,0,    0,    0,    0,    0, 
==> 0,  0,   7/10,0,   0,   0,0,    0,    0,    0,    0, 
==> 0,  0,   0,   9/10,0,   0,0,    0,    0,    0,    0, 
==> 0,  0,   0,   0,   9/10,0,0,    0,    0,    0,    0, 
==> 0,  0,   0,   0,   0,   1,0,    0,    0,    0,    0, 
==> 0,  0,   0,   0,   0,   0,11/10,0,    0,    0,    0, 
==> 0,  0,   0,   0,   0,   0,0,    11/10,0,    0,    0, 
==> 0,  0,   0,   0,   0,   0,0,    0,    13/10,0,    0, 
==> 0,  0,   0,   0,   0,   0,0,    0,    0,    13/10,0, 
==> 0,  0,   0,   0,   0,   0,0,    0,    0,    0,    3/2
print(A[3]);
==> -1445/64,0,  0,  0,0,85/8,0,0,0,0,1/2,
==> 0,       125,0,  0,0,0,   0,0,1,0,0,  
==> 0,       0,  0,  5,0,0,   1,0,0,0,0,  
==> 0,       0,  0,  0,4,0,   0,0,0,0,0,  
==> 2,       0,  0,  0,0,1,   0,0,0,0,0,  
==> 0,       0,  16, 0,0,0,   0,0,0,0,0,  
==> 0,       0,  125,0,0,0,   0,0,0,1,0,  
==> 0,       0,  0,  0,5,0,   0,1,0,0,0,  
==> 0,       0,  0,  4,0,0,   0,0,0,0,0,  
==> 0,       16, 0,  0,0,0,   0,0,0,0,0,  
==> -1,      0,  0,  0,0,0,   0,0,0,0,0   
print(A[4]);
==> y5,
==> y4,
==> y3,
==> y2,
==> xy,
==> y,
==> x4,
==> x3,
==> x2,
==> x,
==> 1

<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
</font>

</body>
</html>
