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D.6.7.10 tmatrix

Procedure from library gmssing.lib (see gmssing_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 "gmssing.lib";
ring R=0,(x,y),ds;
poly t=x5+x2y2+y5;
list l=tmatrix(t);
print(l[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(l[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(l[3]);
==> 85/4,0,  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(l[4]);
==> y5,
==> y4,
==> y3,
==> y2,
==> xy,
==> y,
==> x4,
==> x3,
==> x2,
==> x,
==> 1