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D.6.9.10 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''
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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
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