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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 |