#### D.6.13.10 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 ```

User manual for Singular version 4.3.2, 2023, generated by texi2html.