D.5.4.5 monodromy

Procedure from library gaussman.lib (see gaussman_lib).

Usage:

monodromy(t); poly t

Assume:

characteristic 0; local degree ordering;
isolated critical point 0 of t

Return:

list l; Jordan data jordan(M) of monodromy matrix exp(-2*pi*i*M) ideal l[1]; number l[1][i]; eigenvalue of i-th Jordan block of M intvec l[2]; int l[2][i]; size of i-th Jordan block of M intvec l[3]; int l[3][i]; multiplicity of i-th Jordan block of M

Example:

LIB "gaussman.lib";
ring R=0,(x,y),ds;
poly t=x5+x2y2+y5;
monodromy(t);
→ [1]:
→    _[1]=1/2
→    _[2]=7/10
→    _[3]=9/10
→    _[4]=1
→    _[5]=11/10
→    _[6]=13/10
→ [2]:
→    2,1,1,1,1,1
→ [3]:
→    1,2,2,1,2,2

See also: linalg_lib; mondromy_lib.