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D.5.6.4 monodromyB
Procedure from library mondromy.lib (see mondromy_lib).
- Usage:
monodromyB(f[,opt]); f poly, opt int
- Assume:
The polynomial f in a series ring (local ordering) defines an isolated hypersurface singularity.
- Return:
The procedure returns a residue matrix M of the meromorphic Gauss-Manin connection of the singularity defined by f or an empty matrix if the assumptions are not fulfilled. If opt=0 (default), exp(-2*pi*i*M) is a monodromy matrix of f, else, only the characteristic polynomial of exp(-2*pi*i*M) coincides with the characteristic polynomial of the monodromy of f.
- Display:
The procedure displays more comments for higher printlevel.
Example:
LIB "mondromy.lib"; ring R=0,(x,y),ds; poly f=x2y2+x6+y6; matrix M=monodromyB(f); print(M); → 7/6,0, 0,0, 0, 0,0, 0,-1/2,0, 0, 0, 0, → 0, 7/6,0,0, 0, 0,-1/2,0,0, 0, 0, 0, 0, → 0, 0, 1,0, 0, 0,0, 0,0, 0, 0, 0, 0, → 0, 0, 0,4/3,0, 0,0, 0,0, 0, 0, 0, 0, → 0, 0, 0,0, 4/3,0,0, 0,0, 0, 0, 0, 0, → 0, 0, 0,0, 0, 1,0, 0,0, 0, 0, 0, 0, → 0, 0, 0,0, 0, 0,5/6, 0,0, 0, 0, 0, 0, → 0, 0, 0,0, 0, 0,0, 1,0, 0, 0, 0, 0, → 0, 0, 0,0, 0, 0,0, 0,5/6, 0, 0, 0, 0, → 0, 0, 0,0, 0, 0,0, 0,0, 2/3,0, 0, 0, → 0, 0, 0,0, 0, 0,0, 0,0, 0, 2/3,0, 0, → 0, 0, 0,0, 0, 0,0, 0,0, 0, 0, 47/44,-625/396, → 0, 0, 0,0, 0, 0,0, 0,0, 0, 0, 9/44, -3/44 |