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D.6.17.4 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, 1, -1/3,
==> 0, 0, 0,0, 0, 0,0, 0,0, 0, 0, 3/4,0
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