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%body SINGULAR - A Computer Algebra System for Polynomial Computations Overview Objects Functionality Libraries Examples Applications Availability History Contributors Future %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
SINGULAR Examples Build. Blocks Comb. Appl. HCA Proving
Arrangements Branches Classify Coding Deformations Equidim Part Existence Finite Groups Flatness Genus Hilbert Series Membership Nonnormal Locus Normalization Primdec Puiseux Plane Curves Saturation Solving Space Curves Spectrum %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
SINGULAR Applications Robotics Circuit Design Medicine Glass Melting %body
Sao Carlos, 08/02 http://www.singular.uni-kl.de
Task: Compute the spectral pairs of an isolated hypersurface singularity f.

The implemented algorithm is based on standard basis methods for the microlocal structure of the Brieskorn lattice:

ring R=0,(x,y),ds;
poly f=x5+x2y2+y5;
LIB "gaussman.lib";
sppairs(f);
[1]: _[1]=-1/2 _[2]=-3/10 _[3]=-1/10 _[4]=0 _[5]=1/10 _[6]=3/10 _[7]=1/2 [2]: // the weight indices 2,1,1,1,1,1,0 [3]: // the multiplicities 1,2,2,1,2,2,1
We can also display the spectral pairs (with multiplicities) in a more compact format:
sppprint(sppairs(f));
((-1/2,2),1), ((-3/10,1),2), ((-1/10,1),2), ((0,1),1), ((1/10,1),2), ((3/10,1),2), ((1/2,0),1) A more complicated example.