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Singularity Spectrum
Task: |
Compute the singularity spectrum of an isolated hypersurface
singularity f.
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There are two different algorithms implemented in
SINGULAR
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- if f is Newton-nondegenerate, one can use
the procedure
spectrumnd in the library
spectrum.lib , which is based on a computation of the
Newton filtration.
- for arbitrary f, one can use
the procedure
spectrum in the library
gaussman.lib , which 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 "spectrum.lib";
spprint(spectrumnd(f)); // Spectral numbers with multiplicities
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==>
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(-1/2,1),(-3/10,2),(-1/10,2),(0,1),(1/10,2),(3/10,2),(1/2,1)
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LIB "gaussman.lib";
spprint(spectrum(f));
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==>
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(-1/2,1),(-3/10,2),(-1/10,2),(0,1),(1/10,2),(3/10,2),(1/2,1)
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