There are two different algorithms implemented in SINGULAR :

• 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

==>

(-1/2,1),(-3/10,2),(-1/10,2),(0,1),(1/10,2),(3/10,2),(1/2,1)

LIB "gaussman.lib";
spprint(spectrum(f));

==>

(-1/2,1),(-3/10,2),(-1/10,2),(0,1),(1/10,2),(3/10,2),(1/2,1)

There is a conjecture by C. Hertling concerning the variance of the spectral numbers.