Algorithms for the Gauss–Manin Connection

We give an introduction to the theory of the Gauss–Manin connection of an isolated hypersurface singularity and describe an algorithm to compute the V-filtration on the Brieskorn lattice. We use an implementation in the computer algebra system Singular to prove C. Hertling’s conjecture about the variance of the spectrum for Milnor numberμ ≤ 16.