Monodromy of Hypersurface Singularities

We describe algorithmic methods for the Gauss-Manin connection of an isolated hypersurface singularity based on the microlocal structure of the Brieskorn lattice. They lead to algorithms for computing invariants like the monodromy, the spectrum, and the spectral pairs. These algorithms use a normal form algorithm for the Brieskorn lattice, standard basis methods for localized polynomial rings, and univariate factorization. We give a detailed description of the algorithm to compute the monodromy.