A normal form algorithm for the Brieskorn lattice
arXiv:math/0108144 · doi:10.1016/j.jsc.2003.08.005
Abstract
This article describes a normal form algorithm for the Brieskorn lattice of an isolated hypersurface singularity. It is the basis of efficient algorithms to compute the Bernstein-Sato polynomial, the complex monodromy, and Hodge-theoretic invariants of the singularity such as the spectral pairs and good bases of the Brieskorn lattice. The algorithm is a variant of Buchberger's normal form algorithm for power series rings using the idea of partial standard bases and adic convergence replacing termination.
23 pages, 1 figure, 4 tables