2001/08/31 by Mathias Schulze
Mathematics · #math.CV #math.AC #msc:13N10 #msc:13P10 #msc:32S35 #msc:32S40
paper · pdf · doi:10.1016/j.jsc.2003.08.005
published as J. Symb. Comp. 38,4 (2004), 1207-1225 · 23 pages, 1 figure, 4 tables
arxiv created 2004/08/15 · arxiv updated 2009/11/30
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.