A normal form algorithm for the Brieskorn lattice

Details A normal form algorithm for the Brieskorn lattice A normal form algorithm for the Brieskorn lattice

2001-08-21

arxiv.org/abs/math/0108144v5

J. Symb. Comp. 38,4 (2004), 1207-1225

Mathematics

Complex Variables

23 pages, 1 figure, 4 tables

Scientific paper

10.1016/j.jsc.2003.08.005

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.

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