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A normal form algorithm for the Brieskorn lattice

Mathias Schulze
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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.

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Mathias Schulze. 2004-08-15. A normal form algorithm for the Brieskorn lattice. https://doi.org/10.1016/j.jsc.2003.08.005

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