On the Free Resolution Induced by a Pommaret Basis

Co-author(s): Mario Albert, Matthias Fetzer and Eduardo Saenz-de-Cabezon

Reference: Journal of Symbolic Computation, 68/2 (2015) 4-26

Description: We combine the free resolution induced by a Pommaret basis with a construction by Sködberg using discrete Morse theory. This combination leads to a closed form for the resolution of the resolution. Furthermore, this approach allows us to determine the Betti numbers of a polynomial module without computing a resolution. Besides the theory, we describe an implementation in CoCoA and discuss some benchmarks. In particular for the computation of Betti numbers, our new approach seems to outperform other implementations.

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