On the free resolution induced by a pommaret basis

  1. Albert, M. 1
  2. Fetzer, M. 1
  3. Sáenz-de-Cabezón, E. 2
  4. Seiler, W.M. 1
  1. 1 University of Kassel
    info

    University of Kassel

    Kassel, Alemania

    ROR https://ror.org/04zc7p361

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Journal of Symbolic Computation

ISSN: 0747-7171

Year of publication: 2015

Volume: 68

Issue: P2

Pages: 4-26

Type: Article

DOI: 10.1016/J.JSC.2014.09.008 SCOPUS: 2-s2.0-84919345723 WoS: WOS:000347767600002 GOOGLE SCHOLAR

More publications in: Journal of Symbolic Computation

Institutional repository: lockOpen access Editor

Abstract

We combine the theory of Pommaret bases with a (slight generalisation of a) recent construction by Sköldberg based on discrete Morse theory. This combination allows us the explicit determination of a (generally non-minimal) free resolution for a graded polynomial module with the computation of only one Pommaret basis. If only the Betti numbers are needed, one can considerably simplify the computations by determining only the constant part of the differential. For the special case of a quasi-stable monomial ideal, we show that the induced resolution is a mapping cone resolution. We present an implementation within the CoCoALib and test it with some common benchmark ideals.