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Resolutions and Betti Numbers of Polynomial Modules via Involutive Bases
Author(s) -
Albert Mario,
Fetzer Matthias,
Seiler Werner M.
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610002
Subject(s) - betti number , computation , mathematics , polynomial , resolution (logic) , algebraic number , algebra over a field , pure mathematics , computer science , algorithm , mathematical analysis , artificial intelligence
We describe a novel approach to the computation of free resolutions and of Betti numbers of polynomial modules based on a combination of the theory of involutive bases with algebraic discrete Morse theory. This approach allows for the first time to compute Betti numbers (even single ones) without determining a whole resolution which in many cases drastically reduces the computation time. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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