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Improving incremental signature-based Gröbner basis algorithms

Christian Eder 1
1 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : In this paper we describe a combination of ideas to improve incremental signature-based Gröbner basis algorithms having a big impact on their performance. Besides explaining how to combine already known optimizations to achieve more efficient algorithms, we show how to improve them even more. Although our idea has a positive affect on all kinds of incremental signature-based algorithms, the way this impact is achieved can be quite different. Based on the two best-known algorithms in this area, F5 and G2V, we explain our idea, both from a theoretical and a practical point of view.
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https://hal.inria.fr/hal-00930293
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Submitted on : Tuesday, January 14, 2014 - 3:41:38 PM
Last modification on : Friday, January 21, 2022 - 3:21:46 AM

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Christian Eder. Improving incremental signature-based Gröbner basis algorithms. ACM Communications in Computer Algebra, Association for Computing Machinery (ACM), 2013, 47 (1), pp.1-13. ⟨10.1145/2503697.2503699⟩. ⟨hal-00930293⟩

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