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Improving incremental signature-based Gröbner basis algorithms

Published: 15 July 2013 Publication History

Abstract

In this paper we describe a combination of ideas to improve incremental signature-based Gröbner basis algorithms which have 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 further. Although our idea has a postive effect 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.

References

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Cited By

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  • (2021)Determining implicit equation of conic section from quadratic rational Bézier curve using Gröbner basisJournal of Physics: Conference Series10.1088/1742-6596/2106/1/0120172106:1(012017)Online publication date: 1-Nov-2021
  • (2017)A survey on signature-based algorithms for computing Gröbner basesJournal of Symbolic Computation10.1016/j.jsc.2016.07.03180(719-784)Online publication date: May-2017

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Published In

cover image ACM Communications in Computer Algebra
ACM Communications in Computer Algebra  Volume 47, Issue 1/2
March/June 2013
72 pages
ISSN:1932-2232
EISSN:1932-2240
DOI:10.1145/2503697
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 15 July 2013
Published in SIGSAM-CCA Volume 47, Issue 1/2

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View all
  • (2021)Determining implicit equation of conic section from quadratic rational Bézier curve using Gröbner basisJournal of Physics: Conference Series10.1088/1742-6596/2106/1/0120172106:1(012017)Online publication date: 1-Nov-2021
  • (2017)A survey on signature-based algorithms for computing Gröbner basesJournal of Symbolic Computation10.1016/j.jsc.2016.07.03180(719-784)Online publication date: May-2017

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