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Reducing the size and number of linear programs in a dynamic Gröbner basis algorithm

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Abstract

The goal of the Dynamic Buchberger Algorithm is to compute a Gröbner basis quickly by adjusting the term ordering as the computation proceeds. A known problem concerns the size and number of linear progams to be solved when refining the ordering. This paper describes two methods for reducing both their size and number.

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Notes

  1. This notion is essentially Caboara’s notion of a potential leading term with respect to \(F\), \(\mathrm{lt}\left( F\right) \). Our choice of different vocabulary allows us to emphasize that a “potential” leading term for one polynomial is not usually “compatible” with previous choices.

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Acknowledgments

The authors would like to thank Nathann Cohen for some stimulating conversations, and his assistance with Sage’s linear programming facilities. Suggestions by the anonymous referees greatly improved the exposition, particularly the abstract.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

    Massimo Caboara

  2. Department of Mathematics, University of Southern Mississippi, 118 College Drive Box #5045, Hattiesburg , MS , 39406, USA

    John Perry

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  1. Massimo Caboara
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  2. John Perry
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Correspondence to John Perry.

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Caboara, M., Perry, J. Reducing the size and number of linear programs in a dynamic Gröbner basis algorithm. AAECC 25, 99–117 (2014). https://doi.org/10.1007/s00200-014-0216-5

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  • DOI: https://doi.org/10.1007/s00200-014-0216-5

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