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
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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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