F4/5

Martin Albrecht; John Perry

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arXiv · 1006.4933

F4/5

Martin Albrecht·John Perry

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Abstract

We describe an algorithm to compute Gr\"obner bases which combines F4-style reduction with the F5 criteria. Both F4 and F5 originate in the work of Jean-Charles Faug\`ere, who has successfully computed many Gr\"obner bases that were previously considered intractable. Another description of a similar algorithm already exists in Gwenole Ars' dissertation; unfortunately, this is only available in French, and although an implementation exists, it is not made available for study. We not only describe the algorithm, we also direct the reader to a study implementation for the free and open source Sage computer algebra system. We conclude with a short discussion of how the approach described here compares and contrasts with that of Ars' dissertation.

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Martin Albrecht, John Perry. 2010-06-25. F4/5. https://arxiv.org/abs/1006.4933

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