F4/5
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.
Keywords
Cite
@article{arxiv.1006.4933,
title = {F4/5},
author = {Martin Albrecht and John Perry},
journal= {arXiv preprint arXiv:1006.4933},
year = {2010}
}