We describe an algorithm to compute Grobner 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 Grobner 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.
