The F5 Algorithm in Buchberger's Style

TL;DR

This paper simplifies the original F5 algorithm for computing Gröbner bases into a more understandable and implementable Buchberger's style version called F5B, introducing F5-reduction and demonstrating their equivalence.

Contribution

The paper presents a simplified, more accessible version of the F5 algorithm, called F5B, with a new reduction method and proof of equivalence to the original.

Findings

F5B is equivalent to the original F5 algorithm.

F5-reduction maintains polynomial signatures after reduction.

Several versions of the F5 algorithm are illustrated.

Abstract

The famous F5 algorithm for computing \gr basis was presented by Faug\`ere in 2002. The original version of F5 is given in programming codes, so it is a bit difficult to understand. In this paper, the F5 algorithm is simplified as F5B in a Buchberger's style such that it is easy to understand and implement. In order to describe F5B, we introduce F5-reduction, which keeps the signature of labeled polynomials unchanged after reduction. The equivalence between F5 and F5B is also shown. At last, some versions of the F5 algorithm are illustrated.