The termination of the F5 algorithm revisited

Abstract

The F5 algorithm [8] is generally believed as one of the fastest algorithms for computing Gröbner bases. However, its termination problem is still unclear. The crux lies in the non-determinacy of the F5 in selecting which from the critical pairs of the same degree. In this paper, we construct a generalized algorithm F5GEN which contain the F5 as its concrete implementation. Then we prove the correct termination of the F5GEN algorithm. That is to say, for any finite set of homogeneous polynomials, the F5 terminates correctly.