Details:
Title  The F5 criterion revised  Author(s)  Alberto Arri, John Perry  Type  Article in Journal  Abstract  The purpose of this work is to generalize part of the theory behind Faugère’s “F5” algorithm. This is one of the fastest known algorithms to compute a Gröbner basis of a polynomial ideal I generated by polynomials f_1, … , f_m . A major reason for this is what Faugère called the algorithm’s “new” criterion, and we call “the F5 criterion”; it provides a sufficient condition for a set of polynomials G to be a Gröbner basis. However, the F5 algorithm is difficult to grasp, and there are unresolved questions regarding its termination. This paper introduces some new concepts that place the criterion in a more general setting: S Gröbner bases and primitive S irreducible polynomials. We use these to propose a new, simple algorithm based on a revised F5 criterion. The new concepts also enable us to remove various restrictions, such as proving termination without the requirement that f_1, … , f_m be a regular sequence.  Keywords  F5, Gröbner bases, Syzygies  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111000642 
Language  English  Journal  Journal of Symbolic Computation  Volume  46  Number  9  Pages  1017  1029  Year  2011  Edition  0  Translation 
No  Refereed 
No 
