Computing Gröbner bases and syzygies using second syzygies
Theo de Jong · 2000
this paper, we propose a new criterion, which is a generalization of the chain criterion. The main idea is to use the second syzygies between the leading monomials. We use them to show that, under suitable assumptions, if S(f j ; f k ) and S(f i ; f k ) are reduced to zero then S(f i ; f j ) reduces to zero, without actually doing the calculation.