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Since Buchberger's initial algorithm for computing Gröbner bases in 1965 [1] many attempts have been taken to detect zero reductions in advance. Buchberger's Product and Chain criteria may be known the most, especially in the installaton of Gebauer and Möller [9]. Signature-based criteria were first used in Faugère's F5 algorithm in 2002 [5]. Here we give a detailed discussion on zero reductions and the corresponding syzygies and explain how the different methods to predict them compare to each other. We extend the notation introduced in [4].

Predicting zero reductions in Gröbner basis computations