Abstract
Buchberger's algorithm calculates Groebner bases of polynomial ideals. Its efficiency dependsstrongly on practical criteria for detecting superfluous reductions. Buchberger recommends two criteria. The more important one is interpreted in this paper as a criterion for detecting redundant elements in a basis of a module of syzygies. We present a method for obtaining a reduced, nearly minimal basis of that module. The simple procedure for detecting (redundant syzygies and) superfluous reductions is incorporated now in our installation of Buchberger's algorithm in SCRATCHPAD II and REDUCE 3.3. The paper concludes with statistics stressing the good computational properties of these installations.
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