The computation of Gröbner bases on a shared memory multiprocessor

This article presents a system which computes Grobner bases on a shared memory multiprocessor. The basic idea is that each processor picks an element in the set of unreduced critical pairs, reduces the S-polynomial associated with it and updates the basis and the set of pairs according to the result. The originality of this algorithm relies on the small amount of synchronization it requires among the processes. The details of an implementation on a 16 processors Encore machine are given together with results of tests performed with well-known examples of the literature.

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