A Parallel Factorization Tree Gr?bner Basis Algorithm

The idea using polynomial factorization for speeding up the computation of Buch-berger's Grr obner bases algorithm for the purpose of polynomial equation solving leads to major improvements in the computation time. In this paper we show how one may introduce factoriza-tion within a parallel Grr obner basis algorithm, without unnecessary doubling parts of the work. A reformulation of the sequential optimization criteria for avoiding unnecessary computation is given, to t the needs of a parallel version. The approach has been implemented in kMAPLEk (speak: parallel Maple), a computer algebra system, in which logic programming provides parallelism and imperative programming provides eeciency. In rst experiments with a prototype implementation, we managed to solve examples within a few minutes on a couple of SGI workstations, which can not be solved with a conventional, sequential implementation.