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TitleA Parallel Factorization Tree Gröbner Basis Algorithm
Author(s) Kurt Siegl
TypeTechnical Report, Misc
AbstractThe idea using polynomial factorization for speeding up the computation of Buchberger's Gröbner 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 factorization within a parallel Gröbner basis algorithm, without unnecessary doubling parts of the work. A reformulation of the sequential optimization criteria for avoiding unnecessary computation is given, to fit 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 efficiency. In first 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.
KeywordsParallel Gröbner Bases Computation, Parallel Computer Algebra Systems, Logic Programming
PublisherWorld Scientific Publishing Company
AddressJohannes Kepler University, Linz, Austria
Translation No
Refereed No
Organization Johannes Kepler University Linz
Institution RISC (Research Institute for Symbolic Computation)