Parallel computation of Janet and Gr�bner bases over rational numbers

Abstract

In this paper, a parallel algorithm for computation of polynomial Janet bases is considered. After construction of a Janet basis, a reduced Grobner basis (which is a subset of the Janet basis) is extracted from it without any additional reductions. The algorithm discussed is an improved version of an earlier suggested parallel algorithm. The efficiency of a C implementation of the algorithm and its scalability are illustrated by way of the standard test examples that are often used for comparing various algorithms and codes for computing Grobner bases.