Towards efficient parallelizations of a computer algebra algorithm

The authors summarize the results of a preliminary study that examines the feasibility of implementing computer algebra systems on massively parallel single-instruction multiple-data architectures. On serial computers, these systems rely on B.Buchberger´s (1970, 1985) algorithm for computing Grobner bases. A parallelization of this algorithm that addresses the potential growth in the number of polynomials that can be generated during the computation is proposed. The parallel algorithm was implemented on a Connection Machine CM-200 System. The experimental results which were obtained for seven test problems are evaluated. The results of this study provide insights into ongoing research to develop more efficient parallel algorithms for finding Grobner bases