The computation of Gröbner bases on a shared memory multiprocessor

Abstract

The principal result described in this report is the design and implementation of a parallel version of Buchberger's algorithm. Its correctness is stated and some experimental results are given. The first parts are devoted to a partial review of Grobner bases, of Buchberger's algorithm which computes them, and of some of their applications.

Strategy Compliant Multi-Threaded Term Completion

“…Using the switches of OTTER, the workers can even be instructed to follow different strategies (but without refereeing). In the shared memory polynomial case, this scheme was used by Vidal (1990). It has also been applied to general closure computations by Slaney and Lusk (1990), and Lusk and McCune (1990) report a shared memory parallelization of OTTER including Knuth-Bendix completion.…”

The shared-memory language pSather on a distributed-memory multiprocessor

“…We have a running system and have implemented several applications including programs for travelingsalesman problem and Grbbner basis computation ( [7]). …”

Parallelization of Perturbation Analysis: Application to Large-scale Engineering Problems

“…These include real root isolation and Gröbner basis computation (Vidal, 1990;Siegl, 1993;Sawada et al, 1994); solution of Toeplitz-like linear systems (Kaltofen and Pan, 1994); indefinite summation of rational functions (Pirastu and Siegl, 1995); Karatsuba and 3-primes fast fourier transform algorithms (Cesari and Maeder, 1996a,b); term rewriting (Bundgen et al, 1996), quantifier elimination and variables elimination (Hong et al, 1998); resultant computation (Blochinger et al, 1999) and others.…”