Evaluation of Parallel Computations of Gr¨obner and Involutive Bases on the Massive SMP Computer

In previous papers author presented realizations of two different approaches to parallelization of computation of Gr¨obner and involutive bases of polynomial systems with benchmarking on the 8-cores SMP computer: reduction-level parallelism with coefficients of polynomials in Z-ring and basis-level parallelism using modular basis computation and lifting. In this work further development of this algorithms described, benchmarking results and maximal speedup achieved on the massive 32-cores computer presented, scalability differences of algorithms investigated.

Gr¨obner bases, Janet bases, parallel computations, scalability