Computation of Involutive and Gröbner Bases Using the Tableau Representation of Polynomials

Abstract

For the work with polynomials such data representations as lists of terms, geobuckets, and heaps are usually used. In this paper, an attempt to give a new look on the representation of polynomials for computing involutive and Grobner bases of systems of nonlinear polynomial equations is made. The proposed approach makes it possible to execute a part of this computational task on the GPU, which opens prospects for solving more complicated problems.