Detecting Superfluous Reductions in Computing Involutive Bases

The main aim of this paper is to improve the computation of involutive bases. For this purpose we present first a signature-based variant of Gerdt’s algorithm to compute minimal involutive bases. Furthermore, by applying the involutive form of Hilbert-driven strategy we propose a new efficient algorithm to compute Pommaret bases. All the presented algorithms in this paper have been implemented in Maple and their performances are compared via a set of benchmark polynomials.