Improved Computation of Involutive Bases

In this paper, we describe improved algorithms to compute Janet and Pommaret bases. To this end, based on the method proposed by Moller et al. [20], we present a more efficient variant of Gerdt's algorithm (than the algorithm presented in [16]) to compute minimal involutive bases. Furthermore, by using an involutive version of the Hilbert driven technique along with the new variant of Gerdt's algorithm, we modify the algorithm given in [23] to compute a linear change of coordinates for a given homogeneous ideal so that the new ideal (after performing this change) possesses a finite Pommaret basis. All the proposed algorithms have been implemented in Maple and their efficiency is discussed via a set of benchmark polynomials.