  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., we present a
more efficient variant of Gerdt's algorithm (than the algorithm presented by
Gerdt-Hashemi-M.Alizadeh) to compute minimal involutive bases. Further, by
using the involutive version of Hilbert driven technique, along with the new
variant of Gerdt's algorithm, we modify the algorithm, given by Seiler, 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.
