The main objective of this dissertation is to describe a new and efficient algorithm to compute pommaret bases. To this end, based on the method proposed by M amp;#???;oller et al. [??], we present a more efficient variant of Gerdt's algorithm 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 Seiler's algorithm [??] to compute a linear change of coordinates for a given homogeneous ideal so that the new ideal (after performing this change) possesses a nite Pommaret basis.
