2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110088We consider three modifications of our involutive algorithm for computing Janet bases. These modifications are related to degree compatible monomial orders and specify selection strategies for non-multiplicative prolongations. By using the standard data base of polynomial benchmarks for \Gr bases software we compare the modifications and confront them with Magma that implements Faugère's $F_4$ algorithm.11 pages, Proceedings of the 10th Rhine Workshop on Computer Algebra (March 16-17, 2006, Basel, Switzerland), J.Draisma and H.Kraft (Eds.), University of Basel, 2006, pp.107--117Commutative AlgebraRings and Algebras13P10; 68W30text