Janet Bases and Resolutions in CoCoALib

Recently, the authors presented a novel approach to computing resolutions and Betti numbers using Pommaret bases. For Betti numbers, this algorithm is for most examples much faster than the classical methods (typically by orders of magnitude). As the problem of δ-regularity often makes the determination of a Pommaret basis rather expensive, we extend here our algorithm to Janet bases. Although in δsingular coordinates, Janet bases may induce larger resolutions than the corresponding Pommaret bases, our benchmarks demonstrate that this happens rarely and has no significant effect on the computation costs.