Section: Software

Stafford

Participants : Alban Quadrat [correspondent] , Daniel Robertz [Univ. Aachen] .

The Stafford package of OreModules [106] contains an implementation of two constructive versions of Stafford's famous but difficult theorem [132] stating that every ideal over the Weyl algebra $A_n\left(k\right)$ (resp., $B_n\left(k\right)$) of partial differential operators with polynomial (resp., rational) coefficients over a field $k$ of characteristic 0 (e.g., $k=\mathbb{Q}$, $ℝ$) can be generated by two generators. Based on this implementation and algorithmic results developed in [128] by the authors of the package, two algorithms which compute bases of free modules over the Weyl algebras $A_n\left(\mathbb{Q}\right)$ and $B_n\left(\mathbb{Q}\right)$ have been implemented. The development of the Stafford package was motivated by the problem of computing injective parametrizations of underdetermined linear systems of partial differential equations with polynomial or rational coefficients (the so-called Monge problem), differential flatness, the reduction and decomposition problems and Serre's reduction problem. To our knowledge, the Stafford package is the only implementation of Stafford's theorems nowadays available. The binary of the package is freely available at http://wwwb.math.rwth-aachen.de/OreModules/ .