In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Grobner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Grobner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic methods introduced here are particularly useful for studying the systems of multidimensional hypergeometric PDEs introduced by Gelfand, Kapranov and Zelevinsky. The...

In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Grobner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Grobner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic methods introduced here are particularly useful for studying the systems of multidimensional hypergeometric PDEs introduced by Gelfand, Kapranov and Zelevinsky. The...