Spencer Cohomology, Differential Equations, and Pommaret Bases

Reference: Proc. Gröbner Bases and Symbolic Analysis, M. Rosenkranz, D.M. Wang (eds); de Gruyter, Berlin 2007, Radon Series on Computational and Applied Mathematics 2, pp. 169-216

Description: This article is mainly a review of the Spencer cohomology of a differential equation (or more precisely of its symbol comodule) and its duality to the Koszul homology of the symbol module. Special emphasis is put on the Cartan test and on the question of delta- and quasi-regularity, respectively. It is shown that the two notions are equivalent (this point is treated in more details in [80] ). As another novel aspect the relation to Pommaret bases is clarified.

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