Section: New Results

Algorithmic study of linear PD systems and Stafford's theorems

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

In [121] ,[82] , algorithmic versions of Stafford's results [124] (e.g., computation of unimodular elements, decomposition of modules, Serre's splitting-off theorem, Stafford's reduction, Bass' cancellation theorem, minimal number of generators) were obtained and implemented in the Stafford package [82] . In particular, we show how a determined/overdetermined linear system of partial differential equations with either polynomial, rational, formal power series or locally convergent power series coefficients is equivalent to a linear system of partial differential equations with at most two unknowns. This result is a large generalization of the cyclic vector theorem which plays an important role in the theory of linear ordinary differential equations.