Complexity of a standard basis of a d-module

International audienceA double-exponential upper bound is obtained for the degree and for the complexity of constructing a standard basis of a D-module. This generalizes a well-known bound for the complexity of a Grobner basis of a module over the algebra of polynomials. It should be emphasized that the bound obtained cannot be deduced immediately from the commutative case. To get the bound in question, a new technique is developed for constructing all the solutions of a linear system over a homogeneous version of a Weyl algebra