We consider an algebraic D-module M on the affine space, i.e. a system of linear partial differential equations with polynomial coefficients. We give an algorithm for computing the cohomology groups of the restriction of M to a linear subvariety by using a free resolution of M adapted to the V-filtration. Our algorithm works, at least, if M is holonomic. As applications, we obtain algorithms for computing tensor product, localization, and algebraic local cohomology groups of holonomic systems. (C) 2001 Elsevier Science B.V. All rights reserved. MSG: 13P10; 13N10; 14B15; 14Q20; 35A27. [References: 41]
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