ABSTRACT
We review two different methods for computing algebraic local cohomology groups using D-modules. The first one is due to U. Walther and is based on the construction of a certain Cech complex of holonomic D-modules. The second is due to T. Oaku and N. Takayama and relies on their algorithm for computing the derived restriction modules of holonomic D-modules. We provide a discussion of the advantages and disadvantages of these approaches, accompanied by examples of computation done in the computer algebra system Macaulay 2 using the package “D-modules for Macaulay 2” developed jointly by M. Stillman, H. Tsai and ourselves. Also we compare the effectiveness of both methods in terms of machine time.
