Local cohomology was introduced by A. Grothendieck in the early 1960s and quickly became an indispensable tool in Commutative Algebra. Despite the effort of many authors in the study of these modules, their structure is still quite unknown. C
Over the last 20 years there were many advances made in the computational theory of D-modules. Nowadays, the most common computer algebra systems such as Macaulay2 or Singular have important available packages for working with D-modules. In particular, the package D-modules  for Macaulay 2  developed by A. Leykin and H. Tsai contains an implementation of the algorithms given by U. Walther  and T. Oaku and N.