ABSTRACT
This chapter aims to give some results of our study concerning to the Grothendieck residue with the viewpoint of 𝒟-module. There is an algorithm for algebraic local cohomology groups as a left 𝒟X-module implemented by using a computer algebra system Kan. When given regular sequence of holomorphic function is not so complicated, this algorithm is carried out and provide proper operators generating Ann. But given sequence become complicated, this procedure is often too slow or fails. So, it is necessary to study the properties of Ann more detail.
