We want to obtain new results regarding the multigraded Hilbert depth, the Stanley depth and depth and 
also to develope specialized software in order to compute them.
Bellow we make a brief description of the expected results.   

A) The  multigraded Hilbert depth, Stanley depth and depth.

1) New relations between the multigraded Hilbert depth, Stanley depth and depth;
2) Prove Stanley’s conjecture for new classes of modules;
3) Find an algorithm for computing the multigraded Hilbert depth for modules;
4) Find an algorithm for computing the Stanley depth for modules.

B) Algorithms and software for computing Hilbert series, Hilbert depth and Stanley depth.

1) Implementation an algorithm for computing the multigraded Hilbert depth for modules;
2) Implementation an algorithm for computing the Stanley depth for modules;
3) Development of the algorithms implemented in Normaliz.