The paper presents procedures to check solvability and to compute solutions to the Block Decoupling Problem over a Noetherian ring and procedures to compute a feedback law that assigns the coefficients of the compensated system while mantaining the decoupled structure over a Principal Ideal Domain. The algorithms have been implemented using MapleV$\circledR$ and CoCoA [A. Capani, G. Niesi and L. Robbiano: CoCoA, a system for doing Computations in Commutative Algebra].