Based on our method for determining endomorphism rings, we describe an algorithm to compute decompositions of modules of finite-dimensional algebras over finite fields. The algorithm is implemented in M. Ringe, “The C-Meat-Axe."
Klaus M. Lux. Magdolna Szőke. "Computing Decompositions of Modules over Finite-Dimensional Algebras." Experiment. Math. 16 (1) 1 - 6, 2007.