We consider a module whose elements are n-tuples over a field K with an action given by a matrix representation of an associative algebra A. We will refer to these modules as A-modules. These include K[G]-modules.
The four fundamental algorithms for computational module theory are echelonization, the spinning algorithm, the meataxe algorithm and an algorithm for Hom(U, V). For the important case of modules over finite fields, different representations of vector arithmetic, depending upon the field, have been implemented.