An Algorithm for Computing Graded Algebras

In this article I describe an algorithm for computing finite dimensional graded algebras, and I describe an implementation of the algorithm. As an application of the algorithm, I investigate associative algebras satisfying the identity x4 = 0. I show that if A is an associative algebra over a field of characteristic zero, and if a4 = 0 for all a ε A, then A10 = {0}.