Gröbner Bases in Clifford and Grassmann algebras

We give an account of the theory of Gröbner bases for Clifford and Grassmann algebras, both important in physical applications. We describe a characterization criterion tailored to these algebras which is significantly simpler than those given earlier or for more general non-commuting algebras. Our particular applications admit some tests for reducing the amount of calculation which are discussed along with an algorithm for calculating Gröbner bases in these algebras. Finally we describe a REDUCE implementation of our algorithm and give an application example.