Gröbner bases in Clifford and Grassmann algebras (Q1911398)

The paper develops a theory of Gröbner bases for the specific non-commutative algebras given by the Clifford and Grassmann algebras. After introducing the suitable notion of reduction, normal form, \(S\)-polynomial etc. for the elements of these algebras, an algorithm is given for the explicit computation of the Gröbner basis of a (left) ideal (which is a suitable modification of the Buchberger algorithm). Moreover a discussion is given of the optimization of the algorithm in terms of the number of \(S\)-polynomials that are necessary to compute. The algorithm was implemented by the authors in the computer algebra system ``REDUCE''.