Using Periodicity Theorems for Computations in Higher Dimensional Clifford Algebras

摘要

We present different methods for symbolic computer algebra computations in higher dimensional (≥ 9) Clifford algebras using CLIFFORD and Bigebra packages for Maple R?. This is achieved using graded tensor decompositions, periodicity theorems and matrix spinor representations over Clifford numbers. We show how to code the graded algebra isomorphisms and the main involutions, and we provide some benchmarks.