Computations with Clifford and Grassmann Algebras

Abstract

Various computations in Grassmann and Clifford algebras can be performed with a Maple package CLIFFORD. It can solve algebraic equations when searching for general elements satisfying certain conditions, solve an eigenvalue problem for a Clifford number, and find its minimal polynomial. It can compute with quaternions, octonions, and matrices with entries in Cl(B) - the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B. It uses standard (undotted) Grassmann basis in Cl(Q) but when the antisymmetric part of B is non zero, it can also compute in a dotted Grassmann basis. Some examples of computations are discussed.