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.
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The first six sections of this paper overlap with Mathematics of CLIFFORD: A Maple package for Clifford and Grassmann algebras (with Bertfried Fauser), Advances in Applied Clifford Algebras, Vol. 15, No. 2 (2005), 157-181.
Received: June 2006. Accepted: November 2006.
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Abłamowicz, R. Computations with Clifford and Grassmann Algebras. AACA 19, 499 (2009). https://doi.org/10.1007/s00006-009-0182-3
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DOI: https://doi.org/10.1007/s00006-009-0182-3