Mathematics of CLIFFORD - A Maple package for Clifford and Grassmann algebras

Abstract

CLIFFORD performs various computations in Grassmann and Clifford algebras. 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. Two user-selectable algorithms for Clifford product are implemented: 'cmulNUM' - based on Chevalley's recursive formula, and 'cmulRS' - based on non-recursive Rota-Stein sausage. Grassmann and Clifford bases can be used. Properties of reversion in undotted and dotted wedge bases are discussed.

24 pages, update contains new material included in published version

References in corpus (3)

• A Treatise on Quantum Clifford Algebras
• A Hopf laboratory for symmetric functions
• Clifford and Grassmann Hopf algebras via the BIGEBRA package for Maple

Cited by in corpus (8)

• Clifford and Grassmann Hopf algebras via the BIGEBRA package for Maple
• Sparse Representations of Clifford and Tensor algebras in Maxima
• Symbolic and User-friendly Geometric Algebra Routines (SUGAR) for Computations in Matlab
• The Dirichlet Hopf algebra of arithmetics
• Complexifying the spacetime algebra by means of an extra timelike dimension: Pin, Spin and algebraic spinors
• Symbolic Computations in Higher Dimensional Clifford Algebras
• Clifford algebra in R
• On parallelizing the Clifford algebra product for CLIFFORD