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We present, as a proof of concept, a way to parallelize the Clifford product in Cℓ p,q  for a diagonalized quadratic form as a new procedure cmulWpar in the CLIFFORD package for Maple ® . The procedure uses a new Threads module available under Maple 15 (and later) and a new CLIFFORD procedure cmulW which computes the Clifford product of any two Grassmann monomials in Cℓ p,q  with a help of Walsh functions. We benchmark cmulWpar and compare it to two other procedures cmulNUM and cmulRS from CLIFFORD. We comment on how to improve cmulWpar by taking advantage of multi-core processors and multithreading available in modern processors.

On Parallelizing the Clifford Algebra Product for CLIFFORD