A Geometric Algebra Implementation using Binary Tree

Abstract : This paper presents an efficient implementation of geometric algebra, based on a recursive representation of the algebra elements using binary trees. The proposed approach consists in restructuring a state of the art recursive algorithm to handle parallel optimizations. The resulting algorithm is described for the outer product and the geometric product. The proposed implementation is usable for any dimensions, including high dimension (e.g. algebra of dimension 15). The method is compared with the main state of the art geometric algebra implementations , with a time complexity study as well as a practical benchmark. The tests show that our implementation is at least as fast as the main geometric algebra implementations.
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Submitted on : Wednesday, May 3, 2017 - 3:14:02 AM
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Stéphane Breuils, Vincent Nozick, Laurent Fuchs. A Geometric Algebra Implementation using Binary Tree. Advances in Applied Clifford Algebras, Springer Verlag, 2017, 1, pp.1-19. ⟨10.1007/s00006-017-0770-6⟩. ⟨hal-01510078v2⟩

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