CLIFFORD

CLIFFORD performs various computations in Grass mann and Clifford algebras. CLIFFORD performs various computations in Graßmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in C(B) – the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B. Two user-selectable algorithms for the Clifford product are implemented: cmulNUM-based on Chevalley’s recursive formula, and cmuIRS-based on a non-recursive Rota-Stein sausage. Graßmann and Clifford bases can be used. Properties of reversion in undotted and dotted wedge bases are discussed.


References in zbMATH (referenced in 36 articles , 2 standard articles )

Showing results 1 to 20 of 36.
Sorted by year (citations)

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  1. Ahmad Hosney Awad Eid: Optimized Automatic Code Generation for Geometric Algebra Based Algorithms with Ray Tracing Application (2016) arXiv
  2. Castro, Carlos: Moyal deformations of Clifford gauge theories of gravity (2016)
  3. Catarino, Paula: The modified Pell and the modified $k$-Pell quaternions and octonions (2016)
  4. Benger, Werner; Heinzl, René; Hildenbrand, Dietmar; Weinkauf, Tino; Theisel, Holger; Tschumperlé, David: Differential methods for multi-dimensional visual data analysis (2015)
  5. Abłamowicz, Rafał; Fauser, Bertfried: On parallelizing the Clifford algebra product for CLIFFORD (2014)
  6. Abłamowicz, Rafał; Fauser, Bertfried: Using periodicity theorems for computations in higher dimensional Clifford algebras (2014)
  7. Fuchs, Laurent; Théry, Laurent: Implementing geometric algebra products with binary trees (2014)
  8. Hitzer, Eckhard: Two-sided Clifford Fourier transform with two square roots of $-1$ in $Cl(p,q)$ (2014)
  9. Wang, Haimeng; Wang, Wei: On octonionic regular functions and the Szeg\Hoprojection on the octonionic Heisenberg group (2014)
  10. Hitzer, Eckhard; Helmstetter, Jacques; Abłamowicz, Rafał: Square roots of $-1$ in real Clifford algebras (2013)
  11. Hitzer, Eckhard; Nitta, Tohru; Kuroe, Yasuaki: Applications of Clifford’s geometric algebra (2013)
  12. Helmstetter, Jacques: A survey of Lipschitz monoids (2012)
  13. Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore: Fixed-size quadruples for a new, hardware-oriented representation of the 4D Clifford algebra (2011)
  14. Guo, Liqiang; Zhu, Ming; Ge, Xinhong: Reduced biquaternion canonical transform, convolution and correlation (2011)
  15. Helmstetter, Jacques: Lipschitzian subspaces in Clifford algebras (2011)
  16. Hitzer, Eckhard; Abłamowicz, Rafał: Geometric roots of $-1$ in Clifford algebras $C \ell_p,q$ with $p + q \leq 4$ (2011)
  17. Scharnhorst, K.; van Holten, J.-W.: Nonlinear Bogolyubov-Valatin transformations: two modes (2011)
  18. Assefa, Dawit; Mansinha, Lalu; Tiampo, Kristy F.; Rasmussen, Henning; Abdella, Kenzu: Local quaternion Fourier transform and color image texture analysis (2010)
  19. Sobczyk, Garret: Geometric matrix algebra (2008)
  20. da Rocha, R.; Vaz, J.: Isotopic liftings of Clifford algebras and applications in elementary particle mass matrices (2007)

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Further publications can be found at: http://math.tntech.edu/rafal/citing/CBpublications.html