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 46 articles , 2 standard articles )

Showing results 1 to 20 of 46.
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  1. Franchini, Silvia; Gentile, Antonio; Sorbello, Filippo; Vassallo, Giorgio; Vitabile, Salvatore: Embedded coprocessors for native execution of geometric algebra operations (2017)
  2. Helmstetter, Jacques: Conformal groups and Vahlen matrices (2017)
  3. Korepanov, I.G.: Free fermions on a piecewise linear four-manifold. I: Exotic chain complex (2017)
  4. Prodanov, D.; Toth, V.T.: Sparse representations of Clifford and tensor algebras in maxima (2017)
  5. Sangwine, Stephen J.; Hitzer, Eckhard: Clifford multivector toolbox (for MATLAB) (2017)
  6. Ulrych, S.: Conformal numbers (2017)
  7. Ahmad Hosney Awad Eid: Optimized Automatic Code Generation for Geometric Algebra Based Algorithms with Ray Tracing Application (2016) arXiv
  8. Castro, Carlos: Moyal deformations of Clifford gauge theories of gravity (2016)
  9. Catarino, Paula: The modified Pell and the modified $k$-Pell quaternions and octonions (2016)
  10. Soh, Célestin Wafo; Mahomed, Fazal M.: Hypercomplex analysis and integration of systems of ordinary differential equations (2016)
  11. Trayling, Greg: Metric and involution scores of Clifford algebras (2016)
  12. Benger, Werner; Heinzl, René; Hildenbrand, Dietmar; Weinkauf, Tino; Theisel, Holger; Tschumperlé, David: Differential methods for multi-dimensional visual data analysis (2015)
  13. Abłamowicz, Rafał; Fauser, Bertfried: Using periodicity theorems for computations in higher dimensional Clifford algebras (2014)
  14. Abłamowicz, Rafał; Fauser, Bertfried: On parallelizing the Clifford algebra product for CLIFFORD (2014)
  15. Fuchs, Laurent; Théry, Laurent: Implementing geometric algebra products with binary trees (2014)
  16. Hitzer, Eckhard: Two-sided Clifford Fourier transform with two square roots of $-1$ in $Cl(p,q)$ (2014)
  17. Wang, Haimeng; Wang, Wei: On octonionic regular functions and the Szeg\Hoprojection on the octonionic Heisenberg group (2014)
  18. Hitzer, Eckhard; Helmstetter, Jacques; Abłamowicz, Rafał: Square roots of $-1$ in real Clifford algebras (2013)
  19. Hitzer, Eckhard; Nitta, Tohru; Kuroe, Yasuaki: Applications of Clifford’s geometric algebra (2013)
  20. Abłamowicz, Rafał; Fauser, Bertfried: On the transposition anti-involution in real Clifford algebras. III: The automorphism group of the transposition scalar product on spinor spaces (2012)

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