The Essentials of Clifford Algebras with Maple Programming

Yıl 2021, Cilt: 25 Sayı: 2, 610 - 618, 15.04.2021

Mutlu Akar

https://doi.org/10.16984/saufenbilder.869402

Cited By: 2

Öz

Clifford algebra (geometric algebra) which has many applications in physics, robotics, CAD (Computer-Aided Design) /CAM (Computer-Aided Manufacture), computer graphics, image processing, etc. is one of the important subjects in mathematics. In this paper, after we give the definition of Clifford algebras, introduce their subspaces. Firstly, we develop an algorithm which obtain some concepts of Clifford algebras using by Maple programming. Secondly, another algorithm calculates the norm of the multivector obtained by finding the Clifford product of any two vectors of the same finite dimension.

Anahtar Kelimeler

Clifford algebras, Clifford product, Multivector, Maple

Kaynakça

• [1] Akar, M., Sirakov, N. M. (2019), Support vector machine skin lesion classification in Clifford algebra subspaces, Applications of Mathematics, 64(5), 581-598.
• [2] Brackx, F., De Schepper, N. ve Sommen F. (2006), Clifford-Hermite and two-dimensional Clifford-Gabor filters for early vision, 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering K. Gürlebeck and C. Könke (eds.) Weimar, Germany, 12-14 July.
• [3] Lounesto, P. (2001), Clifford Algebras and Spinors, 2nd edition, Cambridge University Press.
• [4] Aragon, J.L., Aragon-Camarasa, G., Aragon-Gonzalez, G. ve Rodriguez-Andrade, M.A. (2018), Clifford algebra with mathematica, arXiv:0810.2412v2 [math-ph] 22 January.
• [5] Roy, S., Mitra, A. ve Setua, S. K. (2014), Color image representation using multivector, 2014 Fifth International Conference on Intelligent Systems, Modelling and Simulation, Langkawi, Malaysia, 27-29 January 2014, IEEE Xplore.
• [6] Bayro-Corrochano, E. J. ve Arana-Daniel, N. (2010), Clifford support vector machines for classification, regression, and recurrence, IEEE Transactions on Neural Networks, 21(11), 1731-1746.
• [7] Franchini, S., Vassallo, G. ve Sorbello, F. (2010), A brief introduction to Clifford algebra, University of Palermo, Department of Computer Engineering, Technical Report N. 2/2010.
• [8] Vaz, J., Jr. ve Da Rocha, R., Jr., (2016), An introduction to Clifford algebras and spinors, Oxford University Press.
• [9] Hitzer, E., Nitta , T. ve Kuroe, Y. (2013), Applications of Clifford’s geometric algebra, arXiv:1305.5663v1 [math.RA] 24 May.