CLIFFORD swMATH ID: 131 Software Authors: Ablamowicz, Rafal; Fauser, Bertfried Description: 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. Homepage: http://math.tntech.edu/rafal/ Dependencies: Maple Keywords: quantum Clifford algebra; contraction; dotted wedge product; grade involution; Hopf algebra; multivector; reversion; wedge product; quaternions; octonions Related Software: Maple; BIGEBRA; CLICAL; Gaigen; CLUCalc; Gaalop; GABLE; Clifford Multivector Toolbox; Mathematica; SymGroupAlgebra; GMac; GitHub; GAlgebra; HOL Light; Cliplus; SchurFkt; GfG; GluCat; SINGULAR; LUCY Cited in: 85 Publications Further Publications: http://math.tntech.edu/rafal/citing/CBpublications.html Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Mathematics of Clifford – a Maple package for Clifford and Graßmann algebras. Zbl 1099.65520Ablamowicz, Rafal; Fauser, Bertfried 2005 Matrix exponential via Clifford algebras. Zbl 0951.15024Abłamowicz, Rafał 1998 all top 5 Cited by 115 Authors 23 Abłamowicz, Rafał 12 Fauser, Bertfried 9 Hitzer, Eckhard 4 Helmstetter, Jacques 3 Hrdina, Jaroslav 3 Lounesto, Pertti 3 Návrat, Aleš 3 Sangwine, Stephen J. 3 Vašík, Petr 2 Franchini, Silvia 2 Gentile, Antonio 2 Hildenbrand, Dietmar 2 Sobczyk, Garret E. 2 Sorbello, Filippo 2 Vassallo, Giorgio 2 Vitabile, Salvatore 1 Abdella, Kenzu 1 Aragon, Gustavo 1 Arcodía, Marcos R. A. 1 Assefa, Dawit 1 Baylis, William E. 1 Bayro-Corrochano, Eduardo 1 Bektaş, Özcan 1 Benger, Werner 1 Bergdolt, G. 1 Bhatta, Vadiraja G. R. 1 Bory Reyes, Juan 1 Branson, Thomas Patrick 1 Breuils, Stéphane 1 Byrtus, Roman 1 Catarino, Paula Maria Machado Cruz 1 Cen, Julia 1 Cheng, Tao 1 Cnops, Jan 1 da Rocha, Roldão Jun. 1 Delanghe, Richard 1 Derevianko, Anna 1 Dinh, Doan Cong 1 Dray, Tevian 1 Du, Zhenhong 1 Eid, Ahmad Hosny 1 Floquet, Sergio 1 Fring, Andreas 1 Fuchs, Laurent 1 Ge, Xinhong 1 Gebken, Christian 1 Graves-Morris, Peter R. 1 Guan, Yong 1 Guo, Liqiang 1 Heinzl, René 1 Jiang, Xiaomin 1 Kamal, Alaa 1 Korepanov, Igor Germanovich 1 Kuroe, Yasuaki 1 Lávička, Roman 1 Li, Huilan 1 Li, Liming 1 Li, Yongdong 1 Liu, Renyi 1 Manogue, Corinne A. 1 Mansinha, Lalu 1 Nitta, Tohru 1 Panackal, Harikrishnan 1 Pappas, Richard C. 1 Parra, Josep Manel 1 Pérez-Regalado, Cesar Octavio 1 Perwass, Christian B. U. 1 Pinazo-Ojer, José-Manuel 1 Pinto, Eric 1 Poojary, Prasanna 1 Porteous, Ian R. 1 Prodanov, Dimiter 1 Rasmussen, Henning 1 Roberts, D. E. 1 Sarabia-Escrivá, Emilio-José 1 Scharnhorst, Klaus 1 Schmeikal, Bernd 1 Schott, René 1 Selig, J. M. 1 Shapiro, Michael V. 1 Shi, Zhiping 1 Shirokov, Dmitry S. 1 Sommer, Gerald 1 Song, Utensil 1 Soto-Francés, Víctor-Manuel 1 Soucek, Vladimir 1 Staples, George Stacey 1 Steinmetz, Christian 1 Tachibana, Kanta 1 Theisel, Holger 1 Théry, Laurent 1 Tiampo, Kristy F. 1 Toth, Viktor T. 1 Trayling, Greg 1 Trindade, Marco A. S. 1 Tschumperlé, David 1 Ulrych, S. 1 van Holten, Jan-Willem 1 Van Iseghem, Jeannette 1 Varahagiri, Manisha ...and 15 more Authors all top 5 Cited in 22 Serials 43 Advances in Applied Clifford Algebras 3 Computer Physics Communications 3 Linear and Multilinear Algebra 3 Mathematical Methods in the Applied Sciences 2 International Journal of Theoretical Physics 2 Signal Processing 2 Mathematical Problems in Engineering 2 Journal of Nonlinear Mathematical Physics 2 Complex Analysis and Operator Theory 1 General Relativity and Gravitation 1 Journal of Mathematical Analysis and Applications 1 Ukrainian Mathematical Journal 1 Applied Mathematics and Computation 1 Journal of Algebra 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Journal of Automated Reasoning 1 Annals of Physics 1 Linear Algebra and its Applications 1 Computational and Applied Mathematics 1 International Journal of Geometric Methods in Modern Physics 1 Korean Journal of Mathematics all top 5 Cited in 33 Fields 64 Linear and multilinear algebra; matrix theory (15-XX) 25 Computer science (68-XX) 15 Number theory (11-XX) 14 Functions of a complex variable (30-XX) 12 Quantum theory (81-XX) 10 Numerical analysis (65-XX) 7 Associative rings and algebras (16-XX) 7 Information and communication theory, circuits (94-XX) 6 Group theory and generalizations (20-XX) 5 Geometry (51-XX) 5 Differential geometry (53-XX) 5 Relativity and gravitational theory (83-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 3 Mechanics of particles and systems (70-XX) 2 Combinatorics (05-XX) 2 Nonassociative rings and algebras (17-XX) 2 Category theory; homological algebra (18-XX) 2 Approximations and expansions (41-XX) 2 Functional analysis (46-XX) 1 General and overarching topics; collections (00-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year