xTensor swMATH ID: 4984 Software Authors: José M. Martín-García Description: xTensor: Fast abstract tensor computer algebra. xTensor extends Mathematica capabilities in abstract tensor calculus, specially in General Relativity. It works with tensors with arbitrary symmetries under permutations of indices, defined on several different manifolds and products of them. It computes covariant derivatives, Lie derivatives and parametric derivatives. It allows the presence of a metric in each manifold and defines all the associated tensors (Riemann, Ricci, Einstein, Weyl, etc.) xTensor does not perform component calculations. Use the companion package xCoba. xTensor needs the package xPerm in order to compute the canonical form of a list of indices under permutation symmetry groups. Homepage: http://www.xact.es/xTensor/index.html Dependencies: Mathematica Related Software: Invar; xPert; xPerm; xAct; xTras; Mathematica; Cadabra; MathTensor; Maple; NP; xCore; Spinors; xPand; Riegeom; ATENSOR; NPspinor; GRTensorII; Canon; EFTofPNG; Maxima Cited in: 33 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year The Invar tensor package: differential invariants of Riemann. Zbl 1197.15001Martín-García, J. M.; Yllanes, D.; Portugal, R. 2008 all top 5 Cited by 57 Authors 4 Knorr, Benjamin 3 Saueressig, Frank 3 Weissenbacher, Matthias 2 Eichhorn, Astrid 2 Grimm, Thomas W. 2 Liu, Jiang 2 Mayer, Kilian 2 Ripken, Chris 2 Schmude, Johannes 1 Alvarez, Enrique E. 1 Brizuela, David 1 Broccoli, Matteo 1 Burby, Joshua W. 1 Coley, Alan Albert 1 de Brito, Gustavo P. 1 dos Santos, Rafael Robson Lino 1 Draper, Tom 1 Dunsby, Peter K. S. 1 Eager, Richard 1 Emond, William T. 1 Endlich, Solomon 1 García-Parrado Gómez-Lobo, Alfonso 1 González-Martín, Sergio 1 Gorbenko, Victor 1 Held, Aaron 1 Herrero-Valea, Mario 1 Hervik, Sigbjørn 1 Huang, Junwu 1 Laporte, Cristobal 1 Lozanovski, Con 1 Manssur, L. R. U. 1 Martín, Carmelo P. 1 Mena Marugán, Guillermo A. 1 Moynihan, Nathan 1 Ni, Feng 1 Nutma, Teake A. 1 Pelavas, Nicos 1 Pereira, Antônio Duarte 1 Pini, Alessandro 1 Pitrou, Cyril 1 Portugal, R. D. 1 Rodríguez-Gómez, Diego 1 Roy, Xavier 1 Ruhdorfer, Maximilian 1 Saffer, Alexander 1 Senatore, Leonardo 1 Serra, Javi 1 Sikhonde, Muzikayise E. 1 Squire, John M. 1 Umeh, Obinna 1 Villani, Mattia 1 Virmani, Amitabh 1 Wang, Jian 1 Weiler, Andreas 1 Yagi, Kent 1 Yllanes, D. 1 Yunes, Nicolás all top 5 Cited in 9 Serials 14 Journal of High Energy Physics 7 Classical and Quantum Gravity 5 Computer Physics Communications 2 General Relativity and Gravitation 1 Physics Letters. B 1 Programming and Computer Software 1 Journal of Symbolic Computation 1 Journal of Systems Science and Complexity 1 Journal of Cosmology and Astroparticle Physics all top 5 Cited in 11 Fields 22 Relativity and gravitational theory (83-XX) 16 Quantum theory (81-XX) 8 Differential geometry (53-XX) 3 Commutative algebra (13-XX) 3 Algebraic geometry (14-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Computer science (68-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) Citations by Year