xTensor

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.


References in zbMATH (referenced in 20 articles , 1 standard article )

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  1. Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias: Higher derivatives in type II and M-theory on Calabi-Yau threefolds (2018)
  2. Saffer, Alexander; Yunes, Nicolás; Yagi, Kent: The gravitational wave stress-energy (pseudo)-tensor in modified gravity (2018)
  3. Endlich, Solomon; Gorbenko, Victor; Huang, Junwu; Senatore, Leonardo: An effective formalism for testing extensions to general relativity with gravitational waves (2017)
  4. Michele Levi, Jan Steinhoff: EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity (2017) arXiv
  5. Sikhonde, Muzikayise E.; Dunsby, Peter K. S.: Reviving the shear-free perfect fluid conjecture in general relativity (2017)
  6. Álvarez, Enrique; González-Martín, Sergio; Herrero-Valea, Mario; Martın, Carmelo P.: Quantum corrections to unimodular gravity (2015)
  7. Eager, Richard; Schmude, Johannes: Superconformal indices and M2-branes (2015)
  8. Pini, Alessandro; Rodriguez-Gomez, Diego; Schmude, Johannes: Rigid supersymmetry from conformal supergravity in five dimensions (2015)
  9. Lozanovski, C.: An example of non-Weyl preserving complex transformation (2014)
  10. Nutma, Teake: \itxTras: a field-theory inspired \itxAct package for Mathematica (2014)
  11. Squire, J.; Burby, J.; Qin, H.: VEST: Abstract vector calculus simplification in Mathematica (2014)
  12. Pitrou, Cyril; Roy, Xavier; Umeh, Obinna: $\textxPand$: an algorithm for perturbing homogeneous cosmologies (2013)
  13. Gómez-Lobo, Alfonso García-Parrado; Martín-García, José M.: \itSpinors: a Mathematica package for doing spinor calculus in general relativity (2012)
  14. Virmani, Amitabh: Supertranslations and holographic stress tensor (2012)
  15. Brizuela, David; Martín-García, José M.; Mena Marugán, Guillermo A.: $xPert$: Computer algebra for metric perturbation theory (2009)
  16. Coley, Alan; Hervik, Sigbjørn; Pelavas, Nicos: Spacetimes characterized by their scalar curvature invariants (2009)
  17. Martín-García, J. M.; Yllanes, D.; Portugal, R.: The Invar tensor package: differential invariants of Riemann (2008)
  18. Martin-Garcia, Jose M.; Yllanes, David; Portugal, Renato: The invar tensor package: Differential invariants of Riemann (2008) ioport
  19. Martín-García, J. M.; Portugal, R.; Manssur, L. R. U.: The Invar tensor package (2007)
  20. Martin-Garcia, Jose M.; Portugal, Renato; Manssur, Leon R. U.: The invar tensor package (2007) ioport