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 30 articles , 1 standard article )

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  1. Liu, Jiang; Ni, Feng: Distance invariant method for normalization of indexed differentials (2021)
  2. Draper, Tom; Knorr, Benjamin; Ripken, Chris; Saueressig, Frank: Graviton-mediated scattering amplitudes from the quantum effective action (2020)
  3. Ruhdorfer, Maximilian; Serra, Javi; Weiler, Andreas: Effective field theory of gravity to all orders (2020)
  4. Weissenbacher, Matthias: F-theory vacua and (\alpha’)-corrections (2020)
  5. Emond, William T.; Moynihan, Nathan: Scattering amplitudes, black holes and leading singularities in cubic theories of gravity (2019)
  6. Knorr, Benjamin: Lorentz symmetry is relevant (2019)
  7. Shpiz, G.; Kryukov, A.: Canonical representation of polynomial expressions with indices (2019)
  8. Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias: Higher derivatives in type II and M-theory on Calabi-Yau threefolds (2018)
  9. Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias: One-modulus Calabi-Yau fourfold reductions with higher-derivative terms (2018)
  10. Knorr, Benjamin: Infinite order quantum-gravitational correlations (2018)
  11. Liu, Jiang: Normalization in Riemann tensor polynomial ring (2018)
  12. Saffer, Alexander; Yunes, Nicolás; Yagi, Kent: The gravitational wave stress-energy (pseudo)-tensor in modified gravity (2018)
  13. Endlich, Solomon; Gorbenko, Victor; Huang, Junwu; Senatore, Leonardo: An effective formalism for testing extensions to general relativity with gravitational waves (2017)
  14. Michele Levi, Jan Steinhoff: EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity (2017) arXiv
  15. Sikhonde, Muzikayise E.; Dunsby, Peter K. S.: Reviving the shear-free perfect fluid conjecture in general relativity (2017)
  16. Álvarez, Enrique; González-Martín, Sergio; Herrero-Valea, Mario; Martın, Carmelo P.: Quantum corrections to unimodular gravity (2015)
  17. Eager, Richard; Schmude, Johannes: Superconformal indices and M2-branes (2015)
  18. Pini, Alessandro; Rodriguez-Gomez, Diego; Schmude, Johannes: Rigid supersymmetry from conformal supergravity in five dimensions (2015)
  19. Lozanovski, C.: An example of non-Weyl preserving complex transformation (2014)
  20. Nutma, Teake: \textitxTras: a field-theory inspired \textitxActpackage for Mathematica (2014)

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