xPerm: fast index canonicalization for tensor computer algebra. We present a very fast implementation of the Butler-Portugal algorithm for index canonicalization with respect to permutation symmetries. It is called xPerm, and has been written as a combination of a Mathematica package and a C subroutine. The latter performs the most demanding parts of the computations and can be linked from any other program or computer algebra system. We demonstrate with tests and timings the effectively polynomial performance of the Butler-Portugal algorithm with respect to the number of indices, though we also show a case in which it is exponential. Our implementation handles generic tensorial expressions with several dozen indices in hundredths of a second, or one hundred indices in a few seconds, clearly outperforming all other current canonicalizers. The code has been already under intensive testing for several years and has been essential in recent investigations in large-scale tensor computer algebra (Source: http://cpc.cs.qub.ac.uk/summaries/)

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  1. Mogull, Gustav; Plefka, Jan; Steinhoff, Jan: Classical black hole scattering from a worldline quantum field theory (2021)
  2. Draper, Tom; Knorr, Benjamin; Ripken, Chris; Saueressig, Frank: Graviton-mediated scattering amplitudes from the quantum effective action (2020)
  3. García-Parrado, Alfonso: Type D conformal initial data (2020)
  4. Markus B. Fröb: FieldsX - An extension package for the xAct tensor computer algebra suite to include fermions, gauge fields and BRST cohomology (2020) arXiv
  5. Weissenbacher, Matthias: On (\alpha’)-effects from (D)-branes in (4d) ( \mathcalN= 1) (2020)
  6. Weissenbacher, Matthias: F-theory vacua and (\alpha’)-corrections (2020)
  7. García-Parrado, Alfonso; Khavkine, Igor: Conformal Killing initial data (2019)
  8. Knorr, Benjamin: Lorentz symmetry is relevant (2019)
  9. Gómez-Lobo, A. García-Parrado; Minguzzi, Ettore: Pseudo-Finsler spaces modeled on a pseudo-Minkowski space (2018)
  10. Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias: One-modulus Calabi-Yau fourfold reductions with higher-derivative terms (2018)
  11. Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias: Higher derivatives in type II and M-theory on Calabi-Yau threefolds (2018)
  12. Knorr, Benjamin: Infinite order quantum-gravitational correlations (2018)
  13. Linander, Hampus; Nilsson, Bengt E. W.: The non-linear coupled spin 2-spin 3 cotton equation in three dimensions (2016)
  14. Meusburger, C.; Schönfeld, T.: Gauge fixing and classical dynamical (r)-matrices in (\mathrmISO(2, 1))-Chern-Simons theory (2014)
  15. Nutma, Teake: \textitxTras: a field-theory inspired \textitxActpackage for Mathematica (2014)
  16. Squire, J.; Burby, J.; Qin, H.: \textttVEST: Abstract vector calculus simplification in \textttMathematica (2014)
  17. Cuchí, J. E.; Gil-Rivero, A.; Molina, A.; Ruiz, E.: An approximate global solution of Einstein’s equation for a rotating compact source with linear equation of state (2013)
  18. D.A. Bolotin, S.V. Poslavsky: Introduction to Redberry: a computer algebra system designed for tensor manipulation (2013) arXiv
  19. Gómez-Lobo, Alfonso García-Parrado; Senovilla, José M. M.: A set of invariant quality factors measuring the deviation from the Kerr metric (2013)
  20. Gómez-Lobo, Alfonso García-Parrado; Martín-García, José M.: \textitSpinors: a Mathematica package for doing spinor calculus in general relativity (2012)

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