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. Prabhu, Kartik; Shehzad, Ibrahim: Asymptotic symmetries and charges at spatial infinity in general relativity (2020)
  6. Villani, Mattia: Quasi-normal mode of a regular Schwarzschild black hole (2020)
  7. Weissenbacher, Matthias: F-theory vacua and (\alpha’)-corrections (2020)
  8. Weissenbacher, Matthias: On (\alpha’)-effects from (D)-branes in (4d) ( \mathcalN= 1) (2020)
  9. Aghapour, Sajad; Jafari, Ghadir; Golshani, Mehdi: On variational principle and canonical structure of gravitational theory in double-foliation formalism (2019)
  10. Carrilho, Pedro; Malik, Karim A.: Magnetogenesis from isocurvature initial conditions (2019)
  11. García-Parrado, Alfonso; Khavkine, Igor: Conformal Killing initial data (2019)
  12. Knorr, Benjamin: Lorentz symmetry is relevant (2019)
  13. Knorr, Benjamin; Ripken, Chris; Saueressig, Frank: Form factors in asymptotic safety: conceptual ideas and computational toolbox (2019)
  14. Carrilho, Pedro; Malik, Karim A.: Isocurvature initial conditions for second order Boltzmann solvers (2018)
  15. Gómez-Lobo, A. García-Parrado; Minguzzi, Ettore: Pseudo-Finsler spaces modeled on a pseudo-Minkowski space (2018)
  16. Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias: Higher derivatives in type II and M-theory on Calabi-Yau threefolds (2018)
  17. Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias: One-modulus Calabi-Yau fourfold reductions with higher-derivative terms (2018)
  18. Knorr, Benjamin: Infinite order quantum-gravitational correlations (2018)
  19. Linander, Hampus; Nilsson, Bengt E. W.: The non-linear coupled spin 2-spin 3 cotton equation in three dimensions (2016)
  20. Meusburger, C.; Schönfeld, T.: Gauge fixing and classical dynamical (r)-matrices in (\mathrmISO(2, 1))-Chern-Simons theory (2014)

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