xPerm

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/)


References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Meusburger, C.; Schönfeld, T.: Gauge fixing and classical dynamical $r$-matrices in $\mathrmISO(2, 1)$-Chern-Simons theory (2014)
  2. Nutma, Teake: \itxTras: a field-theory inspired \itxAct package for Mathematica (2014)
  3. Squire, J.; Burby, J.; Qin, H.: VEST: Abstract vector calculus simplification in Mathematica (2014)
  4. 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)
  5. Gómez-Lobo, Alfonso García-Parrado; Senovilla, José M.M.: A set of invariant quality factors measuring the deviation from the Kerr metric (2013)
  6. Gómez-Lobo, Alfonso García-Parrado; Martín-García, José M.: \itSpinors: a Mathematica package for doing spinor calculus in general relativity (2012)
  7. Vera, Agustín Sabio; Campillo, Eduardo Serna; Vázquez-Mozo, Miguel Á.: Graviton emission in Einstein-Hilbert gravity (2012)
  8. Virmani, Amitabh: Supertranslations and holographic stress tensor (2012)
  9. Steinhoff, J.: Canonical formulation of spin in general relativity (2011)
  10. Brewin, Leo: A brief introduction to Cadabra: a tool for tensor computations in general relativity (2010)
  11. Tessmer, M.; Hartung, J.; Schäfer, G.: Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin-orbit and leading order in spin(1)-spin(2) and spin-squared couplings (2010)
  12. Edgar, S.Brian; Gómez-Lobo, Alfonso García-Parrado; Martín-García, José M.: Petrov D vacuum spaces revisited: Identities and invariant classification (2009)
  13. Martín-García, José M.: xPerm: fast index canonicalization for tensor computer algebra (2008)