Large scale tensor analysis by computer. The paper contains a description of the software package MathTensor which can be loaded into the Mathematica computer algebra system. The package is useful for manipulating large systems of equations and for detecting symmetries in tensor structures. The author addresses problems emerging from quantum field theory of curved space-times for instance to describe the distance along a geodesic curve between two points on a curved surface. It is a demanding task to convert a large Riemann tensor term into a linear combination of a minimal set of such terms. In quite a few examples the author illustrates how to tackle this problem by applying the package.

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  1. Liu, Jiang; Ni, Feng: Distance invariant method for normalization of indexed differentials (2021)
  2. Liu, Jiang: Normalization in Riemann tensor polynomial ring (2018)
  3. Liu, Jiang: Normalization of indexed differentials based on function distance invariants (2017)
  4. Squire, J.; Burby, J.; Qin, H.: \textttVEST: Abstract vector calculus simplification in \textttMathematica (2014)
  5. Korol’kova, A. V.; Kulyabov, D. S.; Sevast’yanov, L. A.: Tensor computations in computer algebra systems (2013)
  6. Balaž, Antun; Vidanović, Ivana; Stojiljković, Danica; Vudragović, Dušan; Belić, Aleksandar; Bogojević, Aleksandar: SPEEDUP code for calculation of transition amplitudes via the effective action approach (2012)
  7. Brewin, Leo: A brief introduction to \textttCadabra: a tool for tensor computations in general relativity (2010)
  8. Gusev, Yuri V.: Heat kernel expansion in the covariant perturbation theory (2009)
  9. Liu, Jiang; Li, Hongbo; Cao, Yuanhao: Simplification and normalization of indexed differentials involving coordinate transformation (2009)
  10. Martín-García, José M.: xPerm: fast index canonicalization for tensor computer algebra (2008)
  11. Martín-García, J. M.; Portugal, R.; Manssur, L. R. U.: The Invar tensor package (2007)
  12. Peeters, Kasper: Cadabra: a field-theory motivated symbolic computer algebra system (2007)
  13. Edgar, S. Brian; Senovilla, José M. M.: A weighted de Rham operator acting on arbitrary tensor fields and their local potentials (2006)
  14. Husa, Sascha; Hinder, Ian; Lechner, Christiane: Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations (2006)
  15. Manssur, L. R. U.; Portugal, R.: The Canon package: a fast kernel for tensor manipulators (2004)
  16. Bebbington, David; Göbel, Manfred: KLEIN: a Mathematica package for radar polarimetry based on spinor and tensor algebra (2001)
  17. Christensen, Steven M.: Large scale tensor analysis by computer (1998)
  18. Fiedler, B.: A characterization of the dependence of the Riemannian metric on the curvature tensor by Young symmetrizers (1998)
  19. Portugal, R.: An algorithm to simplify tensor expressions (1998)
  20. Socorro, José; Macías, Alfredo; Hehl, Friedrich W.: Computer algebra in gravity: Reduce-Excalc programs for (non-)Riemannian space-times. I (1998)

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