The Riegeom package: abstract tensor calculation This paper describes a new package for abstract tensor calculation. Riegeom can efficiently simplify generic tensor expressions written in the indicial format. It addresses the problem of the cyclic symmetric and the dimension dependent relations of Riemann tensor polynomials. There are tools to manipulate tensors such as substitution and symmetrization functions. The main tensors of the Riemannian geometry have been implemented. The underlying algorithms are based on a precise mathematical formulation of canonical form of tensor expressions described elsewhere. Riegeom is implemented over the Maple system. (Source: http://cpc.cs.qub.ac.uk/summaries/)

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  1. Liu, Jiang; Ni, Feng: Distance invariant method for normalization of indexed differentials (2021)
  2. Shpiz, G. B.; Kryukov, A. P.: The method of colored graphs for simplifying expressions with indices (2021)
  3. Bonetti, Federico; Klemm, Dietmar; Sabra, Wafic A.; Sloane, Peter: Spinorial geometry, off-shell Killing spinor identities and higher derivative 5D supergravities (2018)
  4. Liu, Jiang: Normalization in Riemann tensor polynomial ring (2018)
  5. Nutma, Teake: \textitxTras: a field-theory inspired \textitxActpackage for Mathematica (2014)
  6. Ulmer, Douglas: Curves and Jacobians over function fields (2014)
  7. Chen, Ze Jun; Xiao, Hong: The vectorization expressions of Taylor series multipole-BEM for 3D elasticity problems (2009)
  8. Grigorian, Sergey; Yau, Shing-Tung: Local geometry of the (G_2) moduli space (2009)
  9. Liu, Jiang; Li, Hongbo; Cao, Yuanhao: Simplification and normalization of indexed differentials involving coordinate transformation (2009)
  10. Paulos, Miguel F.: Higher derivative terms including the Ramond-Ramond five-form (2008)
  11. Peeters, Kasper: Cadabra: a field-theory motivated symbolic computer algebra system (2007)
  12. Hatzinikitas, A.; Portugal, R.: The (d=6) trace anomaly from quantum field theory four-loop graphs in one dimension (2001)
  13. Portugal, R.: The Riegeom package: Abstract tensor calculation (2000)
  14. Portugal, R.: An algorithm to simplify tensor expressions (1998)
  15. Il’in, V. A.; Kryukov, A. P.: Algorithm for simplifying tensor expression in computer algebra. (1994) ioport
  16. Il’in, V. A.; Kryukov, A. P.: Algorithm for simplifying tensor expression in computer algebra (1994)