Ricci — A Mathematica package for doing tensor calculations in differential geometry. Ricci is a Mathematica package for doing symbolic tensor computations that arise in differential geometry. It has the following features and capabilities: Manipulation of tensor expressions with and without indices; Implicit use of the Einstein summation convention; Correct manipulation of dummy indices; Display of results in mathematical notation, with upper and lower indices; Automatic calculation of covariant derivatives; Automatic application of tensor symmetries; Riemannian metrics and curvatures; Differential forms; Any number of vector bundles with user-defined characteristics; Names of indices indicate which bundles they refer to; Complex bundles and tensors; Conjugation indicated by barred indices; Connections with and without torsion.

References in zbMATH (referenced in 14 articles )

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  1. Lazaroiu, Calin Iuliu; Babalic, Elena Mirela; Coman, Ioana Alexandra: Geometric algebra techniques in flux compactifications (2016)
  2. Babalic, Elena Mirela; Lazaroiu, Calin Iuliu: Singular foliations for M-theory compactification (2015)
  3. Babalic, Elena Mirela; Lazaroiu, Calin Iuliu: Foliated eight-manifolds for M-theory compactification (2015)
  4. D.A. Bolotin, S.V. Poslavsky: Introduction to Redberry: a computer algebra system designed for tensor manipulation (2013) arXiv
  5. Lazaroiu, Calin-Iuliu; Babalic, Elena-Mirela: Geometric algebra techniques in flux compactifications. II (2013)
  6. Gusev, Yuri V.: Heat kernel expansion in the covariant perturbation theory (2009)
  7. Liu, Jiang; Li, Hongbo; Cao, Yuanhao: Simplification and normalization of indexed differentials involving coordinate transformation (2009)
  8. Husa, Sascha; Hinder, Ian; Lechner, Christiane: Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations (2006)
  9. Fiedler, Bernd: Generators of algebraic covariant derivative curvature tensors and Young symmetrizers (2004)
  10. Avramidi, Ivan; Branson, Thomas: A discrete leading symbol and spectral asymptotics for natural differential operators (2002)
  11. Fiedler, Bernd: On the symmetry classes of the first covariant derivatives of tensor fields (2002)
  12. Fiedler, Bernd: Determination of the structure of algebraic curvature tensors by means of Young symmetrizers (2002)
  13. Portugal, R.: An algorithm to simplify tensor expressions (1998)
  14. Fiedler, B.: A use of ideal decomposition in the computer algebra of tensor expressions (1997)