Symbolic tensor calculus on manifolds: a SageMath implementation
Journées Nationales de Calcul Formel. 22 – 26 Janvier 2018, Les cours du CIRM, no. 1 (2018), Exposé no. 1, 54 p.
DOI : 10.5802/ccirm.26
Gourgoulhon, Éric 1 ; Mancini, Marco 

1 Laboratoire Univers et Théories CNRS, Observatoire de Paris, Université Paris Diderot, Université Paris Sciences et Lettres 92190 Meudon, France
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Gourgoulhon, Éric; Mancini, Marco. Symbolic tensor calculus on manifolds: a SageMath implementation, dans Journées Nationales de Calcul Formel. 22 – 26 Janvier 2018, Les cours du CIRM, no. 1 (2018), Exposé no. 1, 54 p. doi : 10.5802/ccirm.26. http://archive.numdam.org/articles/10.5802/ccirm.26/

[1] I.M. Anderson and C.G. Torre: New symbolic tools for differential geometry, gravitation, and field theory, J. Math. Phys. 53, 013511 (2012); http://digitalcommons.usu.edu/dg/ | DOI | MR

[2] http://digi-area.com/Maple/atlas/

[3] G.V. Bard Sage for Undergraduates, Americ. Math. Soc. (2015); preprint freely downloadable from http://www.gregorybard.com/ | DOI | Zbl

[4] T. Birkandan, C. Güzelgün, E. Şirin and M. Can Uslu: Symbolic and Numerical Analysis in General Relativity with Open Source Computer Algebra Systems, arXiv:1703.09738v2 (2018). | DOI | MR

[5] D.A. Bolotin and S.V. Poslavsky: Introduction to Redberry: the computer algebra system designed for tensor manipulation, arXiv:1302.1219 (2013); http://redberry.cc/ | DOI

[6] M. Culler, N. M. Dunfield, M. Goerner, and J. R. Weeks: SnapPy, a computer program for studying the geometry and topology of 3-manifolds; http://snappy.computop.org

[7] J.G. Fletcher, R. Clemens, R. Matzner, K.S. Thorne and B.A. Zimmerman: Computer Programs for Calculating General-Relativistic Curvature Tensors, Astrophys. J. 148, L91 (1967). | DOI

[8] https://github.com/grtensor/grtensor

[9] D. Joyner and W. Stein: Sage Tutorial, CreateSpace (2014).

[10] A.V. Korol’kova, D.S. Kulyabov and L.A. Sevast’yanov: Tensor computations in computer algebra systems, Prog. Comput. Soft. 39, 135 (2013). | DOI | MR

[11] J. M. Lee : Riemannian Manifolds: An Introduction to Curvature, Springer, New-York (1997). | Zbl

[12] J. M. Lee : Introduction to Smooth Manifolds, 2nd edition, Springer, New-York (2013). | DOI | Zbl

[13] M.A.H. MacCallum: Computer Algebra in General Relativity, Int. J. Mod. Phys. A 17, 2707 (2002). | DOI | MR

[14] M.A.H. MacCallum: Computer algebra in gravity research, Liv. Rev. Relat. 21, 6 (2018); | DOI

[15] J.-M. Martin-Garcia: xPerm: fast index canonicalization for tensor computer algebra, Comput. Phys. Commun. 179, 597 (2008); http://www.xact.es | DOI | Zbl

[16] J. W. Milnor : On manifolds homeomorphic to the 7-sphere, Ann. Math. 64, 399 (1956). | DOI | MR

[17] B. O’Neill : Semi-Riemannian Geometry, with Applications to Relativity, Academic Press, New York (1983). | DOI

[18] https://opendreamkit.org

[19] K. Peeters: Symbolic field theory with Cadabra, Comput. Phys. Commun. 15, 550 (2007); https://cadabra.science/ | DOI | Zbl

[20] http://www.math.washington.edu/~lee/Ricci/

[21] https://sagemanifolds.obspm.fr

[22] J.E.F. Skea: Applications of SHEEP (1994), lecture notes available at http://www.computeralgebra.nl/systemsoverview/special/tensoranalysis/sheep/

[23] N. Steenrod: The Topology of Fibre Bundles, Princeton Univ. Press (Princeton) (1951) | DOI | Zbl

[24] W. Stein and D. Joyner: SAGE: System for Algebra and Geometry Experimentation, Commun. Comput. Algebra, 39, 61 (2005). | DOI | Zbl

[25] C. H. Taubes : Gauge theory on asymptotically periodic 4-manifolds, J. Differential Geom. 25, 363 (1987). | DOI | MR | Zbl

[26] V. Toth: Tensor manipulation in GPL Maxima, arXiv:cs/0503073 (2005).

[27] P. Zimmermann et al.: Calcul mathématique avec Sage, CreateSpace (2013); freely downloadable from http://sagebook.gforge.inria.fr/

[28] P. Zimmermann et al.: Computational Mathematics with SageMath (2018); freely downloadable from http://sagebook.gforge.inria.fr/english.html

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