Center for diffusion of mathematic journals


Les cours du CIRM

Table of contents for this issue | Next article
Éric Gourgoulhon; Marco Mancini
Symbolic tensor calculus on manifolds: a SageMath implementation
Les cours du CIRM, 6 no. 1: Journées Nationales de Calcul Formel (2018), Exp. No. 1, 54 p., doi: 10.5802/ccirm.26
Article PDF


[1] I.M. Anderson and C.G. Torre: New symbolic tools for differential geometry, gravitation, and field theory, J. Math. Phys. 53, 013511 (2012);  MR 2919550
[3] G.V. Bard Sage for Undergraduates, Americ. Math. Soc. (2015); preprint freely downloadable from
[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).
[5] D.A. Bolotin and S.V. Poslavsky: Introduction to Redberry: the computer algebra system designed for tensor manipulation, arXiv:1302.1219 (2013);
[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;
[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).
[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).
[11] J. M. Lee : Riemannian Manifolds: An Introduction to Curvature, Springer, New-York (1997).
[12] J. M. Lee : Introduction to Smooth Manifolds, 2nd edition, Springer, New-York (2013).
[13] M.A.H. MacCallum: Computer Algebra in General Relativity, Int. J. Mod. Phys. A 17, 2707 (2002).  MR 1925723
[14] M.A.H. MacCallum: Computer algebra in gravity research, Liv. Rev. Relat. 21, 6 (2018);
[15] J.-M. Martin-Garcia: xPerm: fast index canonicalization for tensor computer algebra, Comput. Phys. Commun. 179, 597 (2008);
[16] J. W. Milnor : On manifolds homeomorphic to the 7-sphere, Ann. Math. 64, 399 (1956).  MR 82103
[17] B. O’Neill : Semi-Riemannian Geometry, with Applications to Relativity, Academic Press, New York (1983).
[19] K. Peeters: Symbolic field theory with Cadabra, Comput. Phys. Commun. 15, 550 (2007);
[22] J.E.F. Skea: Applications of SHEEP (1994), lecture notes available at
[23] N. Steenrod: The Topology of Fibre Bundles, Princeton Univ. Press (Princeton) (1951)
[24] W. Stein and D. Joyner: SAGE: System for Algebra and Geometry Experimentation, Commun. Comput. Algebra, 39, 61 (2005).
[25] C. H. Taubes : Gauge theory on asymptotically periodic 4-manifolds, J. Differential Geom. 25, 363 (1987).
[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
[28] P. Zimmermann et al.: Computational Mathematics with SageMath (2018); freely downloadable from
Copyright Cellule MathDoc 2019 | Credit | Site Map