Abstract
This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. We briefly overview the current state of tensor computations in different computer algebra systems. The tensor computations are illustrated with appropriate examples implemented in specific systems: Cadabra and Maxima.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Kulyabov, D.S., Korolkova, A.V., and Korolkov, V.I., Maxwell’s equations in arbitrary coordinate system, Bull. PFUR. Ser. Math. Inf. Sci. Phys., 2012, no. 1, pp. 96–106.
Kulyabov, D.S. and Nemchaninova, N.A., Maxwell’s equations in curvilinear coordinates, Bull. PFUR. Ser. Math. Inf. Sci. Phys., 2011, no. 2, pp. 172–179.
Sardanishvili, G.A., Sovremennye metody teorii polja (Modern Methods of the Field Theory), vol. 2: Geometriya i klassicheskaya mekhanika (Geometry and Classical Mechanics), Moscow: URSS, 1998.
Cartan, E., The Theory of Spinors, Paris: Hermann, 1966.
Gerdt, V.P., Tarasov, O.V., and Shirkov, D.V., Analytical calculations on digital computers for applications in physics and mathematics, Sov. Phys. Usp., 1980, vol. 130, no. 1, pp. 59–78. http://ufn.ru/ru/articles/1980/1/d/
Barut, A. and Raczka, R., Theory of Group Representations and Applications Warsaw: Polish Scientific Publishers, 1980.
Penrose, R. and Rindler, W., Spinors and Space-Time. Two-Spinor Calculus and Relativistic Fields, Cambridge Univ. Press, 1987, vol. 1.
Computer Algebra Information Network. http://www.computeralgebra.nl/systemsoverview/special/systems.html
Kulyabov, D.S. and Kokotchikova, M.G., Analytical review of symbolic computing systems, Bull. PFUR. Ser. Math. Inf. Sci. Phys., 2007, nos. 1–2, pp. 38–45.
Sevastianov, L.A., Kulyabov, D.S., and Kokotchikova, M.G., An application of computer algebra system Cadabra to scientific problems of physics, Phys. Part. Nucl. Lett., 2009, no. 6, no. 7, pp. 530–534.
Toth, V., Tensor manipulation in GPL Maxima, 2005. arXiv:cs/0503073v2
Gerdt, V.P. and Tiller, P., A reduce program for symbolic computation of Puiseux expansions, Dubna: Joint Inst. Nucl. Res., 1991.
Parker, L. and Christensen, S.M., MathTensor: A System for Doing Tensor Analysis by Computer, Addison-Wesley, 1994.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Korol’kova, D.S. Kulyabov, L.A. Sevast’yanov, 2013, published in Programmirovanie, 2013, Vol. 39, No. 3.
Rights and permissions
About this article
Cite this article
Korol’kova, A.V., Kulyabov, D.S. & Sevast’yanov, L.A. Tensor computations in computer algebra systems. Program Comput Soft 39, 135–142 (2013). https://doi.org/10.1134/S0361768813030031
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0361768813030031