×

zbMATH — the first resource for mathematics

The program ORTOCARTAN for algebraic calculations in relativity. (English) Zbl 0769.53041
Summary: The program ORTOCARTAN can calculate the curvature tensors (Riemann, Ricci, Einstein and Weyl) from a given orthonormal tetrad representation of the metric tensor. It was first announced in 1981, but since then has undergone several extensions and transplants onto other computers. This article reviews the current status of the program from the point of view of a user. The following topics are discussed: the problems that the program can be applied to, the special features of the algorithms that make the program powerful, the technical requirements to run the program and two simple examples of applications.

MSC:
53Z05 Applications of differential geometry to physics
83-04 Software, source code, etc. for problems pertaining to relativity and gravitational theory
53-04 Software, source code, etc. for problems pertaining to differential geometry
Software:
SHEEP; ORTOCARTAN
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Frick, I. (1977). ”SHEEP–user’s guide.” University of Stockholm Report 77-15.
[2] MacCallum, M. A. H. (1984). InClassical general relativity. Proc. Conf. on Classical (non-quantum) General Relativity (London 1983), W. B. Bonnor, J. N. Islam, M. A. H. MacCallum, eds. (Cambridge University Press, Cambridge).
[3] Krasiński, A., Perkowski, M. (1992).The system ORTOCARTAN–User’s manual (4th ed., Warsaw, available on diskette only).
[4] Krasiński, A. (1983).SIGSAM Bulletin 17, 12.
[5] Krasiński, A. (1986). InInternational Conference on Computer Algebra and its Applications in Theoretical Physics, N. N. Govorun, ed. (Joint Institute for Nuclear Research, Dubna).
[6] Krasiński, A. (1991). InComputer Algebra in Physical Research, D. V. Shirkov, V. A. Rostovtsev and V. P. Gerdt, eds. (World Scientific, Singapore).
[7] Krasiński, A., Perkowski, M., Otwinowski, Z., Kwaśniewski, M. (1984).The system ORTOCARTAN for analytic calculations, detailed description (2nd ed., Warsaw, available on diskette).
[8] Krasiński, A., Perkowski, M. (1981).Gen. Rel. Grav. 13, 67.
[9] Chandrasekhar, S. (1979). InGeneral Relativity: An Einstein Centenary Survey, S. W. Hawking and W. Israel, eds. (Cambridge University Press, Cambridge).
[10] Wardcecki, M. (1973). ”Some heuristic methods of symbolic integration” M. S. thesis (in Polish), Department of Mathematics and Mechanics, Warsaw University.
[11] d’Inverno, R. A. (1975).Gen. Rel. Grav. 6, 567.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.