Abstract
We study three computer algebra systems, namely SageMath (with SageManifolds package), Maxima (with ctensor package) and Python language (with GraviPy module), which allow tensor manipulation for general relativity calculations along with general algebraic calculations. We present a benchmark of these systems using simple examples. After the general analysis, we focus on the SageMath and SageManifolds system to derive, analyze and visualize the solutions of the massless Klein–Gordon equation and geodesic motion with Hamilton–Jacobi formalism. We compare our numerical result of the Klein–Gordon equation with the asymptotic form of the analytical solution to see that they agree.
| Original language | English |
|---|---|
| Article number | 4 |
| Journal | General Relativity and Gravitation |
| Volume | 51 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2019 |
Bibliographical note
Publisher Copyright:© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Funding
Acknowledgements WewouldliketothankProfs.Nes¸eÖzdemir,Durmus¸AliDemirandÉricGourgoulhon for stimulating discussions. We also thank our anonymous referee for the constructive comments which helped us to improve the manuscript. This work is partially supported by TÜB˙TAK, the Scientific and Technological Council of Turkey.
| Funders | Funder number |
|---|---|
| Scientific and Technological Council of Turkey |
Keywords
- Geodesic motion
- Numerical analysis
- Symbolic analysis
- Wave equations