Symbolic and Numerical Analysis in General Relativity with Open Source Computer Algebra Systems. Tolga Birkandan; Ceren Güzelgün; Elif Şirin; and Mustafa Can Uslu arXiv.
Symbolic and Numerical Analysis in General Relativity with Open Source Computer Algebra Systems [link]Paper  abstract   bibtex   
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. We present simple examples and give a benchmark of these systems. After the general analysis, we focus on the SageMath+SageManifolds system to analyze and visualize the solutions of the massless Klein-Gordon equation and geodesic motion with Hamilton-Jacobi formalism
@article{tolga_birkandan_symbolic_nodate,
	title = {Symbolic and {Numerical} {Analysis} in {General} {Relativity} with {Open} {Source} {Computer} {Algebra} {Systems}},
	url = {http://export.arxiv.org/abs/1703.09738},
	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. We present simple examples and give a benchmark of these systems. After the general analysis, we focus on the SageMath+SageManifolds system to analyze and visualize the solutions of the massless Klein-Gordon equation and geodesic motion with Hamilton-Jacobi formalism},
	journal = {arXiv},
	author = {{Tolga Birkandan} and {Ceren Güzelgün} and {Elif Şirin} and {Mustafa Can Uslu}},
	keywords = {General Relativity, computational physics, uses sympy}
}
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