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Symbolic and numerical analysis in general relativity with open source computer algebra systems. (English) Zbl 1409.83001

Summary: 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.

MSC:

83-08 Computational methods for problems pertaining to relativity and gravitational theory
83C10 Equations of motion in general relativity and gravitational theory
70H20 Hamilton-Jacobi equations in mechanics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35L05 Wave equation
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