The aim of this notebook is to compare Mathematica and free and open-source Python-based alternatives for symbolic computations and analysis. The main focus is on GR applications. Since calculations in General Relativity (GR) are notoriously complicated (i.e. lengthy tensorial and differential calculations), CA (computer Algebra) methods have shown immensely useful in many research aspects related to GR.See also “Symbolic and numerical analysis in general relativity with open source computer algebra systems” (2018), “Computer algebra in gravity research”(2018) and "Using Maple and GRTensorIII in relativistic spherical models" for recent explorations of GR symbolic computation using SageMath and Maple. One of the main reasons for this project is that scientific research funded with public money should not stick to commercial, proprietary software if a valid free alternative exists. In this notebook, we, thus, specifically explore open-source, community-driven CA implementations. First, we generate a test notebook with basic features used in Mathematica and RGCT. We then use two similar open-source Python packages that implement the same features using SymPy: 1. EinsteinPy 2. GraviPy We compare the results and give some final judgments. This notebook was realised as a project for a Master course (“Abilità informatiche e telematiche”) in theoretical physics at the University of Trieste., For the introduction part of the Python notebook, we adapted the words of "Computer algebra in gravity research" by Malcolm A. H. MacCallum and "Overview of Computer Algebra in Relativity" by D. Hartley., {"references":["Hartley, D. (1996). Overview of computer algebra in relativity. In Relativity and Scientific Computing (pp. 173-191). Springer, Berlin, Heidelberg.","MacCallum, M. A. (2018). Computer algebra in gravity research. Living reviews in relativity, 21(1), 1-93.","Deprit, A., Henrard, J., & Rom, A. (1970). Lunar ephemeris: Delaunay's theory revisited. Science, 168(3939), 1569-1570.","Bondi, H., Van der Burg, M. G. J., & Metzner, A. W. K. (1962). Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 269(1336), 21-52.","Birkandan, T., Güzelgün, C., Şirin, E., & Uslu, M. C. (2019). Symbolic and numerical analysis in general relativity with open source computer algebra systems. General Relativity and Gravitation, 51(1), 1-22.","MacCallum, M. A. (2018). Computer algebra in gravity research. Living reviews in relativity, 21(1), 1-93.","Medina, V. (2022). Using Maple and GRTensorIII in relativistic spherical models. arXiv preprint arXiv:2205.11985.","Maldacena, J., Stanford, D., & Yang, Z. (2016). Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space. Progress of Theoretical and Experimental Physics, 2016(12)."]}