SageManifolds swMATH ID: 27192 Software Authors: Eric Gourgoulhon, Micha l Bejger et.al. Description: The SageManifolds project aims at extending the modern computer algebra system SageMath towards differential geometry and tensor calculus. All SageManifolds code is included in SageMath, i.e. it does not require any separate installation. SageManifolds deals with differentiable manifolds of arbitrary dimension. Various coordinate charts and vector frames can be introduced on the manifold, which does not need to be parallelizable. A given tensor field is then described by its sets of components in each vector frame, with automatic change-of-frame transformations for overlapping vector frames. Generic pseudo-Riemannian manifolds can be considered, among which Riemannian manifolds and Lorentzian manifolds, with applications to General Relativity. In particular, the computation of the Riemann curvature tensor and associated tensors (Ricci, Weyl, Schouten and Cotton tensors) is implemented. SageManifolds can also deal with generic affine connections, not necessarily Levi-Civita ones. Homepage: https://sagemanifolds.obspm.fr/ Dependencies: SageMath Related Software: SageMath; simsilun; Maxima; confluent_Heun_functions; ctensor; opensourceGR; GraviPy; GYOTO; GitHub; Redberry; Python; Cadabra Cited in: 3 Publications all top 5 Cited by 8 Authors 1 Birkandan, Tolga 1 Brunswic, Léo 1 Buchert, Thomas 1 Güzelgün, Ceren 1 Rathinam, Chandramohan 1 Shriethar, Natarajan 1 Şirin, Elif 1 Uslu, Mustafa Can Cited in 3 Serials 1 Classical and Quantum Gravity 1 General Relativity and Gravitation 1 International Journal of Theoretical Physics all top 5 Cited in 6 Fields 3 Relativity and gravitational theory (83-XX) 1 Partial differential equations (35-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) Citations by Year