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SageManifolds (following styling of SageMath) is an extension fully integrated into SageMath, to be used as a package for differential geometry and tensor calculus. The official page for the project is sagemanifolds.obspm.fr. It can be used on CoCalc.
SageManifolds deals with differentiable manifolds of arbitrary dimension. The basic objects are tensor fields and not tensor components in a given vector frame or coordinate chart. In other words, various charts and frames can be introduced on the manifold and a given tensor field can have representations in each of them.
An important class of treated manifolds is that of pseudo-Riemannian manifolds, among which Riemannian manifolds and Lorentzian manifolds, with applications to General Relativity. In particular, SageManifolds implements the computation of the Riemann curvature tensor and associated objects (Ricci tensor, Weyl tensor). SageManifolds can also deal with generic affine connections, not necessarily Levi-Civita ones.
pseudo-Riemannian manifolds, among which Riemannian manifolds and Lorentzian manifolds, with applications to General Relativity. In particular, SageManifolds implements...
group theory, differentiable manifolds, numerical analysis, number theory, calculus and statistics. The first version of SageMath was released on 24 February...
macros in TensorOperations.jl. SageManifolds: tensor calculus on smooth manifolds; all SageManifolds code is included in SageMath since version 7.5; it allows...
to express the curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold (i.e., it is a tensor field). It is a local...
Gareth Sager (born 10 August 1960 in Edinburgh, Scotland) is a Scottish guitarist, keyboardist, musician, composer and songwriter, and is a founding member...
curse. The creator-god Brahma, on the advice of his son and divine sage Narada or the sage, himself give the princesses the boon to be wives of Vishnu. Narakasura...
Cars is a media franchise including the 2006 film Cars, the 2011 film Cars 2, the 2017 film Cars 3, the 2022 series Cars on the Road, the 2013 film Planes...
products will be drilled from freestanding beams, which are coupled to manifolds prior to pipeline transfer to MST Odin via a riser base. There are also...
1142/S0217732397000546. S2CID 11779832. Hübsch, Tristan (1994). Calabi-Yau Manifolds: A Bestiary for Physicists. World Scientific. ISBN 978-981-02-1927-7....
Perelman, Grisha (10 March 2003). "Ricci flow with surgery on three-manifolds". arXiv:math.DG/0303109. Perelman, Grisha (July 17, 2003). "Finite extinction...
approximates non-linear principal manifolds. This approach is based on a mechanical analogy between principal manifolds, that are passing through "the middle"...
Wilburn R., ed. The Social History of Crime and Punishment in America. London: SAGE Publications. p. 1006 Archived 30 September 2020 at the Wayback Machine....
Skinn, Steve Parkhouse, Paul Neary, John Stokes Incredible Hulk Weekly #57 Sage (Tessa) 1980-04 Chris Claremont, John Byrne Uncanny X-Men #132 Dansen Macabre...
conceited of herself that she is the main reason for this victory. Meanwhile, Sage Nārada brings the Pārijāta flower from heaven, gives it to Kṛṣṇa, while he’s...
doi:10.2307/27757115. JSTOR 27757115. Morgan, Frank (February 2009). "Manifolds with Density and Perelman's Proof of the Poincaré Conjecture". The American...
super-space extensions, was developed by J. Harnad and S. Shnider. Hyperkähler manifolds of dimension 4 k {\displaystyle 4k} also admit a twistor correspondence...
field theory. The manifolds that are used in this formulation are 4-dimensional Riemannian manifolds instead of pseudo Riemannian manifolds. It is also assumed...
two-dimensional non-linear sigma models with target space on simple geometric manifolds, whose renormalization behavior is controlled by a Ricci flow, which includes...
Unreliable narrator E. Bruce Goldstein (2010). Encyclopedia of Perception. SAGE Publications. p. 492. ISBN 978-1-4129-4081-8., Quote: The ancient Hindu parable...
(2007). Human Sexuality: Personality and Social Psychological Perspectives. SAGE Publications. pp. 265–266. ISBN 978-1-5063-2012-0. Archived from the original...
mythology, the Gita was written by the god Ganesha, as told to him by the sage Veda Vyasa. The Gita forms the chapters 23–40 in book 6 of the Mahabharata...
Ilya (2013). "Hilbert's 6th Problem: Exact and approximate hydrodynamic manifolds for kinetic equations". Bulletin of the American Mathematical Society...
Retrieved 2 September 2010. Woodman, Dan (2015). Youth and Generation. London: Sage Publications Ltd. p. 132. ISBN 978-1-4462-5905-4. Cabral, J. (2010). "Is...
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