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Sage Manifolds
SageManifolds (following styling of SageMath) is an extension fully integrated into SageMath, to be used as a Package (package management system), package for differential geometry and tensor calculus. The official page for the project isagemanifolds.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, General Relativity. In particular, SageManifolds implements the computation of the Riemann curvature tensor and associated objects (Ricci tensor, Weyl tensor). SageManifolds can also de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SageMath
SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, number theory, calculus and statistics. The first version of SageMath was released on 24 February 2005 as free and open-source software under the terms of the GNU General Public License version 2, with the initial goals of creating an "open source alternative to Magma, Maple, Mathematica, and MATLAB". The originator and leader of the SageMath project, William Stein, was a mathematician at the University of Washington. SageMath uses a syntax resembling Python's, supporting procedural, functional and object-oriented constructs. Development Stein realized when designing Sage that there were many open-source mathematics software packages already written in different languages, namely C, C++, Common Lisp, Fortran and Python. R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weyl Tensor
In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic. The Weyl tensor differs from the Riemann curvature tensor in that it does not convey information on how the volume of the body changes, but rather only how the shape of the body is distorted by the tidal force. The Ricci curvature, or trace component of the Riemann tensor contains precisely the information about how volumes change in the presence of tidal forces, so the Weyl tensor is the traceless component of the Riemann tensor. This tensor has the same symmetries as the Riemann tensor, but satisfies the extra condition that it is trace-free: metric contraction on any pair of indices yields zero. It is obtained from the Riemann tensor by subtracting a tensor that is a linear expression ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Software Programmed In Python
Free may refer to: Concept * Freedom, having the ability to do something, without having to obey anyone/anything * Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism * Emancipate, to procure political rights, as for a disenfranchised group * Free will, control exercised by rational agents over their actions and decisions * Free of charge, also known as gratis. See Gratis vs libre. Computing * Free (programming), a function that releases dynamically allocated memory for reuse * Free format, a file format which can be used without restrictions * Free software, software usable and distributable with few restrictions and no payment * Freeware, a broader class of software available at no cost Mathematics * Free object ** Free abelian group ** Free algebra ** Free group ** Free module ** Free semigroup * Free variable People * Free (surname) * Free (rapper) (born 1968), or Free Marie, American rapper and media pers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language) Scientific Libraries
Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (programming language), a widely used programming language * Python, a native code compiler for CMU Common Lisp * Python, the internal project name for the PERQ 3 computer workstation People * Python of Aenus (4th-century BCE), student of Plato * Python (painter), (ca. 360–320 BCE) vase painter in Poseidonia * Python of Byzantium, orator, diplomat of Philip II of Macedon * Python of Catana, poet who accompanied Alexander the Great * Python Anghelo (1954–2014) Romanian graphic artist Roller coasters * Python (Efteling), a roller coaster in the Netherlands * Python (Busch Gardens Tampa Bay), a defunct roller coaster * Python (Coney Island, Cincinnati, Ohio), a steel roller coaster Vehicles * Python (automobile maker), an Australian car ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Mathematics Software
Free may refer to: Concept * Freedom, having the ability to do something, without having to obey anyone/anything * Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism * Emancipate, to procure political rights, as for a disenfranchised group * Free will, control exercised by rational agents over their actions and decisions * Free of charge, also known as gratis. See Gratis vs libre. Computing * Free (programming), a function that releases dynamically allocated memory for reuse * Free format, a file format which can be used without restrictions * Free software, software usable and distributable with few restrictions and no payment * Freeware, a broader class of software available at no cost Mathematics * Free object ** Free abelian group ** Free algebra ** Free group ** Free module ** Free semigroup * Free variable People * Free (surname) * Free (rapper) (born 1968), or Free Marie, American rapper and media personal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNU General Public License
The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end user In product development, an end user (sometimes end-user) is a person who ultimately uses or is intended to ultimately use a product. The end user stands in contrast to users who support or maintain the product, such as sysops, system administrat ...s the Four Freedoms (Free software), four freedoms to run, study, share, and modify the software. The license was the first copyleft for general use and was originally written by the founder of the Free Software Foundation (FSF), Richard Stallman, for the GNU Project. The license grants the recipients of a computer program the rights of the Free Software Definition. These GPL series are all copyleft licenses, which means that any derivative work must be distributed under the same or equivalent license terms. It is more restrictive than the GNU Lesser General Public License, Lesser General Public License ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically-typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language and first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000 and introduced new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 3.0, released in 2008, was a major revision that is not completely backward-compatible with earlier versions. Python 2 was discontinued with version 2.7.18 in 2020. Python consistently ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open-source Software
Open-source software (OSS) is computer software that is released under a license in which the copyright holder grants users the rights to use, study, change, and distribute the software and its source code to anyone and for any purpose. Open-source software may be developed in a collaborative public manner. Open-source software is a prominent example of open collaboration, meaning any capable user is able to participate online in development, making the number of possible contributors indefinite. The ability to examine the code facilitates public trust in the software. Open-source software development can bring in diverse perspectives beyond those of a single company. A 2008 report by the Standish Group stated that adoption of open-source software models has resulted in savings of about $60 billion per year for consumers. Open source code can be used for studying and allows capable end users to adapt software to their personal needs in a similar way user scripts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Software
Free software or libre software is computer software distributed under terms that allow users to run the software for any purpose as well as to study, change, and distribute it and any adapted versions. Free software is a matter of liberty, not price; all users are legally free to do what they want with their copies of a free software (including profiting from them) regardless of how much is paid to obtain the program.Selling Free Software (gnu.org) Computer programs are deemed "free" if they give end-users (not just the developer) ultimate control over the software and, subsequently, over their devices. The right to study and modify a computer program entails that source code< ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apache Subversion
Apache Subversion (often abbreviated SVN, after its command name ''svn'') is a software versioning and revision control system distributed as open source under the Apache License. Software developers use Subversion to maintain current and historical versions of files such as source code, web pages, and documentation. Its goal is to be a mostly compatible successor to the widely used Concurrent Versions System (CVS). The open source community has used Subversion widely: for example, in projects such as Apache Software Foundation, Free Pascal, FreeBSD, SourceForge, and from 2006 to 2019, GCC. CodePlex was previously a common host for Subversion repositories. Subversion was created by CollabNet Inc. in 2000, and is now a top-level Apache project being built and used by a global community of contributors. History CollabNet founded the Subversion project in 2000 as an effort to write an open-source version-control system which operated much like CVS but which fixed the bug ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Connection
In Riemannian or pseudo Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the ( pseudo-) Riemannian metric and is torsion-free. The fundamental theorem of Riemannian geometry states that there is a unique connection which satisfies these properties. In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection. The components (structure coefficients) of this connection with respect to a system of local coordinates are called Christoffel symbols. History The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel. Levi-Civita, along with Gregorio Ricci-Curbastro, used Christoffel's symbols to define the notion of parallel transport and explore the relationship of par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affine Connection
In differential geometry, an affine connection is a geometric object on a smooth manifold which ''connects'' nearby tangent spaces, so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space. Connections are among the simplest methods of defining differentiation of the sections of vector bundles. The notion of an affine connection has its roots in 19th-century geometry and tensor calculus, but was not fully developed until the early 1920s, by Élie Cartan (as part of his general theory of connections) and Hermann Weyl (who used the notion as a part of his foundations for general relativity). The terminology is due to Cartan and has its origins in the identification of tangent spaces in Euclidean space by translation: the idea is that a choice of affine connection makes a manifold look infinitesimally like Euclidean space not just smoothly, but as an affine space. On any manifold of positive dimension ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
