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GAP Computer Algebra System
GAP (Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra with particular emphasis on computational group theory. History GAP was developed at Lehrstuhl D für Mathematik (LDFM), Rheinisch-Westfälische Technische Hochschule Aachen, Germany from 1986 to 1997. After the retirement of Joachim Neubüser from the chair of LDFM, the development and maintenance of GAP was coordinated by the School of Mathematical and Computational Sciences at the University of St Andrews, Scotland. In the summer of 2005 coordination was transferred to an equal partnership of four 'GAP Centres', located at the University of St Andrews, RWTH Aachen, Technische Universität Braunschweig, and Colorado State University at Fort Collins; in April 2020, a fifth GAP Centre located at the TU Kaiserslautern was added. Distribution GAP and its sources, including packages (sets of user contributed programs), data library (including a list of small groups) and the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Group Theory
In mathematics, computational group theory is the study of groups by means of computers. It is concerned with designing and analysing algorithms and data structures to compute information about groups. The subject has attracted interest because for many interesting groups (including most of the sporadic groups) it is impractical to perform calculations by hand. Important algorithms in computational group theory include: * the Schreier–Sims algorithm for finding the order of a permutation group * the Todd–Coxeter algorithm and Knuth–Bendix algorithm for coset enumeration * the product-replacement algorithm for finding random elements of a group Two important computer algebra systems (CAS) used for group theory are GAP and Magma. Historically, other systems such as CAS (for character theory) and Cayley (a predecessor of Magma) were important. Some achievements of the field include: * complete enumeration of all finite groups of order less than 2000 * computation of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algebra System Software For MacOS
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation. This term may also refer to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of industrial and consumer products use computers as control systems. Simple special-purpose devices like microwave ovens and remote controls are included, as are factory devices like industrial robots and computer-aided design, as well as general-purpose devices like personal computers and mobile devices like smartphones. Computers power the Internet, whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algebra System Software For Linux
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation. This term may also refer to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of industrial and consumer products use computers as control systems. Simple special-purpose devices like microwave ovens and remote controls are included, as are factory devices like industrial robots and computer-aided design, as well as general-purpose devices like personal computers and mobile devices like smartphones. Computers power the Internet, which links bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comparison Of Computer Algebra Systems
The following tables provide a comparison of computer algebra systems (CAS). A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language. A CAS may include a user interface and graphics capability; and to be effective may require a large library of algorithms, efficient data structures and a fast kernel. General These computer algebra systems are sometimes combined with "front end" programs that provide a better user interface, such as the general-purpose GNU TeXmacs. Functionality Below is a summary of significantly developed ''symbolic'' functionality in each of the systems. via SymPy via qepcad optional package Those which do not "edit equations" may have a GUI, plotting, ASCII graphic formulae and math font printing. The ability to generate plaintext files is also a sought-after feature because it allows a work to be understood by people wh ... [...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. Rather th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singular (software)
Singular (typeset ) is a computer algebra system for polynomial computations with special emphasis on the needs of commutative and non-commutative algebra, algebraic geometry, and singularity theory. Singular has been released under the terms of GNU General Public License. Problems in non-commutative algebra can be tackled with the Singular offspring Plural. Singular is developed under the direction of Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister, and Hans Schönemann, who head Singular's core development team within the Department of Mathematics of the Technische Universität Kaiserslautern. In the DFG Priority Program 1489, interfaces to GAP, Polymake and Gfan are being developed in order to cover recently established areas of mathematics involving convex and algebraic geometry, such as toric and tropical geometry. See also *Comparison of computer algebra systems The following tables provide a comparison of computer algebra systems (CAS). A CAS is a package com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peer Review
Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work ( peers). It functions as a form of self-regulation by qualified members of a profession within the relevant field. Peer review methods are used to maintain quality standards, improve performance, and provide credibility. In academia, scholarly peer review is often used to determine an academic paper's suitability for publication. Peer review can be categorized by the type of activity and by the field or profession in which the activity occurs, e.g., medical peer review. It can also be used as a teaching tool to help students improve writing assignments. Henry Oldenburg (1619–1677) was a German-born British philosopher who is seen as the 'father' of modern scientific peer review. Professional Professional peer review focuses on the performance of professionals, with a view to improving quality, upholding standards, or providing certification. In academia, p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apple Macintosh
The Mac (known as Macintosh until 1999) is a family of personal computers designed and marketed by Apple Inc., Apple Inc. Macs are known for their ease of use and minimalist designs, and are popular among students, creative professionals, and software engineers. The current lineup includes the MacBook Air and MacBook Pro laptops, as well as the iMac, Mac Mini, Mac Studio and Mac Pro desktops. Macs run the macOS operating system. The Macintosh 128K, first Mac was released in 1984, and was advertised with the highly-acclaimed 1984 (advertisement), "1984" ad. After a period of initial success, the Mac languished in the 1990s, until co-founder Steve Jobs returned to Apple in 1997. Jobs oversaw the release of many successful products, unveiled the modern Mac OS X, completed the Mac transition to Intel processors, 2005-06 Intel transition, and brought features from the iPhone back to the Mac. During Tim Cook's tenure as CEO, the Mac underwent a period of neglect, but was later reinv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microsoft Windows
Windows is a group of several Proprietary software, proprietary graphical user interface, graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for servers, and Windows IoT for embedded systems. Defunct Windows families include Windows 9x, Windows Mobile, and Windows Phone. The first version of Windows was released on November 20, 1985, as a graphical operating system shell for MS-DOS in response to the growing interest in graphical user interfaces (GUIs). Windows is the most popular desktop operating system in the world, with Usage share of operating systems, 75% market share , according to StatCounter. However, Windows is not the most used operating system when including both mobile and desktop OSes, due to Android (operating system), Android's massive growth. , the most recent version of Windows is Windows 11 for consumer Personal compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unix
Unix (; trademarked as UNIX) is a family of multitasking, multiuser computer operating systems that derive from the original AT&T Unix, whose development started in 1969 at the Bell Labs research center by Ken Thompson, Dennis Ritchie, and others. Initially intended for use inside the Bell System, AT&T licensed Unix to outside parties in the late 1970s, leading to a variety of both academic and commercial Unix variants from vendors including University of California, Berkeley ( BSD), Microsoft ( Xenix), Sun Microsystems ( SunOS/ Solaris), HP/ HPE ( HP-UX), and IBM ( AIX). In the early 1990s, AT&T sold its rights in Unix to Novell, which then sold the UNIX trademark to The Open Group, an industry consortium founded in 1996. The Open Group allows the use of the mark for certified operating systems that comply with the Single UNIX Specification (SUS). Unix systems are characterized by a modular design that is sometimes called the " Unix philosophy". According to thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copyleft
Copyleft is the legal technique of granting certain freedoms over copies of copyrighted works with the requirement that the same rights be preserved in derivative works. In this sense, ''freedoms'' refers to the use of the work for any purpose, and the ability to modify, copy, share, and redistribute the work, with or without a fee. Licenses which implement copyleft can be used to maintain copyright conditions for works ranging from computer software, to documents, art, scientific discoveries and even certain patents. Copyleft software licenses are considered ''protective'' or ''reciprocal'' in contrast with permissive free software licenses, and require that information necessary for reproducing and modifying the work must be made available to recipients of the software program, which are often distributed as binary executables. This information is most commonly in the form of source code files, which usually contain a copy of the license terms and acknowledge the author ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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