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List Of Open-source Software For Mathematics
This is a list of open-source software to be used for high-order mathematical calculations. This software has played an important role in the field of mathematics. Open-source software in mathematics has become pivotal in education because of the high cost of textbooks. Computer algebra systems A computer algebra system is a type of software set that is used in manipulation of mathematical formulae. The principal objective of a computer algebra system is to systematize monotonous and sometimes problematic algebraic manipulation tasks. The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations. Computer algebra system often include facilities for graphing equations and provide a programming language for the us ... [...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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algebra System
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of " computer algebra" or " symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials. Computer algebra systems may be divided into two classes: specialized and general-purpose. The specialized ones are devoted to a specific part of mathematics, such as number theory, group theory, or teaching of elementary mathematics. General-purpose computer algebra systems aim to be useful to a user working in any scientific field that requires manipulation of mathematical expressions. To be useful, a general-purpose computer algebra system must include various features such as: *a user interface ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathics
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 who ... [...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] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathematics), modules, vector spaces, lattice (order), lattices, and algebra over a field, algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variable (mathematics), variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form category (mathematics), mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RWTH Aachen University
RWTH Aachen University (), also known as North Rhine-Westphalia Technical University of Aachen, Rhine-Westphalia Technical University of Aachen, Technical University of Aachen, University of Aachen, or ''Rheinisch-Westfälische Technische Hochschule Aachen'', is a German public research university located in Aachen, North Rhine-Westphalia, Germany. With more than 47,000 students enrolled in 144 study programs, it is the largest technical university in Germany. In 2018, the university was ranked 31st in the world university rankings in the field of engineering and technology, and 36th world-wide in the category of natural sciences.Daten & Fakten – RWTH AACHEN UNIVERSITY – Deutsch Rwth-aachen.de (12 December 2011). Retrieved on 2013-09-18. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GAP (software)
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomials
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry. Etymology The word ''polynomial'' joi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CoCoA
Cocoa may refer to: Chocolate * Chocolate * ''Theobroma cacao'', the cocoa tree * Cocoa bean, seed of ''Theobroma cacao'' * Chocolate liquor, or cocoa liquor, pure, liquid chocolate extracted from the cocoa bean, including both cocoa butter and cocoa solids * Cocoa butter, a pale yellow, edible fat extracted from the cocoa bean * Cocoa solids or cocoa powder * Hot chocolate, also called hot cocoa * Cocoa Mountain, a gourmet chocolate enterprise in Durness in the North West Highlands of Scotland * Cocoa Processing Company, a Ghanaian company Computing * Cocoa (API), an API and programming environment for macOS * Cocoa Touch, an API and programming environment for iOS, iPadOS, watchOS and tvOS * CoCoA, a computer algebra system * COCOA (digital humanities), an early FORTRAN program for generating concordances and word counts from natural language texts * Stagecast Creator, formerly Cocoa, a language developed by Apple to teach programming to children Given name * Cocoa Brown ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves ( wave–particle duality); and there ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physicists
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, through biological physics, to cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: experimental physicists who specialize in the observation of natural phenomena and the development and analysis of experiments, and theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies (also known as applied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
