Magma is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structuremagma. It runs on Unix-likeoperating systems, as well as Windows.
Developer(s) | Computational Algebra Group, School of Mathematics and Statistics, University of Sydney |
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Stable release | |
Operating system | Cross-platform |
Type | Computer algebra system |
License | Cost recovery (non-commercial proprietary) |
Website | magma.maths.usyd.edu.au |
As a general rule, ongoing application costs are about 40 percent to 60 percent of the original development cost for each year in an application's life cycle. Sound like a lot?
Introduction[edit]
Magma is produced and distributed by the Computational Algebra Group within the School of Mathematics and Statistics at the University of Sydney.
In late 2006, the book Discovering Mathematics with Magma was published by Springer as volume 19 of the Algorithms and Computations in Mathematics series.[3]
The Magma system is used extensively within pure mathematics. The Computational Algebra Group maintain a list of publications that cite Magma, and as of 2010 there are about 2600 citations, mostly in pure mathematics, but also including papers from areas as diverse as economics and geophysics.[4]
History[edit]
The predecessor of the Magma system was named Cayley (1982–1993), after Arthur Cayley.
Magma was officially released in August 1993 (version 1.0). Version 2.0 of Magma was released in June 1996 and subsequent versions of 2.X have been released approximately once per year.
In 2013, the Computational Algebra Group finalized an agreement with the Simons Foundation, whereby the Simons Foundation will underwrite all costs of providing Magma to all U.S. non-profit, non-governmental scientific research or educational institutions. All students, researchers and faculty associated with a participating institution will be able to access Magma for free, through that institution.[5]
Mathematical areas covered by the system[edit]
- Magma includes permutation, matrix, finitely presented, soluble, abelian (finite or infinite), polycyclic, braid and straight-line programgroups. Several databases of groups are also included.
- Magma contains asymptotically fast algorithms for all fundamental integer and polynomial operations, such as the Schönhage–Strassen algorithm for fast multiplication of integers and polynomials. Integer factorization algorithms include the Elliptic Curve Method, the Quadratic sieve and the Number field sieve.
- Magma includes the KANT computer algebra system for comprehensive computations in algebraic number fields. A special type also allows one to compute in the algebraic closure of a field.
- Module theory and linear algebra
- Magma contains asymptotically fast algorithms for all fundamental dense matrix operations, such as Strassen multiplication.
- Magma contains the structured Gaussian elimination and Lanczos algorithms for reducing sparse systems which arise in index calculus methods, while Magma uses Markowitz pivoting for several other sparse linear algebra problems.
- Lattices and the LLL algorithm
- Magma has a provable implementation of fpLLL,[6] which is an LLL algorithm for integer matrices which uses floating point numbers for the Gram–Schmidt coefficients, but such that the result is rigorously proven to be LLL-reduced.
- Commutative algebra and Gröbner bases
- Magma has an efficient implementation of the Faugère F4 algorithm for computing Gröbner bases.
- Magma has extensive tools for computing in representation theory, including the computation of character tables of finite groups and the Meataxe algorithm.
- Magma has a type for invariant rings of finite groups, for which one can primary, secondary and fundamental invariants, and compute with the module structure.
See also[edit]
References[edit]
- ^'Summary of New Features in Magma V2.24'.
- ^'Change Log for V2.24-6'.
- ^'Discovering Mathematics with Magma'.
- ^'Published Research Citing Magma'.
- ^http://magma.maths.usyd.edu.au/magma/simons_details
- ^Cannon J. (July 2006). 'Magma 2.13 release notes'.
External links[edit]
- Magma's High Performance for computing Gröbner Bases (2004)
Limited liability company (Gesellschaft mit beschränkter Haftung) | |
Founded | 1988 |
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Headquarters | Aachen, North Rhine-Westphalia , |
Key people | Dr.-Ing. Erwin Flender |
Products | MAGMASOFT® and MAGMA5 - Software for the simulation of casting processes |
200 | |
Website | http://www.magmasoft.de http://www.magmasoft.com |
MAGMA Gießereitechnologie GmbH is a developer and supplier of software for casting process simulation. The company was founded in 1988 and has its Headquarters in Aachen, Germany. MAGMA’s product and service portfolio includes simulation software MAGMASOFT, with the newest release MAGMA5, as well as engineering services for casting design and optimisation. The software is used world-wide by foundries, casting buyers and designers, especially for the optimization of cast components in automotive and heavy industry applications. German newspaper Süddeutsche Zeitung cites MAGMA amongst the global market leaders for simulation software for casting processes.[1]
Worldwide, MAGMA employs more than 200 people in software development, support, marketing, and administration, of which 90 are in Aachen. The company also has offices and subsidiaries in the United States, Singapore, Brazil, Korea, Turkey, India, China, and the Czech Republic.
MAGMA5[edit]
MAGMA5 is the standard solution for the simulation of casting processes. The software stands for the prediction of the entire casting component quality and process chain by providing a better understanding of mold filling, solidification and cooling and allows the quantitative prediction of mechanical properties, thermal stresses and distortions of the resulting castings. Simulation accurately describes a cast component’s quality up-front before production starts and the casting methoding can be designed with respect to the required component properties. This not only results in a reduction in pre-production sampling as the precise layout of the complete casting system leads to energy, material, and tooling savings.
MAGMA5 consists of a base module and a set of additional modules that cover all steps of the casting production. The range of application of MAGMA solutions comprises all cast alloys, from cast iron to aluminum sand casting, permanent mold and die casting up to large steel castings. The software supports the user in the modeling of the component, the determination of melting practice and casting methoding through to model and mold making, heat treatment, and finishing. This saves costs consequently along the entire manufacturing route.
External links[edit]
References[edit]
- ^[Süddeutsche Zeitung]. Ausgabe vom 26.11.2009.