Magma Computational Algebra System Home Page

Magma Computational Algebra System Home Page
Magma is a large, well-supported software package designed for computations in algebra, number theory, algebraic geometry and algebraic combinatorics. It provides a mathematically rigorous environment for defining and working with structures such as groups, rings, fields, modules, algebras, schemes, curves, graphs, designs, codes and many others. Magma also supports a number of databases designed to aid computational research in those areas of mathematics which are algebraic in nature. The overview provides a summary of Magma’s main features. One of the aims whilst developing Magma is to maintain extensive documentation describing the features of the system. This handbook is available online. The documentation section should help introduce new users to the Magma language. Magma is distributed by the Computational Algebra Group at the University of Sydney. Its development has benefited enormously from contributions made by many members of the mathematical community. We encourage all u

John D. Cook Blog

John D. Cook Blog
Suppose you have a number x between 0 and 1. You want to find a rational approximation for x, but you only want to consider fractions with denominators below a given limit. For example, suppose x = 1/e = 0.367879… Rational approximations with powers of 10 in the denominator are trivial to find: 3/10, 36/100, 367/1000, etc. But say you’re willing to have a denominator as large as 10. Could you do better than 3/10? Yes, 3/8 = 0.375 is a better approximation. What about denominators no larger than 100? Then 32/87 = 0.36781… is the best choice, much better than 36/100. How do you find the best approximations? You could do a brute force search. For example, if the maximum denominator size is N, you could try all fractions with denominators less than or equal to N. But there’s a much more efficient algorithm. The algorithm is related to the Farey sequence named after John Farey, though I don’t know whether he invented the algorithm. The idea is to start with two fractions, a/b = 0/1 and

PARI/GP Development Headquarters: computer algebra system designed for fast computations in number theory

PARI/GP Development Headquarters: computer algebra system designed for fast computations in number theory
PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves…), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computations. Originally developed by Henri Cohen and his co-workers (Université Bordeaux I, France), PARI is now under the GPL and maintained by Karim Belabas with the help of many volunteer contributors. PARI is a C library, allowing fast computations. gp is an easy-to-use interactive shell giving access to the PARI functions. GP is the name of gp’s scripting language. gp2c, the GP-to-C compiler, combines the best of both worlds by compiling GP scripts to the C language and transparently loading the resulting functions into gp. (gp2c-compiled scripts will typically r

ox.ac.uk: Nick Trefethen

ox.ac.uk: Nick Trefethen
Professor L N Trefethen FRS Professor of Numerical Analysis, Oxford University Global Distinguished Professor, New York University Fellow of Balliol College Head of Oxford’s Numerical Analysis Group Oxford University Mathematical Institute Woodstock Road Oxford OX2 6GG, UK trefethen (at) maths (dot) ox (dot) ac (dot) uk Assistant: +44 1865 615316 (Lotti Ekert) Books Essays Papers Talks Chebfun PhD students Honors Index card blog Other items

MathJax: MathJax is an open source JavaScript display engine for mathematics that works in all browsers

MathJax: MathJax is an open source JavaScript display engine for mathematics that works in all browsers
MathJax is a project of the MathJax Consortium, a joint venture of the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM) to advance mathematical and scientific content on the web. MathJax is generously supported by the MathJax Sponsors. The core of the MathJax project is the development of its state-of-the-art, open source, JavaScript platform for display of mathematics. Our key design goals are high-quality display of mathematics notation in all browsers no special browser setup required support for LaTeX, MathML and other equation markup directly in the HTML source. an extensible, modular design with a rich API for easy integration into web applications. support for accessibility, copy and paste and other rich functionality interoperability with other applications and math-aware search.

Math-Blog: Mathematics is wonderful!

Math-Blog: Mathematics is wonderful!
Math-Blog.com is dedicated to promoting the beauty of Mathematics at every level. It was started in 2007 by Antonio Cangiano (acangiano@gmail.com), a Software Developer and Technical Evangelist employed by IBM, who is very passionate about math. It began as a personal blog, but following its early success the site is now accepting external submissions and contributions by guest writers, with the long-term goal of making it a hub for those who intend to publish high quality, interesting and easy to follow mathematical articles on the Web.