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
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. nonprofit, 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]
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.
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.
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.
