About Magma
A computer algebra system for computations in algebra, number theory, and geometry.
What is Magma?
Magma is a large, well-supported software package designed to solve computationally hard problems in algebra, number theory, geometry, and combinatorics. It provides a mathematically rigorous environment with a focus on performance and correctness across a broad range of algebraic structures.
Magma is developed and distributed by the Computational Algebra Group at the University of Sydney. It is used by researchers at universities and research institutes worldwide for both pure mathematical research and applied problems in cryptography, coding theory, and computational science.
The system covers approximately 6,500 pages of documented functionality across more than 100 mathematical areas — from permutation groups and algebraic curves to modular forms and quantum error-correcting codes. A full overview of covered areas is available on the Mathematical Areas page.
The Computational Algebra Group
The basic mission of the Computational Algebra Group is the development of computer techniques for solving symbolic problems in mathematics, with particular emphasis on the areas of algebra, number theory, and geometry. The activities extend from the design of algorithms through to the construction of computer algebra packages and languages.
The group concentrates on discrete algebraic and combinatorial structures: groups, rings, fields, modules, algebras, designs, and geometries. A particular strength is its expertise in computational methods across several major branches of mathematics.
The group provides a unique environment by bringing together mathematicians, computer scientists, and software engineers. Good algorithms require the involvement of leading researchers from the relevant areas; their efficient implementation in large integrated software systems requires sophisticated techniques from computer science.
The group holds a regular Computational Algebra Seminar and hosts approximately twenty visitors each year.
History
The Computational Algebra Group has been in existence since the early 1970s, when John Cannon and Greg Butler developed many of the standard permutation group algorithms. Starting in the late 1970s, in joint work with Charles Leedham-Green, the group commenced the design of algorithms for p-groups and soluble groups.
In the early 1970s, in conjunction with Joachim Neubüser's group in Aachen, the group developed the first publicly available software package for group theory: Group. In 1975 it commenced development of the Cayley system for group theory and related areas. Following its release in 1982, Cayley was successfully applied to a very wide variety of problems both within and outside mathematics.
A completely new system, Magma, emerged from the experience gained with Cayley. Distribution of Magma V1 commenced at the end of 1993. Since then, Magma has been cited in over 4,000 research publications and has grown to cover a broad range of mathematical areas.
A timeline of Magma conferences and workshops going back to 1984 reflects the system's long history and its impact on the research community.
Citing Magma
If you use Magma in your research, please cite the system using the standard reference. Full citation information and BibTeX entries are available on the Cite Magma page.