What is Magma?
A computer algebra system for algebra, number theory, geometry, and combinatorics.
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 169 Handbook chapters of documented functionality across 23 mathematical areas — from permutation groups and algebraic curves to modular forms and quantum error-correcting codes.
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 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. It provides a unique environment bringing together mathematicians, computer scientists, and software engineers.
The group holds a regular Computational Algebra Seminar and hosts approximately twenty visitors each year.
Four Decades of Development
Foundations
John Cannon and Greg Butler developed many of the standard permutation group algorithms. In conjunction with Joachim Neubüser's group in Aachen, they developed Group — the first publicly available software package for group theory.
The Cayley System
Development of the Cayley system for group theory and related areas commenced. Starting in the late 1970s, in joint work with Charles Leedham-Green, the group began designing algorithms for p-groups and soluble groups.
Cayley Released
Following its release in 1982, Cayley was successfully applied to a very wide variety of problems both within and outside mathematics, establishing the group's reputation for high-quality computational algebra software.
Magma V1
A completely new system, Magma, emerged from the experience gained with Cayley. Distribution of Magma V1 commenced at the end of 1993, marking the beginning of the modern era of computational algebra at Sydney.
Ongoing Growth
The Computational Algebra Group's citation database records 2918 publications that use or cite Magma, and has grown to cover a broad range of mathematical areas. A timeline of Magma conferences and workshops going back to 1984 reflects its long history and research impact.
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 How to Cite page.
Citation Information