The Magma Project

While computational algebra could potentially play an important role in advanced mathematics, progress is often hindered through a lack of knowledge and skills on the part of researchers. A researcher wishing to take advantage of CA must gain an understanding of the possibilities and master an often arcane CA system. The general CA systems provide poor coverage for many of the areas which are the concern of this meeting. Thus, a user may need to employ three of four different packages in order to solve a particular problem. Each of the packages will come with a different command language further compounding the difficulties. The large investment of time needed to learn how to use the relevant system(s) often coupled with a lack of local expert advice is a severe disincentive to make use of CA techniques.

The Magma project has as its goal the creation of advanced software tools for use by researchers in algebra, number theory and geometry. This is made possible by a unique collaborative effort of a large number of mathematicians and software authors. The Magma system provides an algebraic programming language and a GUI. However, the real power comes from the integration into the system of a vast amount of highly specialized software. The Magma design provides a framework that allows the installation of externally-written implementations of algebraic algorithms in such a way that they are functionally identical to native code. In this way the user can exploit the most advanced software available for a given problem. At present some 30 externally developed programs and packages are included, and many more have yet to be installed. Those already installed include most of the PARI system, all of KANT V4, the Lenstra ECM package, the Leon PERM package and the Havas Todd-Coxeter programs. The language development and package integration are carried out by the Computational Algebra Group at Sydney University.

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