## Section: Application Domains

### Computer Algebra Systems

Some of our software libraries are being used by computer algebra systems. Most of those libraries are free software, with a license that allows proprietary systems to link them. This gives us a maximal visibility, with a large number of users.

#### Magma

Magma is a very large computational algebra package. It provides a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatorial, and geometric objects. It is developed in Sydney, by the team around John Cannon. It is non-commercial (in the sense that its goal is not to make profit), but is not freely distributed and is not open-source.

Several members of the team have visited Sydney — several years ago — to contribute to the development of Magma, by implementing their algorithms or helping in integrating their software. Our link to Magma exists also via the libraries it uses: it currently links GNU MPFR and GNU MPC for its floating-point calculations, and links GMP-ECM as part of its factorization suite.

#### Pari/GP

Pari/GP is a computational number theory system that is composed of a C library and an interpreter on top of it. It is developed in Bordeaux, where Karim Belabas from the Lfant project-team is the main maintainer. Its license is GPL. Although we do not directly contribute to this package, we have good contact with the developers.

#### Sage

Sage is a fairly large scale and open-source computer algebra system written in Python. Sage aggregates a large amount of existing free software, aiming at selecting the fastest free software package for each given task. The motto of Sage is that instead of “reinventing the wheel” all the time, Sage is “building the car”. To date, Sage links GNU MPFR , GMP-ECM, and GNU MPC as standard packages.