WG Computer Algebra

Computer algebra traditionally involves algorithms for manipulating mathematical expressions exactly. A distinction is made between algorithms for the arithmetic of so-called “basic” objects—namely, integers, polynomials, series, and matrices—for which the search for methods with costs as linear as possible is a very active area of research. This basic arithmetic forms the foundation upon which efficient algorithms can be built to solve higher-level computational problems in number theory, commutative and noncommutative algebra, differential algebra, experimental mathematics, combinatorics, cryptography, error-correcting codes, and so on.

In practice, computer algebra is available in the form of specialized software libraries, as well as through comprehensive computational environments featuring user-friendly graphical interfaces. These tools are widely used in university science programs, as well as by engineers in the private sector. Implementation challenges include issues related to high-performance computing, such as data locality, the use of vector hardware architectures, and other higher levels of parallelism.

This working group is a joint initiative with the GDR IFM.

Head: Jérémy Berthomieu, Khalil Ghorbal

Mailing list: gt-cf@gdr-ifm.fr (subscribe to the working group on myGDR to join the mailing list)