The OSCAR Computer Algebra System
2021-07-30, 13:50–14:00 (UTC), Red

We present OSCAR, an Open Source Computer Algebra Research system for abstract algebra, algebraic geometry, group theory, number theory, and more. It joins existing world class systems under a common Julia interface in the Oscar.jl package. Applications exist well beyond pure mathematics (e.g. in coding theory, cryptography, robotics, ...).

We give an overview of existing and planned capabilities. We also discuss what sets us apart from Symbolics.jl.


In this talk we present OSCAR, an Open Source Computer Algebra Research system for computations to support research in abstract algebra, algebraic geometry, group theory, number theory, and more. It builds on decades of experience by extending and integrating our four existing cornerstone systems:
- GAP - group and representation theory (via GAP.jl),
- Singular - commutative and non-commutative algebra, algebraic geometry (via Singular.jl),
- Polymake - polyhedral geometry (via Polymake.jl),
- Antic (Hecke, Nemo) - number theory.

These are joined together under a common Julia interface in the Oscar.jl package.

Applications of our computational capabilities exist well beyond pure mathematics (e.g. in coding theory, cryptography, crystallography, robotics, ...).

While OSCAR is still under heavy development, many useful features are already available, and more are in the works. We will give an overview of existing capabilities and give a preview of what will come in the future. We will also outline what sets us apart from Symbolics.jl (which has a very different scope).

The development of OSCAR is supported by the Deutsche Forschungsgemeinschaft DFG within the Collaborative Research Center TRR 195.
Outside contributions to OSCAR are highly welcome. Please talk to us:
- on our own Slack (use this invite link, or email me if it does not work)
- on the Julia Slack in #oscar or #algebra
- via our mailing list, join at https://mail.mathematik.uni-kl.de/mailman/listinfo/oscar-dev
- via issues and PRs on our various GitHub repositories.

Additional information can be found on our homepage, https://oscar.computeralgebra.de.

See also: Slides

Since April 2020 I am full professor for Algorithmic Algebra and Geometry at TU Kaiserslautern, Germany. My research focuses on computer algebra, group theory and algebraic Lie theory.

Besides being one of the principal investigators on the grant behind OSCAR, and one of its developers, I am also core developer of the GAP computer algebra system for computational group theory.

Outside of mathematics, I've been involved in many open source projects over the past decades; e.g. in the distant past, I served as project leader for ScummVM as well as the Fink project, and contributed to TeXShop.

I am a professor for computational number theory at Kaiserslautern University. I a PI of the DFG (German research association) funded OSCAR project as well as a developer of both OSCAR and Hecke.