Motivation

The ultimate goal of JuLie is to help finding new results in (and around) representation theory. Since there's a lot already in other computer algebra systems (like GAP, Magma, and Sage), it may seem absurd to start a new project and not simply build on the existing systems. But there is a very good reason: the programming language Julia which was introduced in 2012 (see also the Wikipedia article). The advantages of Julia—that may not all exist to such an extend in other systems—are the following:

1. Through its type system and multiple dispatch it is possible to model mathematical structures roughly in the same way you think about them abstractly (this is what I mean by "mathematically sound").
2. It is very fast and memory efficient (see the benchmarks of JuLie).
3. It has a straightforward high-level syntax that makes code easy to write and read.
4. It is open source and community-driven.
5. It is modern.

These points speak in favor of using Julia as basis for modern computer algebra and this is precisely the motivation of the OSCAR project started in 2017 (see also my overview). JuLie may be considered as a contribution to OSCAR in the field of representation theory (which in turn is another motivation for JuLie).

One "milestone" of JuLie is to implement "all" the material from (and as in) the book Introduction to Soergel bimodules by B. Elias, S. Makisumi, U. Thiel, and G. Williamson. Of course, anything else is always welcome: please contribute!