SimpLie is a simple program for Lie algebra. It has been specifically written for level decompositions of infinite-dimensional Lie algebras, but it is not limited to that task. Its current features are:

• Calculation of Lie algebra properties based on Dynkin diagrams:
1. Type
2. Dimension
3. Rank
4. (Dual) Coxeter labels and numbers.
5. Roots
• Calculation of highest weight representations.
• Level decompositions.
• Visualization of root systems by means of Coxeter projections and Hasse diagrams.

On the user end, it has the following benefits:

• A graphical user interface, making it easy to use.
• Cross-platform (written in Java).
• LaTeX & EPS export capability.
• Saving and loading of calculation results (root systems).

Here is the root system of E10 as visualized by SimpLie: