CharLiePy

CharLiePy (Characters of Lie type groups in Python) is a python package which implements algorithms to carry out symbolic computations with Coxeter groups and related mathematical structures. The ultimate goal of CharLiePy is to develop a custom platform for carrying out computations with finite reductive groups and their characters. It may be considered as a Python version of the original CHEVIE package which was written in GAP3 and MAPLE. This was inspired by the Python package PyCox [Gec12] developed by Meinolf Geck. The development version of CHEVIE is currently maintained by Jean Michel.

CharLiePy is a mix of high level Python code and handwritten C extensions. For instance, following GAP, permutations are implemented as arrays in C to permit faster caluclations than are possible in direct Python. By building from the ground up it is possible to make design choices that are specifically tailored to working with finite reductive groups. For instance, unlike GAP, permutations on less than 255 points are stored as 8-bit integers. This saves memory when working with the Weyl group of \(\mathsf{E}_8\), which has a natural permutation representation on 240 points.

The focus of CharLiePy is narrower than that of CHEVIE, in that we do not anticipate working with the more general class of complex reflection groups.

Why Python?

One of the original reasons for choosing Python as the language for CharLiePy is the success of the Sage project. In particular, CharLiePy may be used in Sage by simply importing CharLiePy in an interactive session. Here are some additional reasons:

  • Python is very popular with the wider scientific community (see for instance the SciPy project).
  • It is easy to encorporate C extensions into Python, thus allowing one to obtain speed advantages when needed.
  • As Python is a widely used modern programming language, anyone learning to use CharLiePy for research will simultaneously gain a useful transferable skill.
  • The Python language is syntactically similar to the GAP3 language, on which the original CHEVIE package was based. Thus it should not be difficult for people to switch between the two languages.

Referencing

Coxeter Groups and Cosets