Welcome to brocoli’s documentation!

BRoCoLi - LImit ROots of COxeter groups (eternal Beta version)

This is a package to experiment with limit roots and related objects of geometric representations of Coxeter groups.

With this package you can compute the following:

  • Roots
  • Weights
  • Elements of the group (as matrices)
  • Bilinear form and its signature

For Lorentzian Coxeter groups:

  • Elliptic, Parabolic and Hyperbolic elements
  • limit roots coming from parabolic and hyperbolic elements

You can also visualize:

  • Affine positive cone
  • Isotropic cone
  • roots
  • weights
  • limit roots
  • Tits cone

For rank 3 Coxeter groups, you can obtain tikzpicture of the above structures.

Indices and tables