Welcome to brocoli’s documentation!¶

Contents:

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.