This package deals with limits roots of infinite Coxeter groups and related structures. It allows to compute several related objects such as matrices representing the elements, roots, weights, and obtain properties of the representation. Further, it allows to visualize the isotropic cone, the roots, the weights, the limit roots, and the Tits cone in the affine space spanned by the simple roots.
This code's ultimate goal is to be merged into the Sagemath software. Some tickets related to this project:
You can find the complete documentation at https://jplab.github.io/brocoli/doc/html/
Download the tar ball source and run the following command in the brocoli folder:
$ sage -pip install --upgrade --no-index -v .
TODO: distribute on PyPI.
You can uninstall the brocoli package as follows, once in the brocoli folder:
$ sage -pip uninstall .
Once the package is installed, you can use it on Sage with:
sage: from brocoli import * sage: M1 = CoxeterMatrix([[1,4,4],[4,1,4],[4,4,1]]) sage: GR1 = GeometricRepresentationCoxeterGroup(M1);GR1 Geometric representation of a Coxeter group of rank 3 with Coxeter matrix [1 4 4] [4 1 4] [4 4 1]
The complete documentation is available at https://jplab.github.io/brocoli/doc/html
The html and pdf versions are also available in the docs/build
folder.