Coxeter is a computer program for the study of combinatorial aspects of Coxeter
group theory, particularly those related to the Bruhat ordering and
Kazhdan-Lusztig polynomials.

 The main capabilities of the program are the following :

    Reduced expression and normal form computations;
    Bruhat ordering;
    Ordinary Kazhdan-Lusztig polynomials;
    Kazhdan-Lusztig polynomials with unequal parameters;
    Inverse Kazhdan-Lusztig polynomials;
    Cells and W-graphs.

Note: this port is specially crafted to be used with SageMath, with patches from
Sage.

See also: https://github.com/tscrim/coxeter