Adding upper and lower Bruhat cones of M. Dyer to sage/combinat/root_system/reflection_group_real.py #32669
Description
To a pair of elements x,y in a Coxeter group W one can associate two polyhedral cones. The 'upper bruhat cone' generated by all roots beta such that s_beta * x covers x and s_beta * x <= y and similarly the 'lower bruhat cone' generated by all beta sucht that y covers s_beta * y and x <= s_beta * y .
These cones were used in https://eudml.org/doc/174610 and https://arxiv.org/abs/2103.03715
CC: @tscrim
Component: combinatorics
Keywords: Coxeter groups, reflection groups, Bruhat order, Bruhat cones
Author: Dennis Jahn
Branch/Commit: 648e634
Reviewer: Frédéric Chapoton, Travis Scrimshaw
Issue created by migration from https://trac.sagemath.org/ticket/32669