diff --git a/src/sage/combinat/root_system/reflection_group_real.py b/src/sage/combinat/root_system/reflection_group_real.py index 461019c5f89..2cc7fce485c 100644 --- a/src/sage/combinat/root_system/reflection_group_real.py +++ b/src/sage/combinat/root_system/reflection_group_real.py @@ -709,29 +709,27 @@ def simple_root_index(self, i): def bruhat_cone(self, x, y, side = 'upper'): r""" - Returns the polyhedral cone generated by the set of positive roots ``beta`` - where ``s_beta`` is the reflection corresponding to ``beta`` and: - + Returns the polyhedral cone generated by the set of positive roots ``beta`` where ``s_beta`` is the reflection corresponding to ``beta`` and: + For ``side`` = ``'upper'``: ``s_beta`` ``x`` covers ``x`` and ``x`` <= ``s_beta`` ``x`` <= ``y``. - + For ``side`` = ``'lower'``: ``y`` covers ``s_beta`` ``y`` and ``x`` <= ``s_beta`` ``y`` <= ``y``. - - + INPUT: - ``side`` (default: ``'upper'``) -- must be one of the following: * ``'upper'`` - roots of reflections corresponding to atoms in the interval [``x``, ``y``] * ``'lower'`` - roots of reflections corresponding to coatoms in the interval [``x``, ``y``] - + EXAMPLES:: - + sage: W = ReflectionGroup(['A',2]) # optional - gap3 sage: x = W.from_reduced_word([1]) # optional - gap3 sage: y = W.w0 # optional - gap3 sage: W.bruhat_cone(x, y) # optional - gap3 A 2-dimensional polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 2 rays - + sage: W = ReflectionGroup(['E',6]) # optional - gap3 sage: x = W.one() # optional - gap3 sage: y = W.w0 # optional - gap3