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doc syntax
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DennisJahn committed Oct 14, 2021
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Showing 1 changed file with 7 additions and 9 deletions.
16 changes: 7 additions & 9 deletions src/sage/combinat/root_system/reflection_group_real.py
Original file line number Diff line number Diff line change
Expand Up @@ -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
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