style changes as mentioned by gh-kliem in 32681

src/sage/combinat/root_system/reflection_group_real.py

@@ -707,7 +707,7 @@ def simple_root_index(self, i):
         """
         return self._index_set_inverse[i]
 
-    def bruhat_cone(self, x, y, side = 'upper'):
+    def bruhat_cone(self, x, y, side='upper', backend='cdd'):
         r"""
         Return the polyhedral cone generated by the set of positive roots ``beta`` where ``s_beta`` is the reflection corresponding to ``beta`` and:
 
@@ -721,6 +721,8 @@ def bruhat_cone(self, x, y, side = 'upper'):
 
           * ``'upper'`` - roots of reflections corresponding to atoms in the interval [``x``, ``y``]
           * ``'lower'`` - roots of reflections corresponding to coatoms in the interval [``x``, ``y``]
+        
+        - ``backend`` -- string (default: ``'ccd'``) -- The backend to use to create the polyhedron.
 
         EXAMPLES::
 
@@ -744,12 +746,15 @@ def bruhat_cone(self, x, y, side = 'upper'):
             raise ValueError("side must be either 'upper' or 'lower'")
         from sage.geometry.polyhedron.constructor import Polyhedron
         if self.is_crystallographic():
-            return Polyhedron(vertices = [[0]*self.rank()], rays = roots, ambient_dim = self.rank())
+            return Polyhedron(vertices = [[0]*self.rank()], rays=roots, ambient_dim=self.rank(), backend=backend)
         else:
-            from warnings import warn
-            warn("Using floating point numbers for roots of unity. This might cause numerical errors!")
-            from sage.rings.real_double import RDF
-            return Polyhedron(vertices = [[0]*self.rank()], rays = roots, ambient_dim = self.rank(), base_ring = RDF)
+            if backend == 'cdd':
+                from warnings import warn
+                warn("Using floating point numbers for roots of unity. This might cause numerical errors!")
+                from sage.rings.real_double import RDF as base_ring
+            else:
+                from sage.rings.qqbar import AA as base_ring
+            return Polyhedron(vertices = [[0]*self.rank()], rays=roots, ambient_dim=self.rank(), base_ring=base_ring, backend=backend)
 
     class Element(RealReflectionGroupElement, ComplexReflectionGroup.Element):