merged two methods together to one method with a flag, rearranged stu…

…ff for the docmentation

src/sage/combinat/root_system/reflection_group_real.py

@@ -707,47 +707,43 @@ def simple_root_index(self, i):
         """
         return self._index_set_inverse[i]
 
-    def bruhat_upper_cone(self, x, y):
+    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``, ``s_beta`` ``x`` covers ``x``, and 
-        ``x`` <= ``s_beta`` ``x`` <= ``y``
+        Returns the polyhedral cone generated by the set of positive roots ``beta`` 
+        where ``s_beta`` is the reflection corresponding to ``beta`` and:
         
-        EXAMPLES::
+        For ``side`` = ``'upper'``: ``s_beta`` ``x`` covers ``x`` and ``x`` <= ``s_beta`` ``x`` <= ``y``.
         
-            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_upper_cone(x,y)                              # optional - gap3
-            A 2-dimensional polyhedron in ZZ^2 defined as the convex hull of 1 vertex and 2 rays
-        """
-        roots = [self.reflection_to_positive_root(x*r*x.inverse()) for z, r in x.bruhat_upper_covers_reflections() if z.bruhat_le(y)]
-        from sage.geometry.polyhedron.constructor import Polyhedron
-        if self.is_crystallographic():
-            return Polyhedron(rays = roots, ambient_dim = self.rank())
-        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(rays = roots, ambient_dim = self.rank(), base_ring = RDF)
+        For ``side`` = ``'lower'``: ``y`` covers ``s_beta`` ``y`` and ``x`` <= ``s_beta`` ``y`` <= ``y``.
+        
+        
+        INPUT:
 
-    def bruhat_lower_cone(self, x, y):
-        r"""
-        Returns the polyhedral cone generated by the set of positive roots 
-        ``beta`` where ``s_beta`` is the reflection corresponding to 
-        ``beta``, ``y`` covers ``s_beta`` ``y``, and 
-        ``x`` <= ``s_beta`` ``y`` <= ``y``
+        - ``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_lower_cone(x,y)                              # 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
+            sage: W.bruhat_cone(x, y, side = 'lower')                   # optional - gap3
+            A 6-dimensional polyhedron in ZZ^6 defined as the convex hull of 1 vertex and 6 rays
         """
-        roots = [self.reflection_to_positive_root(y*r*y.inverse()) for z, r in y.bruhat_lower_covers_reflections() if x.bruhat_le(z)]
+        if side == 'upper':
+            roots = [self.reflection_to_positive_root(x*r*x.inverse()) for z, r in x.bruhat_upper_covers_reflections() if z.bruhat_le(y)]
+        elif side == 'lower':
+            roots = [self.reflection_to_positive_root(y*r*y.inverse()) for z, r in y.bruhat_lower_covers_reflections() if x.bruhat_le(z)]
+        else:
+            raise ValueError("side must be either 'upper' or 'lower'")
         from sage.geometry.polyhedron.constructor import Polyhedron
         if self.is_crystallographic():
             return Polyhedron(rays = roots, ambient_dim = self.rank())