fixed construction normal cone

src/sage/geometry/polyhedron/face.py

@@ -701,33 +701,61 @@ def normal_cone(self, direction='outer'):
             ....:     nc = v.normal_cone().rays_list()
             ....:     print("{} has outer normal cone spanned by {}".format(vect,nc))
             ....:
-            (-2, -2) has outer normal cone spanned by [[-1, 0], [0, -1]]
-            (-2, 2) has outer normal cone spanned by [[-1, 0], [0, 1]]
+            (2, 1) has outer normal cone spanned by [[1, 0], [1, 1]]
             (1, 2) has outer normal cone spanned by [[0, 1], [1, 1]]
             (2, -2) has outer normal cone spanned by [[0, -1], [1, 0]]
-            (2, 1) has outer normal cone spanned by [[1, 0], [1, 1]]
+            (-2, -2) has outer normal cone spanned by [[-1, 0], [0, -1]]
+            (-2, 2) has outer normal cone spanned by [[-1, 0], [0, 1]]
 
             sage: for v in p.faces(0):
             ....:     vect = v.vertices()[0].vector()
             ....:     nc = v.normal_cone(direction='inner').rays_list()
             ....:     print("{} has inner normal cone spanned by {}".format(vect,nc))
             ....:
-            (-2, -2) has inner  normal cone spanned by [[0, 1], [1, 0]]
-            (-2, 2) has inner normal cone spanned by [[0, -1], [1, 0]]
+            (2, 1) has inner normal cone spanned by [[-1, -1], [-1, 0]]
             (1, 2) has inner normal cone spanned by [[-1, -1], [0, -1]]
             (2, -2) has inner normal cone spanned by [[-1, 0], [0, 1]]
-            (2, 1) has inner normal cone spanned by [[-1, -1], [-1, 0]]
+            (-2, -2) has inner normal cone spanned by [[0, 1], [1, 0]]
+            (-2, 2) has inner normal cone spanned by [[0, -1], [1, 0]]
 
-        """
-        if direction == 'outer':
-            normal_vectors = [-facet.A() for facet in self.ambient_Hrepresentation()]
-        elif direction == 'inner':
-            normal_vectors = [facet.A() for facet in self.ambient_Hrepresentation()]
-        else:
+        The function works for polytopes that are not full-dimensional::
+
+            sage: p = polytopes.permutahedron(3)
+            sage: f1 = p.faces(0)[0]
+            sage: f2 = p.faces(1)[0]
+            sage: f3 = p.faces(2)[0]
+            sage: f1.normal_cone()
+            A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 1 vertex, 2 rays, 1 line
+            sage: f2.normal_cone()
+            A 2-dimensional polyhedron in ZZ^3 defined as the convex hull of 1 vertex, 1 ray, 1 line
+            sage: f3.normal_cone()
+            A 0-dimensional polyhedron in ZZ^3 defined as the convex hull of 1 vertex
+
+        Normal cones are only defined for non-empty faces::
+
+            sage: f0 = p.faces(-1)[0]
+            sage: f0.normal_cone()
+            Traceback (most recent call last):
+            ...
+            ValueError: the empty face does not have a normal cone
+        """
+        if self.dim() == -1:
+            raise ValueError("the empty face does not have a normal cone")
+        elif direction not in ['outer','inner']:
             raise ValueError("the direction should be either 'outer' or 'inner'")
+        rays = []
+        lines = []
+        for facet in self.ambient_Hrepresentation():
+            if facet.is_equation():
+                lines += [facet.A()]
+            elif direction == 'outer':
+                rays += [-facet.A()]
+            else:  # 'inner'
+                rays += [facet.A()]
         parent = self.polyhedron().parent()
         origin = parent.zero().vertices()[0].vector()
-        return parent.element_class(parent,[[origin], normal_vectors, []], None)
+        return parent.element_class(parent, [[origin], rays, lines], None)
+
 
 def combinatorial_face_to_polyhedral_face(polyhedron, combinatorial_face):
     r"""