tuple -> generator

src/sage/geometry/polyhedron/base.py

@@ -1508,50 +1508,50 @@ def Hrepresentation_str(self, separator='\n', latex=False, style='>=', align=Non
             sage: P = polytopes.permutahedron(3)
             sage: print(P.Hrepresentation_str())
             x0 + x1 + x2 ==  6
-                -x1 - x2 >= -5
-                     -x2 >= -3
-                     -x1 >= -3
+                 x0 + x1 >=  3
+                -x0 - x1 >= -5
                       x1 >=  1
-                 x1 + x2 >=  3
-                      x2 >=  1
+                     -x0 >= -3
+                      x0 >=  1
+                     -x1 >= -3
 
             sage: print(P.Hrepresentation_str(style='<='))
             -x0 - x1 - x2 == -6
-                  x1 + x2 <=  5
-                       x2 <=  3
-                       x1 <=  3
+                 -x0 - x1 <= -3
+                  x0 + x1 <=  5
                       -x1 <= -1
-                 -x1 - x2 <= -3
-                      -x2 <= -1
+                       x0 <=  3
+                      -x0 <= -1
+                       x1 <=  3
 
             sage: print(P.Hrepresentation_str(style='positive'))
             x0 + x1 + x2 == 6
-                       5 >= x1 + x2
-                       3 >= x2
-                       3 >= x1
+                 x0 + x1 >= 3
+                       5 >= x0 + x1
                       x1 >= 1
-                 x1 + x2 >= 3
-                      x2 >= 1
+                       3 >= x0
+                      x0 >= 1
+                       3 >= x1
 
             sage: print(P.Hrepresentation_str(latex=True))
             \begin{array}{rcl}
             x_{0} + x_{1} + x_{2} & =    &  6 \\
-                   -x_{1} - x_{2} & \geq & -5 \\
-                           -x_{2} & \geq & -3 \\
-                           -x_{1} & \geq & -3 \\
+                    x_{0} + x_{1} & \geq &  3 \\
+                   -x_{0} - x_{1} & \geq & -5 \\
                             x_{1} & \geq &  1 \\
-                    x_{1} + x_{2} & \geq &  3 \\
-                            x_{2} & \geq &  1
+                           -x_{0} & \geq & -3 \\
+                            x_{0} & \geq &  1 \\
+                           -x_{1} & \geq & -3
             \end{array}
 
             sage: print(P.Hrepresentation_str(align=False))
             x0 + x1 + x2 == 6
-            -x1 - x2 >= -5
-            -x2 >= -3
-            -x1 >= -3
+            x0 + x1 >= 3
+            -x0 - x1 >= -5
             x1 >= 1
-            x1 + x2 >= 3
-            x2 >= 1
+            -x0 >= -3
+            x0 >= 1
+            -x1 >= -3
 
             sage: c = polytopes.cube()
             sage: c.Hrepresentation_str(separator=', ', style='positive')

src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx

@@ -660,12 +660,12 @@ cdef class CombinatorialPolyhedron(SageObject):
             sage: C = CombinatorialPolyhedron(P)
             sage: C.Hrepresentation()
             (An equation (1, 1, 1) x - 6 == 0,
-             An inequality (0, -1, -1) x + 5 >= 0,
-             An inequality (0, 0, -1) x + 3 >= 0,
-             An inequality (0, -1, 0) x + 3 >= 0,
+             An inequality (1, 1, 0) x - 3 >= 0,
+             An inequality (-1, -1, 0) x + 5 >= 0,
              An inequality (0, 1, 0) x - 1 >= 0,
-             An inequality (0, 1, 1) x - 3 >= 0,
-             An inequality (0, 0, 1) x - 1 >= 0)
+             An inequality (-1, 0, 0) x + 3 >= 0,
+             An inequality (1, 0, 0) x - 1 >= 0,
+             An inequality (0, -1, 0) x + 3 >= 0)
 
             sage: points = [(1,0,0), (0,1,0), (0,0,1),
             ....: (-1,0,0), (0,-1,0), (0,0,-1)]
@@ -1223,10 +1223,10 @@ cdef class CombinatorialPolyhedron(SageObject):
             sage: P = polytopes.permutahedron(2)
             sage: C = CombinatorialPolyhedron(P)
             sage: C.ridges()
-            ((An inequality (0, -1) x + 2 >= 0, An inequality (0, 1) x - 1 >= 0),)
+            ((An inequality (1, 0) x - 1 >= 0, An inequality (-1, 0) x + 2 >= 0),)
             sage: C.ridges(add_equalities=True)
-            (((An inequality (0, -1) x + 2 >= 0, An equation (1, 1) x - 3 == 0),
-              (An inequality (0, 1) x - 1 >= 0, An equation (1, 1) x - 3 == 0)),)
+            (((An inequality (1, 0) x - 1 >= 0, An equation (1, 1) x - 3 == 0),
+              (An inequality (-1, 0) x + 2 >= 0, An equation (1, 1) x - 3 == 0)),)
 
             sage: P = polytopes.cyclic_polytope(4,5)
             sage: C = CombinatorialPolyhedron(P)

src/sage/geometry/polyhedron/library.py

@@ -2535,7 +2535,7 @@ def permutahedron(self, n, project=False, backend=None):
             sage: assert P == Polyhedron(P.vertices())
             sage: assert P == Polyhedron(ieqs=P.inequalities(), eqns=P.equations())
         """
-        verts = tuple(itertools.permutations(range(1, n + 1)))
+        verts = itertools.permutations(range(1, n + 1))
         if project:
             verts = project_points(*verts)
             return Polyhedron(vertices=verts, backend=backend)
@@ -2547,15 +2547,15 @@ def tri(m):
             # Each proper `S \subset [n]` corresponds exactly to
             # a facet that minimizes the coordinates in `S`.
             # The minimal sum for `m` coordinates is `(m*(m+1))/2`.
-            ieqs = tuple((-tri(sum(x)),) + x
-                         for x in itertools.product([0,1], repeat=n)
-                         if 0 < sum(x) < n)
+            ieqs = ((-tri(sum(x)),) + x
+                    for x in itertools.product([0,1], repeat=n)
+                    if 0 < sum(x) < n)
 
             # Adding the defining equality.
             eqns = ((-tri(n),) + tuple(1 for _ in range(n)),)
 
             return parent([verts, [], []], [ieqs, eqns],
-                          Vrep_minimal=True, Hrep_minimal=True)
+                          Vrep_minimal=True, Hrep_minimal=True, pref_rep="Hrep")
 
 
     def generalized_permutahedron(self, coxeter_type, point=None, exact=True, regular=False, backend=None):