normalizing for rational input, when converting polyhedra to RDF

src/sage/geometry/polyhedron/constructor.py

@@ -175,8 +175,8 @@
 
     sage: triangle = Polyhedron([(0,0), (1,0), (1/2, sqrt(3)/2)], base_ring=AA)
     sage: triangle.Hrepresentation()
-    (An inequality (-1, -0.5773502691896258?) x + 1 >= 0, 
-     An inequality (1, -0.5773502691896258?) x + 0 >= 0, 
+    (An inequality (-1, -0.5773502691896258?) x + 1 >= 0,
+     An inequality (1, -0.5773502691896258?) x + 0 >= 0,
      An inequality (0, 1.154700538379252?) x + 0 >= 0)
 
 Without specifying the ``base_ring``, the ``sqrt(3)`` would be a
@@ -196,7 +196,7 @@
 
     sage: K.<sqrt3> = NumberField(x^2-3)
     sage: Polyhedron([(0,0), (1,0), (1/2, sqrt3/2)])
-    A 2-dimensional polyhedron in (Number Field in sqrt3 with defining 
+    A 2-dimensional polyhedron in (Number Field in sqrt3 with defining
     polynomial x^2 - 3)^2 defined as the convex hull of 3 vertices
 
 Base classes

src/sage/geometry/polyhedron/parent.py

@@ -441,18 +441,36 @@ def _element_constructor_(self, *args, **kwds):
         """
         nargs = len(args)
         convert = kwds.pop('convert', True)
+        def convert_base_ring(lstlst):
+            return [ [self.base_ring()(x) for x in lst] for lst in lstlst]
+        # renormalize before converting when going from QQ to RDF, see trac 21270
+        def convert_base_ring_Hrep(lstlst):
+            newlstlst = []
+            for lst in lstlst:
+                if all(c in QQ for c in lst):
+                    m=max(abs(w) for w in lst)
+                    if m == 0:
+                        newlstlst.append(lst)
+                    else:
+                        newlstlst.append([q/m for q in lst])
+                else:
+                    newlstlst.append(lst)
+            return convert_base_ring(newlstlst)
         if nargs==2:
             Vrep, Hrep = args
-            def convert_base_ring(lstlst):
-                return [ [self.base_ring()(x) for x in lst] for lst in lstlst]
             if convert and Hrep:
-                Hrep = [convert_base_ring(_) for _ in Hrep]
+                if self.base_ring==RDF:
+                    Hrep = [convert_base_ring_Hrep(_) for _ in Hrep]
+                else:
+                    Hrep = [convert_base_ring(_) for _ in Hrep]
             if convert and Vrep:
                 Vrep = [convert_base_ring(_) for _ in Vrep]
             return self.element_class(self, Vrep, Hrep, **kwds)
         if nargs==1 and is_Polyhedron(args[0]):
             polyhedron = args[0]
             Hrep = [ polyhedron.inequality_generator(), polyhedron.equation_generator() ]
+            if self.base_ring()==RDF:
+                Hrep = [convert_base_ring_Hrep(_) for _ in Hrep]
             return self.element_class(self, None, Hrep, **kwds)
         if nargs==1 and args[0]==0:
             return self.zero()