fix pickling of representation objects with backend normaliz

Author: Jonathan Kliem

src/sage/geometry/polyhedron/backend_normaliz.py

@@ -1272,12 +1272,28 @@ def __getstate__(self):
            A vertex at (0, 0, 1, 0),
            A vertex at (0, 1, 0, 0),
            A vertex at (1, 0, 0, 0)),
-          '_normaliz_field': Rational Field})
+          '_normaliz_field': Rational Field,
+          '_pickle_equations': [(-1, 1, 1, 1, 1)],
+          '_pickle_inequalities': [(0, 0, 0, 0, 1),
+           (0, 0, 0, 1, 0),
+           (0, 0, 1, 0, 0),
+           (0, 1, 0, 0, 0)],
+          '_pickle_lines': [],
+          '_pickle_rays': [],
+          '_pickle_vertices': [(0, 0, 0, 1),
+           (0, 0, 1, 0),
+           (0, 1, 0, 0),
+           (1, 0, 0, 0)]})
         """
         state = super(Polyhedron_normaliz, self).__getstate__()
         state = (state[0], state[1].copy())
         # Remove the unpicklable entries.
         del state[1]['_normaliz_cone']
+        state[1]["_pickle_vertices"] = [v._vector for v in self.vertices()]
+        state[1]["_pickle_rays"] = [v._vector for v in self.rays()]
+        state[1]["_pickle_lines"] = [v._vector for v in self.lines()]
+        state[1]["_pickle_inequalities"] = [v._vector for v in self.inequalities()]
+        state[1]["_pickle_equations"] = [v._vector for v in self.equations()]
         return state
 
     def __setstate__(self, state):
@@ -1327,16 +1343,32 @@ def __setstate__(self, state):
             sage: P == P2                                         # optional - pynormaliz
             True
         """
+        if "_pickle_vertices" in state[1]:
+            vertices = state[1].pop("_pickle_vertices")
+            rays = state[1].pop("_pickle_rays")
+            lines = state[1].pop("_pickle_lines")
+            inequalities = state[1].pop("_pickle_inequalities")
+            equations = state[1].pop("_pickle_equations")
+        else:
+            vertices = None
+
         super(Polyhedron_normaliz, self).__setstate__(state)
 
         if self.is_empty():
             # Special case to avoid.
             self._normaliz_cone = None
             return
 
+        if vertices is None:
+            vertices = self.vertices()
+            rays = self.rays()
+            lines = self.lines()
+            inequalities = self.inequalities()
+            equations = self.equations()
+
         self._normaliz_cone = \
             self._cone_from_Vrepresentation_and_Hrepresentation(
-                self.vertices(), self.rays(), self.lines(), self.inequalities(), self.equations())
+                vertices, rays, lines, inequalities, equations)
 
     def integral_hull(self):
         r"""