Trac #29223: Pickle cached value of volume and f-vector

Volume, f-vector and Ehrhart polynomial of polyhedra can be hard to
compute, but take little memory when saving.

So we pickle those values, e.g.

{{{#!diff
+    @cached_method(do_pickle=True)
-    @cached_method
     def f_vector(self):
}}}

URL: https://trac.sagemath.org/29223
Reported by: gh-kliem
Ticket author(s): Jonathan Kliem
Reviewer(s): Laith Rastanawi

src/sage/geometry/polyhedron/base.py

@@ -5946,7 +5946,7 @@ def facets(self):
         """
         return self.faces(self.dimension()-1)
 
-    @cached_method
+    @cached_method(do_pickle=True)
     def f_vector(self):
         r"""
         Return the f-vector.
@@ -5996,6 +5996,15 @@ def f_vector(self):
 
             sage: P.f_vector().is_immutable()
             True
+
+        The cache of the f-vector is being pickled::
+
+            sage: P = polytopes.cube()
+            sage: P.f_vector()
+            (1, 8, 12, 6, 1)
+            sage: Q = loads(dumps(P))
+            sage: Q.f_vector.is_in_cache()
+            True
         """
         return self.combinatorial_polyhedron().f_vector()
 
@@ -6827,7 +6836,7 @@ def _volume_normaliz(self, measure='induced'):
         """
         raise TypeError("the backend should be normaliz")
 
-    @cached_method
+    @cached_method(do_pickle=True)
     def volume(self, measure='ambient', engine='auto', **kwds):
         """
         Return the volume of the polytope.
@@ -6999,6 +7008,17 @@ def volume(self, measure='ambient', engine='auto', **kwds):
             The empty polyhedron in ZZ^0
             sage: P.volume()
             0
+
+        TESTS:
+
+        The cache of the volume is being pickled::
+
+            sage: P = polytopes.cube()
+            sage: P.volume()
+            8
+            sage: Q = loads(dumps(P))
+            sage: Q.volume.is_in_cache()
+            True
         """
         from sage.features import FeatureNotPresentError, PythonModule
         if measure == 'induced_rational' and engine not in ['auto', 'latte', 'normaliz']:

src/sage/geometry/polyhedron/base_ZZ.py

@@ -290,7 +290,7 @@ def _ehrhart_polynomial_normaliz(self, variable='t'):
         """
         raise TypeError("The polyhedron's backend should be 'normaliz'")
 
-    @cached_method
+    @cached_method(do_pickle=True)
     def ehrhart_polynomial(self, engine=None, variable='t', verbose=False, dual=None,
             irrational_primal=None, irrational_all_primal=None, maxdet=None,
             no_decomposition=None, compute_vertex_cones=None, smith_form=None,
@@ -439,6 +439,17 @@ def ehrhart_polynomial(self, engine=None, variable='t', verbose=False, dual=None
             Traceback (most recent call last):
             ...
             ValueError: Ehrhart polynomial only defined for compact polyhedra
+
+        TESTS:
+
+        The cache of the Ehrhart polynomial is being pickled::
+
+            sage: P = polytopes.cube()
+            sage: P.ehrhart_polynomial()  # optional - latte_int
+            8*t^3 + 12*t^2 + 6*t + 1
+            sage: Q = loads(dumps(P))
+            sage: Q.ehrhart_polynomial.is_in_cache()  # optional - latte_int
+            True
         """
         if self.is_empty():
             from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing