Trac #19244: Broken doctest in src/sage/categories/fields.py

The following doctest from #14058 breaks sometimes. I have seen it
happen twice, but it's hard to reproduce:
{{{
sage -t --long src/sage/categories/fields.py
**********************************************************************
File "src/sage/categories/fields.py", line 104, in
sage.categories.fields.Fields.__contains__
Failed example:
    len([X for X in gc.get_objects() if isinstance(X,
sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]) - n
Expected:
    0
Got:
    -1
**********************************************************************
}}}

URL: http://trac.sagemath.org/19244
Reported by: jdemeyer
Ticket author(s): Simon King
Reviewer(s): Jeroen Demeyer

src/sage/categories/fields.py

@@ -91,14 +91,27 @@ def __contains__(self, x):
             sage: GR in Fields()
             True
 
-        The following tests against a memory leak fixed in :trac:`13370`::
+        The following tests against a memory leak fixed in :trac:`13370`. In order
+        to prevent non-deterministic deallocation of fields that have been created
+        in other doctests, we introduced a strong reference to all previously created
+        uncollected objects in :trac:`19244`. ::
 
             sage: import gc
             sage: _ = gc.collect()
-            sage: n = len([X for X in gc.get_objects() if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)])
+            sage: permstore = [X for X in gc.get_objects() if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]
+            sage: n = len(permstore)
             sage: for i in prime_range(100):
             ....:     R = ZZ.quotient(i)
             ....:     t = R in Fields()
+
+        First, we show that there are now more quotient rings in cache than before::
+
+            sage: len([X for X in gc.get_objects() if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]) > n
+            True
+
+        When we delete the last quotient ring created in the loop and then do a garbage
+        collection, all newly created rings vanish::
+
             sage: del R
             sage: _ = gc.collect()
             sage: len([X for X in gc.get_objects() if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]) - n