Add weakref support for Basic's

This fixes sympy/sympy#8825:

    >>> import weakref
    >>> import sympy
    >>> x, y = sympy.Symbol('x'), sympy.Symbol('y')
    >>> d = weakref.WeakKeyDictionary([(x, 1), (y, 2)])
    >>> print(list(d.items()))
    [(y, 2), (x, 1)]
    >>> del x
    >>> print(list(d.items()))
    [(y, 2)]

Cache now uses WeakValueDictionary.

sympy/core/basic.py

@@ -41,7 +41,8 @@ class Basic(metaclass=ManagedProperties):
     """
     __slots__ = ['_mhash',              # hash value
                  '_args',               # arguments
-                 '_assumptions'
+                 '_assumptions',
+                 '__weakref__'
                 ]
 
     # To be overridden with True in the appropriate subclasses

sympy/core/cache.py

@@ -1,6 +1,7 @@
 """ Caching facility for SymPy """
 
 from decorator import decorator
+import weakref
 
 
 # TODO: refactor CACHE & friends into class?
@@ -81,7 +82,7 @@ def __cacheit(f):
     set environment variable SYMPY_USE_CACHE to 'debug'.
     """
 
-    func_cache_it_cache = {}
+    f._cache_it_cache = func_cache_it_cache = weakref.WeakValueDictionary()
     CACHE.append((f, func_cache_it_cache))
 
     def wrapper(f, *args, **kw_args):

sympy/core/tests/test_symbol.py

@@ -1,8 +1,11 @@
+import gc
+import weakref
+
 import pytest
 
 from sympy import (Symbol, Wild, GreaterThan, LessThan, StrictGreaterThan,
                    StrictLessThan, pi, I, Rational, sympify, symbols, Dummy,
-                   Integer, Float, sstr)
+                   Integer, Float, sstr, default_sort_key)
 
 
 def test_Symbol():
@@ -332,3 +335,12 @@ def test_call():
     f = Symbol('f')
     assert f(2)
     pytest.raises(TypeError, lambda: Wild('x')(1))
+
+
+def test_weakref():
+    x, y = Symbol('x'), Symbol('y')
+    d = weakref.WeakKeyDictionary([(x, 1), (y, 2)])
+    assert sstr(sorted(d.keys(), key=default_sort_key)) == '[x, y]'
+    del x
+    gc.collect()
+    assert sstr(list(d.keys())) == '[y]'

sympy/utilities/tests/test_pickling.py

@@ -24,7 +24,7 @@
 
 from sympy import symbols, S
 
-excluded_attrs = {'_assumptions', '_mhash'}
+excluded_attrs = {'_assumptions', '_mhash', '__weakref__'}
 
 
 def check(a, exclude=[], check_attr=True):