Trac #31182: Mutability class and pickling

If the class `Mutability` is used as mixin for mutability features, the
pickling goes wrong (see
[https://trac.sagemath.org/ticket/30261#comment:9 here]).

An attempt using this mixin class after #30281, still throws a pickling
test error, e.g. in #30310:

{{{
File "src/sage/manifolds/chart_func.py", line 2944, in
sage.manifolds.chart_func.MultiCoordFunction.__init__
Failed example:
    TestSuite(f).run()
Expected nothing
Got:
    Failure in _test_pickling:
    Traceback (most recent call last):
      File "sage/misc/persist.pyx", line 291, in sage.misc.persist.dumps
(build/cythonized/sage/misc/persist.c:4284)
        return obj.dumps(compress)
      File "sage/structure/sage_object.pyx", line 476, in
sage.structure.sage_object.SageObject.dumps
(build/cythonized/sage/structure/sage_object.c:3790)
        return _base_dumps(self, compress=compress)
      File "sage/misc/persist.pyx", line 264, in
sage.misc.persist._base_dumps
(build/cythonized/sage/misc/persist.c:4012)
        gherkin = SagePickler.dumps(obj)
      File "sage/misc/persist.pyx", line 771, in
sage.misc.persist.SagePickler.dumps
(build/cythonized/sage/misc/persist.c:6801)
        pickler.dump(obj)
    TypeError: cannot pickle 'MultiCoordFunction' object
    <BLANKLINE>
    During handling of the above exception, another exception occurred:
    <BLANKLINE>
    Traceback (most recent call last):
      File "/home/michi/Projekte/sage-devel/local/lib/python3.8/site-
packages/sage/misc/sage_unittest.py", line 297, in run
        test_method(tester=tester)
      File "sage/structure/sage_object.pyx", line 647, in
sage.structure.sage_object.SageObject._test_pickling
(build/cythonized/sage/structure/sage_object.c:5007)
        tester.assertEqual(loads(dumps(self)), self)
      File "sage/misc/persist.pyx", line 293, in sage.misc.persist.dumps
(build/cythonized/sage/misc/persist.c:4337)
        return _base_dumps(obj, compress=compress)
      File "sage/misc/persist.pyx", line 264, in
sage.misc.persist._base_dumps
(build/cythonized/sage/misc/persist.c:4012)
        gherkin = SagePickler.dumps(obj)
      File "sage/misc/persist.pyx", line 771, in
sage.misc.persist.SagePickler.dumps
(build/cythonized/sage/misc/persist.c:6801)
        pickler.dump(obj)
    TypeError: cannot pickle 'MultiCoordFunction' object
    ------------------------------------------------------------
    The following tests failed: _test_pickling
}}}

I found out that a non-cythonized alternative works without errors.

URL: https://trac.sagemath.org/31182
Reported by: gh-mjungmath
Ticket author(s): Michael Jung
Reviewer(s): Travis Scrimshaw

Author: Release Manager

build/pkgs/configure/checksums.ini

@@ -1,4 +1,4 @@
 tarball=configure-VERSION.tar.gz
-sha1=1fd3cc5d2e70fb51853371b2e2c1847d33cb5a78
-md5=b7d6186f022fd3a535e3f7b242b0ccd1
-cksum=3654751019
+sha1=fef34790261a068805f603750635668a09abd0b5
+md5=3af901a6c4bcdaf50e1233277375c2e4
+cksum=1293784084

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-a4fc17efd8cd7e07f4b63a54db2fe0a60d0d2dc1
+b8db1adc405725c00f73645fcda9012d15ab5589

src/sage/structure/mutability.pyx

@@ -177,6 +177,71 @@ cdef class Mutability:
         """
         return not self._is_immutable
 
+    def __getstate__(self):
+        r"""
+        Get the current state of ``self`` including the mutability status.
+        
+        TESTS::
+        
+            sage: class A(SageObject, Mutability):
+            ....:     def __init__(self, val):
+            ....:         self._val = val
+            ....:     def change(self, val):
+            ....:         self._require_mutable()
+            ....:         self._val = val
+            ....:     def __hash__(self):
+            ....:         self._require_immutable()
+            ....:         return hash(self._val)
+            sage: a = A(4)
+            sage: a.__dict__
+            {'_val': 4}
+            sage: a.__getstate__()
+            {'_is_immutable': False, '_val': 4}
+            sage: a.__reduce__()  # indirect doctest
+            (<function _reconstructor at ...>,
+             (<class '__main__.A'>,
+              <class 'sage.structure.sage_object.SageObject'>,
+              <sage.structure.sage_object.SageObject object at ...>),
+             {'_is_immutable': False, '_val': 4})
+            
+        """
+        state = getattr(self, '__dict__', {})
+        state['_is_immutable'] = self._is_immutable
+        return state
+
+    def __setstate__(self, state):
+        r"""
+        Set the state of ``self`` from the dictionary ``state`` including the
+        mutability status.
+
+        TESTS::
+
+            sage: class A(SageObject, Mutability):
+            ....:     def __init__(self, val):
+            ....:         self._val = val
+            ....:     def change(self, val):
+            ....:         self._require_mutable()
+            ....:         self._val = val
+            ....:     def __hash__(self):
+            ....:         self._require_immutable()
+            ....:         return hash(self._val)
+            sage: a = A(4)
+            sage: a.is_immutable()
+            False
+            sage: d = a.__getstate__(); d
+            {'_is_immutable': False, '_val': 4}
+            sage: d['_is_immutable'] = True
+            sage: a.__setstate__(d)
+            sage: a.is_immutable()
+            True
+            sage: a.__getstate__()
+            {'_is_immutable': True, '_val': 4}
+
+        """
+        if hasattr(self, '__dict__'):
+            self.__dict__ = state
+        self._is_immutable = state['_is_immutable']
+
 ##########################################################################
 ## Method decorators for mutating methods resp. methods that assume immutability