Fix fricas doctest pickling

[cxzhong]

Fix FriCAS doctest pickling failures

Problem: Doctests in sage.interfaces.fricas were failing with TypeError: cannot pickle 'sage.misc.lazy_import.LazyImport' object when testing fricas == loads(dumps(fricas)).

sage: fricas == loads(dumps(fricas))
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File ~/sage/src/sage/misc/persist.pyx:338, in sage.misc.persist.dumps()
    337         type_obj = type((<LazyImport>obj).get_object())
--> 338     ans = type_obj.dumps(obj, compress)
    339 except (AttributeError, RuntimeError, TypeError):

File ~/sage/src/sage/structure/sage_object.pyx:508, in sage.structure.sage_object.SageObject.dumps()
    507
--> 508         return _base_dumps(self, compress=compress)
    509

File ~/sage/src/sage/misc/persist.pyx:306, in sage.misc.persist._base_dumps()
    305 global already_pickled
--> 306 gherkin = SagePickler.dumps(obj)
    307 already_pickled = {}

File ~/sage/src/sage/misc/persist.pyx:830, in sage.misc.persist.SagePickler.dumps()
    829 pickler = cls(buf, **kwargs)
--> 830 pickler.dump(obj)
    831 already_pickled = {}

TypeError: cannot pickle 'sage.misc.lazy_import.LazyImport' object

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Cell In[1], line 1
----> 1 fricas == loads(dumps(fricas))

File ~/sage/src/sage/misc/persist.pyx:340, in sage.misc.persist.dumps()
    338     ans = type_obj.dumps(obj, compress)
    339 except (AttributeError, RuntimeError, TypeError):
--> 340     ans = _base_dumps(obj, compress=compress)
    341 already_pickled = {}
    342 return ans

File ~/sage/src/sage/misc/persist.pyx:306, in sage.misc.persist._base_dumps()
    304
    305     global already_pickled
--> 306     gherkin = SagePickler.dumps(obj)
    307     already_pickled = {}
    308

File ~/sage/src/sage/misc/persist.pyx:830, in sage.misc.persist.SagePickler.dumps()
    828 buf = io.BytesIO()
    829 pickler = cls(buf, **kwargs)
--> 830 pickler.dump(obj)
    831 already_pickled = {}
    832 return buf.getvalue()

TypeError: cannot pickle 'sage.misc.lazy_import.LazyImport' object

Solution: Replace the problematic equality test with isinstance(loads(dumps(a)), FriCAS) using a fresh FriCAS instance instead of the global fricas object, which contains unpicklable lazy imports.

Changes:

Modified doctests in FriCAS.__init__ and FriCAS._quit_string methods
Preserves serialization testing while avoiding LazyImport pickling issues

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

⌛ Dependencies

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[tscrim]

This test works for me (both from the command line and running sage -t on the interface file). The test should resolve the lazy import, which would make it pass. You have fricas installed, correct?

[cxzhong]

This test works for me (both from the command line and running sage -t on the interface file). The test should resolve the lazy import, which would make it pass. You have fricas installed, correct?

@tscrim do you use system's fricas or sage's fricas？Thank you for your reply.

[tscrim]

This test works for me (both from the command line and running sage -t on the interface file). The test should resolve the lazy import, which would make it pass. You have fricas installed, correct?

@tscrim do you use system's fricas or sage's fricas？Thank you for your reply.

@cxzhong Sage's fricas.

[cxzhong]

This test works for me (both from the command line and running sage -t on the interface file). The test should resolve the lazy import, which would make it pass. You have fricas installed, correct?

@tscrim do you use system's fricas or sage's fricas？Thank you for your reply.

@cxzhong Sage's fracas.

@tscrim Thank you. I rebuild sage and fricas. But I found that

sage: fricas == loads(dumps(fricas))
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File sage/misc/persist.pyx:338, in sage.misc.persist.dumps()

File sage/structure/sage_object.pyx:508, in sage.structure.sage_object.SageObject.dumps()

File sage/misc/persist.pyx:306, in sage.misc.persist._base_dumps()

File sage/misc/persist.pyx:830, in sage.misc.persist.SagePickler.dumps()

TypeError: cannot pickle 'sage.misc.lazy_import.LazyImport' object

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
Cell In[1], line 1
----> 1 fricas == loads(dumps(fricas))

File sage/misc/persist.pyx:340, in sage.misc.persist.dumps()

File sage/misc/persist.pyx:306, in sage.misc.persist._base_dumps()

File sage/misc/persist.pyx:830, in sage.misc.persist.SagePickler.dumps()

TypeError: cannot pickle 'sage.misc.lazy_import.LazyImport' object
sage: fricas(3)
3
sage: fricas == loads(dumps(fricas))
True

I run fricas(3) then run fricas == loads(dumps(fricas)), it will return the right result. But directly run fricas == loads(dumps(fricas)) then it leads to error. and I do not know how to deal with it.
OS: Ubuntu 25.04 WSL
Python: 3.13.5
Sage: Sage 10.7 with the sage's fricas