[BUG] binding=True causes a mysterious import error

[kwankyu]

This issue arose while we tried to turn on binding=True cython compiler option in SageMath 9.6.rc3:

https://trac.sagemath.org/ticket/26254#comment:64

The function call_registered_function() is defined in the file src/sage/symbolic/pynac_function_impl.pxi, which is included into src/sage/symbolic/expression.pyx by include "pynac_function_impl.pxi".

Then the statement from .expression import call_registered_function in the global scope of src/sage/symbolic/function.pyx throws the exception

ImportError: cannot import name call_registered_function

This may be a bug on cython since we don't have this exception with the default binding=False.

SageMath 9.6.rc3 uses python-3.10.3 and cython-0.29.28.

[da-woods]

To me this looks like a circular import issue possible? From the sage issue:

File "sage/symbolic/expression.pyx", line 1, in init sage.symbolic.expression
    # -*- coding: utf-8 -*-
  File "sage/symbolic/function.pyx", line 144, in init sage.symbolic.function
    from .expression import (

expression import function which imports expression (some of these imports may be generated by cimport though - I'm not sure).

With binding=False functions are defined in PyModuleDef. I think that means they exist very early in the module import process before the main module init function has run, and therefore you may get away with it. With binding=True they're generated in the module init function.

Therefore I provisionally don't think it's a Cython bug - it looks a lot like code that wouldn't work in Python either

[da-woods]

I think if you remove the line

from sage.symbolic.function cimport SymbolicFunction

it'll work. You don't look to actually use the cimport so you're losing nothing by removing it.

However I can't work out how the code is working at all with or without binding. At least on a simplified test locally it makes no difference if it's enabled for not.

[kwankyu]

To me this looks like a circular import issue possible?

Right. There was a circular import. We could fix the problem by changing the global imports to local imports. Your explanation below confirms that we did the right thing.

With binding=False functions are defined in PyModuleDef. I think that means they exist very early in the module import process before the main module init function has run, and therefore you may get away with it. With binding=True they're generated in the module init function.

So binding=True simply revealed the existing circular import. Thank you for the explanation!

[da-woods]

So binding=True simply revealed the existing circular import. Thank you for the explanation!

Possibly... I tried to make a cut-down example to replicate it myself and couldn't make it work with either version!

Anyway - hopefully you have enough information to fix it... I'll close this issue I think