I found something possibly relevant at

https://bugs.python.org/issue42691

although there the complaint was that Homebrew built python against system 
tcl and the suggestion was that Homebrew use its own tcl-tk.  It seems that 
Homebrew is correctly using its own tcl-tk
since the line

5   libtcl8.6.dylib                     0x000000032998c72e AtForkPrepare + 
38

says that python is using tcl 8.6 and system tcl is 8.5.  No idea what's 
going on, but it might be good to try to produce a minimal reproducible 
example to show to the python/tcl people.
On Wednesday, February 3, 2021 at 12:11:54 PM UTC-5 dim...@gmail.com wrote:

>
>
> On Wed, 3 Feb 2021, 17:03 John H Palmieri, <jhpalm...@gmail.com> wrote:
>
>> Right, thank you. Python 3.9 builds successfully.
>>
>> On Monday, February 1, 2021 at 7:14:29 PM UTC-8 zsc...@gmail.com wrote:
>>
>>> For the --with-system-python3=no, I don't know what the problem is but I 
>>> think it was fixed by upgrading to python 3.9 in 
>>> https://trac.sagemath.org/ticket/30589
>>>
>>> On Monday, February 1, 2021 at 9:45:37 PM UTC-5 John H Palmieri wrote:
>>>
>>>> On OS X Big Sur (intel), as of the most recent Xcode and homebrew, I am 
>>>> currently unable to build Sage with either homebrew's Python or with 
>>>> `./configure --with-system-python3=no`.
>>>>
>>>> - With homebrew's Python, actually Sage builds but the documentation 
>>>> does not (similar problems on both Big Sur and Catalina), ending with
>>>
>>>
> yes, I see this too. (with latest Homebrew python 3.9.)
>
> What exactly is broken there?
>
>
>
>>>>
>>>> ------------------------------------------------------------------------
>>>> 0   signals.cpython-39-darwin.so        0x000000010cd40542 
>>>> print_backtrace + 66
>>>> 1   signals.cpython-39-darwin.so        0x000000010cd44167 sigdie + 39
>>>> 2   signals.cpython-39-darwin.so        0x000000010cd4406a 
>>>> cysigs_signal_handler + 282
>>>> 3   libsystem_platform.dylib            0x00007fff203bcd7d _sigtramp + 
>>>> 29
>>>> 4   ???                                 0x000000000000003f 0x0 + 63
>>>> 5   libtcl8.6.dylib                     0x000000032998c72e 
>>>> AtForkPrepare + 38
>>>> 6   libsystem_pthread.dylib             0x00007fff203781a3 
>>>> _pthread_atfork_prepare_handlers + 90
>>>> 7   libSystem.B.dylib                   0x00007fff2a575934 
>>>> libSystem_atfork_prepare + 11
>>>> 8   libsystem_c.dylib                   0x00007fff2025bb1b fork + 12
>>>> 9   _posixsubprocess.cpython-39-darwin. 0x000000010b63db89 
>>>> subprocess_fork_exec + 1573
>>>> 10  Python                              0x000000010af10904 
>>>> cfunction_call + 127
>>>> 11  Python                              0x000000010aedffa3 
>>>> _PyObject_MakeTpCall + 266
>>>> 12  Python                              0x000000010af88027 
>>>> call_function + 455
>>>> ...
>>>> 157 Python                              0x000000010afcf10f Py_BytesMain 
>>>> + 42
>>>> 158 libdyld.dylib                       0x00007fff20393621 start + 1
>>>> ------------------------------------------------------------------------
>>>> Unhandled SIGILL: An illegal instruction occurred.
>>>> This probably occurred because a *compiled* module has a bug
>>>> in it and is not properly wrapped with sig_on(), sig_off().
>>>> Python will now terminate.
>>>> ------------------------------------------------------------------------
>>>> ...
>>>>   File 
>>>> "/Users/palmieri/Desktop/Sage/sage_builds/TESTING/sage-9.3.beta6/local/lib/python3.9/site-packages/sage_setup/docbuild/utils.py",
>>>>  
>>>> line 221, in reap_workers
>>>>     w = bring_out_yer_dead(w, task, exitcode)
>>>>   File 
>>>> "/Users/palmieri/Desktop/Sage/sage_builds/TESTING/sage-9.3.beta6/local/lib/python3.9/site-packages/sage_setup/docbuild/utils.py",
>>>>  
>>>> line 157, in bring_out_yer_dead
>>>>     raise WorkerDiedException(
>>>> sage_setup.docbuild.utils.WorkerDiedException: worker for 
>>>> ('reference/misc', 'en', 'html', {}) died with non-zero exit code -4
>>>>
>>>> - With `./configure --with-system-python3=no`, Python fails to build 
>>>> (on Big Sur only; it succeeds on Catalina), saying
>>>>
>>>> ModuleNotFoundError: No module named 'readline'
>>>>
>>>> and
>>>>
>>>> ModuleNotFoundError: No module named 'zlib'
>>>>
>>>> Any suggestions?
>>>>
>>>> -- 
>>>> John
>>>>
>>>>
>>>> -- 
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>>
>

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