This is to support Python 3.10, which was released on 2021-10-04.
https://docs.python.org/3.10/whatsnew/changelog.html#changelog

Thanks to the following tickets, Sage is mostly ready for
Python 3.10 in addition to 3.9, 3.8, 3.7.

• needs Cython 0.29.23 (cython: Upgrade to 0.29.24, fix Cython 3.0 future-warnings #31445)
• Upgrade gmpy2 to add python 3.10 support #31855 Patch/upgrade gmpy2 to add python 3.10 support
• pyzmq: Update to 22.0.3; babel: Update to 2.9.1 #31856 Upgrade pyzmq, babel - to fix error: implicit declaration of function 'PyObject_AsWriteBuffer' is invalid in C99 with pyzmq-19.0.2
• Update numpy to 1.21.4, networkx to 2.6.3 #32815 numpy
• cffi: Update to 1.15.0 #32837 cffi: Update to 1.15.0
• Update traitlets to 5.1.1 (for python 3.9.8, 3.10) #32852 Update traitlets to 5.1.1 (for python 3.9.8, 3.10)
• Update pip to 21.3.1, distlib to 0.3.3 #32671 Update pip to 21.3.1, distlib to 0.3.3
• Meta-ticket: Replace imports from deprecated distutils #31295 Meta-ticket: Replace imports from deprecated distutils
• IPython/Jupyter upgrade for python 3.10 support #32930 IPython/Jupyter upgrade for python 3.10 support
• Fix tests with Python 3.10 #33013 Fix tests with Python 3.10

In this ticket, we enable use of system Python 3.10 but issue a warning regarding its experimental status for Sage.

The ticket does not include the upgrade of the python3 SPKG to Python 3.10. Many systems already ship Python 3.10. To test, thanks to https://wiki.sagemath.org/ReleaseTours/sage-9.5#Separate_virtual_environment_for_Python_packages, a full rebuild of the Sage distribution is not necessary - only the Python packages will be built from scratch in a separate venv.

Related:

• PEP 619 -- Python 3.10 Release Schedule
• What's new in Python 3.10
• Update Python to 3.10.x #30767: Upgrade to Python 3.10
• Support Python 3.9 #30184: Support Python 3.9
• Adopt the “time window-based” policy for support of Python versions from NEP 29 #30384: Adopt the “time window-based” policy for support of Python versions from NEP 29

Depends on #33013
Depends on #32930
Depends on #33040

CC: @mkoeppe @slel @kiwifb @tornaria @antonio-rojas

Component: packages: standard

Keywords: upgrade, python

Author: Matthias Koeppe, Gonzalo Tornaría

Branch: df9f1d4

Reviewer: Antonio Rojas, Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/30766