I installed python3.10 by using brew install python@3.10 But here's what happened.
$python3.10
zsh : command not found : python3.10
$which python3.9
/usr/local/bin/python3.9
$ls -al /usr/local/bin/python*
lrwxr-xr-x 1 host admin 39 Mar 30 12:17 /usr/local/bin/python3 -> ../Cellar/python@3.9/3.9.12/bin/python3
lrwxr-xr-x 1 host admin 46 Mar 30 12:17 /usr/local/bin/python3-config -> ../Cellar/python@3.9/3.9.12/bin/python3-config
lrwxr-xr-x 1 host admin 41 Mar 30 12:17 /usr/local/bin/python3.9 -> ../Cellar/python@3.9/3.9.12/bin/python3.9
lrwxr-xr-x 1 host admin 48 Mar 30 12:17 /usr/local/bin/python3.9-config -> ../Cellar/python@3.9/3.9.12/bin/python3.9-config
$ls /usr/local/Cellar/python*
/usr/local/Cellar/python@3.10:
3.10.2
/usr/local/Cellar/python@3.9:
3.9.12
So it seems like there is a python3.10 installed on Cellar but there's no symlink in /usr/local/bin for it. When I installed python3.9, I didn't have to setup those things. How can I add&use python3.10? Creating symlink on my own to /usr/local/bin is the last thing I want to do. I hope there's some command for brew to make this done.