Description of pip behaviour when resolving dependencies with --no-deps

Pip --no-deps example

(.test-venv) >>> pip install --no-cache pystan==2.19.1.1 numpy==1.22.1 cython==0.29.26
Collecting pystan==2.19.1.1
  Downloading pystan-2.19.1.1.tar.gz (16.2 MB)
     |████████████████████████████████| 16.2 MB 16.0 MB/s 
Collecting numpy==1.22.1
  Downloading numpy-1.22.1-cp39-cp39-macosx_11_0_arm64.whl (12.8 MB)
     |████████████████████████████████| 12.8 MB 7.3 MB/s 
Collecting cython==0.29.26
  Downloading Cython-0.29.26-py2.py3-none-any.whl (983 kB)
     |████████████████████████████████| 983 kB 16.6 MB/s 
Using legacy 'setup.py install' for pystan, since package 'wheel' is not installed.
Installing collected packages: numpy, cython, pystan
    Running setup.py install for pystan ... done
Successfully installed cython-0.29.26 numpy-1.22.1 pystan-2.19.1.1
WARNING: You are using pip version 21.1.3; however, version 21.3.1 is available.
You should consider upgrading via the '/Users/chesco/code/test-virtualenv/.test-venv/bin/python3 -m pip install --upgrade pip' command.
(.test-venv) >>> ./reset-venv                                                         
(.test-venv) >>> pip freeze                                                           
(.test-venv) >>> pip install --no-deps --no-cache pystan==2.19.1.1 numpy==1.22.1 cython==0.29.26
Collecting pystan==2.19.1.1
  Downloading pystan-2.19.1.1.tar.gz (16.2 MB)
     |████████████████████████████████| 16.2 MB 10.2 MB/s 
Collecting numpy==1.22.1
  Downloading numpy-1.22.1-cp39-cp39-macosx_11_0_arm64.whl (12.8 MB)
     |████████████████████████████████| 12.8 MB 14.0 MB/s 
Collecting cython==0.29.26
  Downloading Cython-0.29.26-py2.py3-none-any.whl (983 kB)
     |████████████████████████████████| 983 kB 22.5 MB/s 
Using legacy 'setup.py install' for pystan, since package 'wheel' is not installed.
Installing collected packages: pystan, numpy, cython
    Running setup.py install for pystan ... error
    ERROR: Command errored out with exit status 1:
     command: /Users/chesco/code/test-virtualenv/.test-venv/bin/python3 -u -c 'import io, os, sys, setuptools, tokenize; sys.argv[0] = '"'"'/private/var/folders/7k/rj1nms8x1y97wpfg01z8h8zh0000gn/T/pip-install-jynjyrsi/pystan_1e2b03aad3d64459af2a330e8f3af036/setup.py'"'"'; __file__='"'"'/private/var/folders/7k/rj1nms8x1y97wpfg01z8h8zh0000gn/T/pip-install-jynjyrsi/pystan_1e2b03aad3d64459af2a330e8f3af036/setup.py'"'"';f = getattr(tokenize, '"'"'open'"'"', open)(__file__) if os.path.exists(__file__) else io.StringIO('"'"'from setuptools import setup; setup()'"'"');code = f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' install --record /private/var/folders/7k/rj1nms8x1y97wpfg01z8h8zh0000gn/T/pip-record-v43dydlx/install-record.txt --single-version-externally-managed --compile --install-headers /Users/chesco/code/test-virtualenv/.test-venv/include/site/python3.9/pystan
         cwd: /private/var/folders/7k/rj1nms8x1y97wpfg01z8h8zh0000gn/T/pip-install-jynjyrsi/pystan_1e2b03aad3d64459af2a330e8f3af036/
    Complete output (1 lines):
    Cython>=0.22 and NumPy are required.
    ----------------------------------------
ERROR: Command errored out with exit status 1: /Users/chesco/code/test-virtualenv/.test-venv/bin/python3 -u -c 'import io, os, sys, setuptools, tokenize; sys.argv[0] = '"'"'/private/var/folders/7k/rj1nms8x1y97wpfg01z8h8zh0000gn/T/pip-install-jynjyrsi/pystan_1e2b03aad3d64459af2a330e8f3af036/setup.py'"'"'; __file__='"'"'/private/var/folders/7k/rj1nms8x1y97wpfg01z8h8zh0000gn/T/pip-install-jynjyrsi/pystan_1e2b03aad3d64459af2a330e8f3af036/setup.py'"'"';f = getattr(tokenize, '"'"'open'"'"', open)(__file__) if os.path.exists(__file__) else io.StringIO('"'"'from setuptools import setup; setup()'"'"');code = f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' install --record /private/var/folders/7k/rj1nms8x1y97wpfg01z8h8zh0000gn/T/pip-record-v43dydlx/install-record.txt --single-version-externally-managed --compile --install-headers /Users/chesco/code/test-virtualenv/.test-venv/include/site/python3.9/pystan Check the logs for full command output.
WARNING: You are using pip version 21.1.3; however, version 21.3.1 is available.
You should consider upgrading via the '/Users/chesco/code/test-virtualenv/.test-venv/bin/python3 -m pip install --upgrade pip' command.