Run Examples in CI.

[MicahGale]

Description

This implemented testing of (almost) all example code blocks. This includes:

• README.md
• doc/source/*.rst
• All docstring examples (there are none currently)
• demo/*.ipynb

This also fixed all bugs found. The only code that wasn't tested is ones where the output are multiline statements. This is too complicated to work with sphinx-doctest.

Fixes #575, fixes #571

Checklist

• [x] I have performed a self-review of my own code
• [x] I have made corresponding changes to the documentation (if applicable)
• [x] I have added tests that prove my fix is effective or that my feature works (if applicable)

[MicahGale]

Using doctest, sphinx-doctest, and papermill to run these tests.

[MicahGale]

TODO: figure out what to do with code-block

[MicahGale]

phmutest README.md --replmode --log https://stackoverflow.com/a/76924724

[MicahGale]

I'm thinking we should override the changelog test.