Magmas inside Monoids

"It's Monoids, Monoids All the Way Down." -- Ancient Babylonian Saying

Some notes in progress on the theory in notion

Running with pre-existing python 3.10+

If you have python3.10 installed, you can run

python3 -m pip install -r requirements.txt
python3 demo.py

This shows the construction of an (unnamed) 21-element monoid adjoint to the "Rock-Paper-Scissors" magma.

If you want to see progress on verifying the adjoint group of the unit octonion loop (slower), as the extraspecial group of order 128 (plus-type);

python3 demo.py --octonions

Upgrading to newer python

If you don't have that version of python, I recommend the following to keep your setup easy-to-maintain. (It allows you to have many versions of python installed and switch between them as needed.)

1. Install pyenv
2. pyenv install 3.11.0 # 3.11 60% faster than previous versions
3. pyenv shell 3.11.0 # makes your current shell use that python version
4. which python3 # should show something with "shims" in it
5. python3 --version # should show 3.11
6. python3 -m pip install -r requirements.txt
7. python3 demo.py # quick RPS-magma demo
8. python3 demo.py --octonions # sit back and watch it compute!

Older notes

Here is where I am writing the first draft of a friendly treatment.