eric-downes/monoids

Its Monoids, All The Way Down

monoids's Issues

octonion demo adjoins identity unneccessarily

Run
python3 row_compose.py --octonions

Row 128 is the identity but so was row 0 before 128 was adjoined...

green's preorders

Motivation: understand topological relation between green's relations and the submagma lattice; latter is more informative, are they distributive lattices? Is the latter a strictly finer description?

We want a general algorithm for generating generator forests $b\Rightarrow a \iff b\in\langle a \rangle$ Right now we have multiple functions that do similar things.

Want:

An algorithm that works wether x is an endo or an element
A possible attack plan

Next Action:

Probably all we need to do to start is document how to use monoids.cyclic_endomonoid and monoids._orbit better... should be obvious once I figure out what I was trying to do there.

fix algebra.py `Algebra()` handling of mul identity index -- should be 1.

tests needed

• quotients
• direct product
• semidirect product

map bet. TDB relation concepts and maps 2^X --> 𝔹

write methods in both paradigms, but dont reuse code; will elucidate interrelationships

Provide labelling w/ dataframes

currently we use numpy for row compositions. this works! but requires giving the octonions weird labels like

8 ~ -e0
9 ~ -e1
...

If we could keep this for internal logic but keep the signed Fano plane rep thatd be great.

Unnecessary `double_rows()` hiding oob bug

In row_compose.py There are two double_rows(a) statements in the row_closure() function; in principle these should not be neccessary but if I don't put them there we get out-of-bounds errors about 3... this is confusing and seems to happen even when I initialize the empty matrix with the max integer. Should be fixed before its ready for real work.

incorporate other alg tools

Can wrap our tables as binops to use this repo's largely complementary features:
https://github.com/naftaliharris/Abstract-Algebra