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Its Monoids, All The Way Down
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
An algorithm that works wether x is an endo or an element
A possible attack plan
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.
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.
Can wrap our tables as binops to use this repo's largely complementary features:
https://github.com/naftaliharris/Abstract-Algebra
write methods in both paradigms, but dont reuse code; will elucidate interrelationships
Run
python3 row_compose.py --octonions
Row 128 is the identity but so was row 0 before 128 was adjoined...
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.
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