Surcomplex Numbers 2026-07-27
Weird day. Not much time. Going to try to sketch out the work that needs to be done.
- (First in presentation order, but work on the others first) Writeup of what I'm hoping to accomplish.
- Transfer definitions of operations to LaTeX or whatever.
- Validate structural equality of basic unary operations under iteration. (That is, most unary operations should be self-inverse, with the exception of rotations, which should form the cyclic group of order 3.)
- Ideally validate the structural equivalence of the rotation operations with multiplication by the third roots of unity. If this doesn't work, hopefully numerical equivalence does.
- Actually, see if rotations with conjugate forms the dihedral group of order 6.
- Anyway, need to validate that: structurally equal triples are numerically equal (or at least that this holds for triples that are numeric); numericity is closed under all basic operations; numeric equality is preserved by all basic operations; trying to remember if there's anything else;
Anyway, that'll all do for a start, and hopefully it'll get my brain working a little better. Later. Because right now I need to get to bed.
Good night.