Consider algebraic non-geometric approaches to segment chain intersections

[apirogov]

• Can polygons be factorized?
• Can we represent linear dependencies as an automatic string property?

Think of this in terms of semigroups and string algorithms and automata

Snakes are semigroups that act on points in the ring

Closed loops are equations that add up to identity (or with canonical starting point fixed, add up to 0)