Polygon enumeration

[apirogov]

I would like to have an enumeration algorithm over simple polygons possible in the ring.

However, the lattice structure for the rings can be very complex and is not 2 dimensional, has infinitely many points in each bounded area, and has no 2D primitive cell etc.

It is unclear if there are finitely many simple polygons possible in a bounded area, need to understand this.

If this is the case, find a way to enumerate them.

1. First approach - using cyclotomic integer structure to enumerate all paths between to ring points, ordered by increasing complexity/length
2. Second approach - finding a finite set of base polygons that can generate all simple polygons in the field using the match operation

A finite base polygon for Z4 is a unit square, a basis for Z6 is a triangle. What do we do for higher levels?

[apirogov]

As I have an idea for an efficient enumeration procedure based on trees of angle sequences with some clever traversal minimizing waste of snakes, this gets higher prio.

High-speed enumeration of polygons would be pretty cool.