My soul as a computer programmer cries out against the idea of representing N particles with N^2 distances between them; it seems wasteful.
When you take into account that d(A, A) = 0 and d(A, B) = d(B, A), you only need N(N − 1)/2 distances.
You’d never even fewer in a flat 3D space, but if the particles can be in an arbitrarily curved space I think you need all of those.
N(N-1)/2 is O(N^2), which is not substantially better. Particularly to the soul of a computer scientist, which largely ignores constant factors anyway.
When you take into account that d(A, A) = 0 and d(A, B) = d(B, A), you only need N(N − 1)/2 distances.
You’d never even fewer in a flat 3D space, but if the particles can be in an arbitrarily curved space I think you need all of those.
N(N-1)/2 is O(N^2), which is not substantially better. Particularly to the soul of a computer scientist, which largely ignores constant factors anyway.