[garba_dlm]

i'm still working on understanding lattices better

but i can imagine, based on my own ignorance, creativity, and lack of correct understanding, would be some kind of factorization.

as I think while trying to better know what's a lattice, I imagine a lattice like a coordinate pair, but instead of each coordinate existing on a line, they exist on a binary tree (or some other directed graph explored from a root outwards without cycles)

which means you have two such binary-trees (not necessarily binary, but it's just easier to work with them seemingly)

and then you combine these into ONE lattice. so then, to de-lattice means to recover the binary trees.

but when I say binary tree I'm thinking about rational numbers (because stern broccott trees)

[tptacek]

A lattice is like a vector space, but with exclusively integer coefficients. It's not a coordinate pair. If you think of vectors as coordinate pairs, a vector space is a (possibly unbounded) set of coordinate pairs. If you haven't done any linear algebra, a decent intuition would be mathematical objects like "the even numbers" or "the odd numbers", but substituting vectors (fixed-sized tuples of numbers) for scalars.