This is a type of HashTable with positive integer keys, used to store the output of stratifyByRank. If M is a module of vector fields and h=stratifyByRank(M) is the StratificationByRank object, then h#i is the radical ideal defining the set of points $p$ such that the generators of $M$ evaluated at $p$ span a subspace of dimension less than $i$.
These objects are primarily used by isFiniteStratification.
If M is a Lie algebra, then this gives some information about the 'orbits' or maximal integral submanifolds of the vector fields.
The object StratificationByRank is a type, with ancestor classes HashTable < Thing.
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/VectorFields.m2:2155:0.