# StratificationByRank -- a type to hold a rank computation

## Description

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.

• stratifyByRank -- compute ideals describing where the vector fields have a particular rank
• isFiniteStratification -- checks if a stratification by integral submanifolds is finite
• VectorFields -- a package for manipulating polynomial vector fields

## Functions and methods returning an object of class StratificationByRank :

• stratifyByRank -- compute ideals describing where the vector fields have a particular rank

## Methods that use an object of class StratificationByRank :

• "isFiniteStratification(StratificationByRank)" -- see isFiniteStratification -- checks if a stratification by integral submanifolds is finite

## For the programmer

The object StratificationByRank is a type, with ancestor classes HashTable < Thing.