b=isFiniteStratification(strat)
Let strat be the output of stratifyByRank applied to a module $L$ of vector fields. When $L$ is a Lie algebra, strat contains information about the integral submanifolds of $L$; under the assumption that $L$ is a Lie algebra, this function checks whether there are a finite number of connected integral submanifolds.
The algorithm used, and perhaps even the term integral submanifold, is only valid in real or complex geometry. This routine checks that, for all $j$, each component of strat#j has dimension $<j$. It is up to the user to check that the answers obtained by Macaulay2 (e.g., in QQ[x,y,z]) would not change if the calculation was done over the real or complex numbers.
The algorithm is motivated by the results of section 4.3 of ``James Damon and Brian Pike. Solvable groups, free divisors and nonisolated matrix singularities II: Vanishing topology. Geom. Topol., 18(2):911962, 2014'', available at http://dx.doi.org/10.2140/gt.2014.18.911 or http://arxiv.org/abs/1201.1579.
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Since D has rank 0 on $a=b=0$, that is, the vector fields all vanish:

the stratification cannot be finite (every point on $a=b=0$ is its own stratum):

This stratification is finite:


The assumption that $L$ is a Lie algebra is not checked.
The object isFiniteStratification is a method function.