H=stratifyByRank(M)
H=stratifyByRank(m)
Computes ideals describing where the provided vector fields have a particular rank. For $1\leq i\leq n$, where $n$ is the dimension of the space, (stratifyByRank(M))#i will be an ideal defining the set of points $p$ such that the generators of $M$ evaluated at $p$ span a subspace of dimension less than $i$. If the vector fields generate a Lie algebra, then this gives some information about their 'orbits' or their maximal integral submanifolds.
For details on the parts of the calculation, make debugLevel positive.
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D has rank 0 on $a=b=0$, that is, the vector fields all vanish there:
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D has rank <3 precisely on the hypersurface $f=0$, and hence rank 3 off the hypersurface:
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This submodule of D has rank $<3$ everywhere since it only has 2 generators:
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The object stratifyByRank is a method function.