isHolonomic -- test whether an algebraic set is holonomic

Test if $X$, the algebraic set defined by I or f, is holonomic. Let $D$ be the module of logarithmic vector fields for I. Then $X$ is called holonomic if at any point $p$ in $X$, the generators of $D$ evaluated at $p$ span the tangent space of the stratum containing $p$ of the canonical Whitney stratification of $X$; equivalently, the maximal integral submanifolds of $D$ equal the the canonical Whitney stratification of $X$ (except that the complement of $X$ forms additional integral submanifold(s)).

The algorithm used amounts to computing isFiniteStratification(stratifyByRank(derlog(I))) (see isFiniteStratification, stratifyByRank, derlog). Details may be found in section 4.3 of ``James Damon and Brian Pike. Solvable groups, free divisors and nonisolated matrix singularities II: Vanishing topology. Geom. Topol., 18(2):911-962, 2014'', available at http://dx.doi.org/10.2140/gt.2014.18.911 or http://arxiv.org/abs/1201.1579. The basic idea, however, is present in (3.13) of ``Kyoji Saito. Theory of logarithmic differential forms and logarithmic vector fields. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 27: 265-291, 1980''.

This hypersurface is not holonomic, since gens(D) has rank 0 on the $1$-dimensional space $a=b=0$:

This is holonomic; the stratification consists of the origin, and the rest of the surface $ac-b^2=0$:

The Whitney Umbrella is also holonomic; the stratification consists of the origin, the rest of the line $a=b=0$, and the rest of the surface:

See the warnings in isFiniteStratification.

Also, this usage of holonomic originates with Kyoji Saito and may vary from other meanings of the word, particularly in D-module theory.