We discuss an approach to the problem of classifying zero-dimensional gradient
quasihomogeneous singularities using simple properties of deformation theory. As an example, we
enumerate all such singularities with modularity ℘ = 0 and with Milnor number not greater than 12.
We also compute normal forms and monomial vector-bases of the first cotangent homology and
cohomology modules, the corresponding Poincar´e polynomials, inner modality, inner modularity,
primitive ideals, etc.