  Our recent extension of Arnold's classification includes all singularities of
corank up to two equivalent to a germ with a non-degenerate Newton boundary,
thus broadening the classification's scope significantly by a class which is
unbounded with respect to modality and Milnor number. This method is based on
proving that all right-equivalence classes within a mu-constant stratum can be
represented by a single normal form derived from a regular basis of a suitably
selected special fiber. While both Arnold's and our preceding work on normal
forms addresses the determination of a normal form family containing the given
germ, this paper takes the next natural step: We present an algorithm for
computing for a given germ the values of the moduli parameters in its normal
form family, that is, a normal form equation in its stable equivalence class.
This algorithm will be crucial for understanding the moduli stacks of such
singularities. The implementation of this algorithm, along with the
foundational classification techniques, is implemented in the library
arnold.lib for the computer algebra system Singular.
