The structure of algebras of differential invariants, particularly their generators, is based on the symbolic invariant calculus provided by the method of equivariant moving frames.  I will discuss a new computational algorithm that will, in many cases, determine whether a given set of differential invariants is generating.  As an example, we establish a new result that the Gaussian curvature generates all the differential invariants for Euclidean surfaces in three-dimensional space.

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