Invariants of Finite and Discrete Group Actions via Moving Frames

A new, elementary algorithm for constructing complete, minimal sets of generating invariants for finite or, more generally, discrete group actions, both linear and nonlinear, is proposed. The resulting fundamental invariants are piecewise analytic and endowed with a rewrite rule that enables one to immediately express any other invariant (polynomial, rational, smooth, analytic, etc.) as a function thereof. The construction is inspired by the method of equivariant moving frames for Lie group actions.