We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our result is well-suited to symbolic calculations performed by a computer and can be implemented to arbitrary order, thus overcoming limitations of usual time-dependent perturbation methods. We also provide a simple diagrammatic tool for calculation and treat illustrative examples. By construction, our method applies directly to both quantum and classical systems; the difference is left to a low-level subroutine. This aspect sheds light on the relationship between seemingly disconnected independently developed methods in the literature.
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