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We describe the Jacobi elliptic function method for finding exact periodic wave solutions to nonlinear evolution equations. We present a Maple packaged automated Jacobi elliptic function method, which can entirely automatically output the exact periodic wave solutions. The effectiveness of the automated Jacobi elliptic function method is demonstrated using as examples the application to a variety of equations with physical interest.Not only are the previously known solutions recovered but in some cases new solutions and more general forms of solutions are obtained.