Fast Algorithm for Computing the Minimal Polynomials of Gaussian Periods

Gaussian Periods, the basis of the theory of compass and straightedge construction, introduced by Gauss, play an important role in the history of mathematics. An efficient way of computing minimal polynomials of Gaussian Periods is proposed. Compared with other methods, the method which is much simpler and much easier to be implemented can avoid approximate computation because its progress is completed in rational integer ring.