Fundamental Computations with Polynomials

In this chapter we recall the known effective algorithms for the major problems of polynomial computations and demonstrate some fundamental techniques of the algorithm design, according to the following line: we first recall fast Fourier transform (FFT), leading to a dramatic improvement of the classical algorithms for the discrete Fourier transform (DFT) and polynomial multiplication (also called convolution). Then we systematically extend such an improvement to other polynomial computations.