  We present a FFT-based algorithm for the computation of a polynomial's
coefficients from its roots, and apply it to obtain the coefficients of
interpolation polynomials, to invert Vandermondians and to evaluate the
symmetric functions of a set of parameters. Analytic and numerical evidence
with problem sizes up to and beyond n=2000 confirms that it is superior over
previous algorithms for these problems in case of parameters taken from uniform
or almost uniform distributions on or near circles in the complex plane, and of
comparable performance in other cases. Its time complexity is O(n*n) and its
storage complexity for tasks other than Vandermondian inversion O(n).
