A direct algorithm for extracting a transfer functionʹs multiple zeros or poles

Use of the elementary symmetric and summation functions has enabled the number of distinct roots of a given polynomial to be calculated by constructing the increasing order discriminants of the polynomial. In this paper, an algorithm is provided for computing the coefficients of a divider polynomial containing only these distinct roots. By repeatedly extracting the divider polynomials from the given polynomial, the multiplicities of the roots of the given polynomial can be determined.