Factorization of polynomials based on the multiplicities of their roots and applications
A method which enables the polynomial \(d(\lambda)\) of the distinct roots of a polynomial \(p(\lambda)\) to be computed by simple algebraic manipulations of the coefficients of \(p(\lambda)\) is examined. In other words, \(d(\lambda)\) is computed by performing only additions and multiplications of the coefficients of \(p(\lambda)\), and not by computing any roots of \(p(\lambda)\). This method of extracting polynomials of distinct roots is then utilized to develop an algorithm for factoring a polynomial in such a way that one can determine the distinct multiplicities of the roots and the number of distinct roots that have a given multiplicity. Finally, both the extraction method and the factorization process are utilized to develop an algorithm for computing the greatest common divisor of a system of polynomials. In a submitted paper of the authors a code is presented which implements the developed algorithm for factorization based on multiplicity.
scientific article; zbMATH DE number 978115