A NEW PARALLEL POLYNOMIAL DIVISION BY A SEPARABLE POLYNOMIAL VIA HERMITE INTERPOLATION WITH APPLICATIONS

Abstract

A new parallel division of polynomials by a common separable divisor over a perfect field is presented and this is done by expressing the remainders as derivatives of a unique polynomial. In order to get this results, a novel variant expression of the classical Lagrange-Sylvester Hermite interpolating polynomial has been utilised, although any known variant may be used. The above findings are utilized to obtain a number of new identities involving polynomial derivatives, including a closed formula for the semi-simple part of the Jordan decomposition of a matrix.