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 result, 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.
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