Fast Solution of Linear Systems with Polynomial Coefficients over the Ring of Integers

Abstract An algorithm is shown for computing both the solution, in unreduced rational form, of a linear system with polynomial entries whose coefficients are from the ring of integers, and the leading terms of its Taylor-Laurent series expansion at z = 0. This algorithm outperforms, in some cases, the previously known algorithms in terms of number of Boolean operations and it is based on the scalar polynomial division algorithm proposed by Bini and Pan.