Schur-Cohn Sub-transforms of a Polynomial

Considering the exponential growth of the size of the coefficients of the Schur-Cohn transforms of a polynomial, we define new polynomials proportional to the latter and whose coefficients remain small. These Schur-Cohn sub-transforms replace the Schur-Cohn transforms in the computation of the number of roots of a polynomial in a disk. This considerably improves the speed of the Schur-Cohn algorithm.