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==The Lehmer method==
The Schur–Cohn test described below allows to determine if a polynomial has no roots in the unit disk and in some cases to determine the exact number of roots. The method proposed by Lehmer test for the presence of roots of a polynomial <math>p(z)</math> on a collection of disks <math>D(c,\rho)</math> in the complex plane by applying the Schur–Cohn test to the shifted and scaled polynomial <math>p(c+\rho z).</math>
▲The Schur–Cohn test described below allows to determine if a polynomial has no roots in the unit disk and in some cases to determine the exact number of roots. The method proposed by Lehmer test for the presence of roots of a polynomial <math>p(z)</math> on a collection of disks <math>D(c,\rho)</math> in the complex plane by applying the Schur–Cohn test to the shifted and scaled polynomial <math>p(c+\rho z)</math>.
Starting with ''c''=0 and ρ=1, the radius in increased or decreased by factors of 2 until the annulus <math>\rho\le|z|\le2\rho</math> is found to contain roots. Then the method is recursively applied to the 8 disks with center <math>c_k=\frac53\rho e^{i\frac{k\pi}4}</math>, <math>k=0,1,\dots,7</math> and initial radius <math>\rho</math> (originally <math>\frac56\rho</math>, which is slightly too small to cover the full annulus).
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