代数方程在任意圆外根的个数

从复变函数论知,复多项式f(u)=sum from l=0 to n (a_1u~(n-1))在u=u_0点的Taylor展开式是u的恒等式:

THE NUMBER OF ROOTS OF AN ALGEBRAIC EQUATION OUTSIDE ARBITRARY CIRCLES

To find the number of roots of an algebraic equation outside the unit circle, [1] givesa computing method, and [2] then extends the applicable range of this method from the unitcircle to certain kind of circles wth the common center at origin. In this paper anothercomputing method is presented which reduces the number of multiplications from O(n~2)to O(n), and can be used to find the number of roots outside any circle with given centerand radius.