Bounds on Polynomials

Abstract

The more sophisticated polynomial algorithms discussed in the following chapters require estimates on the size of the coefficients of factors of a polynomial. The most natural of these results give bounds on the size of linear factors of univariate polynomials,i.e., bounds on the size of zeroes of univariate polynomials. These bounds are very useful when computing the polynomial zeroes numerically. The linear factor estimates can be extended to give bounds on the size of larger degree factors. These estimates are used in calculations of the GCD’s and factorizations of polynomials over the integers.