Pellet定理的实现
Implementation of Pellet's theorem
AI总结：
针对Pellet定理中辅助多项式正根的存在性判定与计算问题，提出显式存在条件及高效计算方法，并推广至矩阵多项式情形。
摘要：
Pellet定理根据辅助多项式是否存在正根，确定多项式的零点能否被分为两个区域，但未提供验证其条件或计算辅助多项式根的方法。我们推导了这些根存在的显式条件，并在它们存在时提出有效的计算方法。对于矩阵多项式的广义Pellet定理，会出现类似的辅助多项式，且可以用相同方式处理。
英文摘要：
Pellet's theorem determines when the zeros of a polynomial can be separated into two regions, based on the presence or absence of positive roots of an auxiliary polynomial, but does not provide a method to verify its conditions or to compute the roots of the auxiliary polynomial when they exist. We derive an explicit condition for these roots to exist and, when they do, propose efficient ways to compute them. A similar auxiliary polynomial appears for the generalized Pellet theorem for matrix polynomials and it can be treated in the same way.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
