论文标题
单变量多项式多样性结构的条件
A Condition for Multiplicity Structure of Univariate Polynomials
论文作者
论文摘要
我们考虑在给出不同根数时找到具有给定多重性结构的单变量多项式的条件的问题。众所周知，这种条件可以通过使用重复的参数GCD来写入几个多项式方程的连词和系数中的一个不一致。在本文中，我们提供了一种新的条件，该条件不是基于重复的GCD。此外，结果表明，条件下的多项式数量是最佳的，并且基于重复的GCD的多项式程度小于先前条件下的多项式。
We consider the problem of finding a condition for a univariate polynomial having a given multiplicity structure when the number of distinct roots is given. It is well known that such conditions can be written as conjunctions of several polynomial equations and one inequation in the coefficients, by using repeated parametric gcd's. In this paper, we give a novel condition which is not based on repeated gcd's. Furthermore, it is shown that the number of polynomials in the condition is optimal and the degree of polynomials is smaller than that in the previous condition based on repeated gcd's.
