论文标题
牛顿的几个单变量多项式的次级反应者
Subresultants of Several Univariate Polynomials in Newton Basis
论文作者
论文摘要
在本文中，我们考虑了在牛顿以几个单变量多项式为基础的多项式制定的问题。要求所得的替代多项式以与输入多项式中使用的牛顿相同的基础表达。为了解决问题，我们在牛顿多项式的伴侣矩阵的帮助下设计了一个特定的矩阵。同时，在牛顿基础上将确定性多项式在功率基础上的决定性多项式的概念扩展到了。事实证明，特殊设计的矩阵的广义决定性多项式为牛顿提供了新公式的多项式，这在牛顿的基础上等效于势力基础上的多项式。此外，我们还展示了新公式在设计一种基础保留方法来计算几种牛顿多项式的GCD方面的应用。
In this paper, we consider the problem of formulating the subresultant polynomials for several univariate polynomials in Newton basis. It is required that the resulting subresultant polynomials be expressed in the same Newton basis as that used in the input polynomials. To solve the problem, we devise a particular matrix with the help of the companion matrix of a polynomial in Newton basis. Meanwhile, the concept of determinantal polynomial in power basis for formulating subresultant polynomials is extended to that in Newton basis. It is proved that the generalized determinantal polynomial of the specially designed matrix provides a new formula for the subresultant polynomial in Newton basis, which is equivalent to the subresultant polynomial in power basis. Furthermore, we show an application of the new formula in devising a basis-preserving method for computing the gcd of several Newton polynomials.
