Newton 基下若干一元多项式的子结式
Subresultants of Several Univariate Polynomials in Newton Basis
AI总结：
针对多个 Newton 基一元多项式，论文利用友矩阵构造特殊矩阵并推广行列式多项式，给出保持 Newton 基的子结式公式，并用于基保持的 gcd 计算。
摘要：
本文研究在 Newton 基下为若干一元多项式建立子结式多项式公式的问题。该问题要求所得子结式多项式必须以与输入多项式相同的 Newton 基表示。为解决此问题，作者借助一个 Newton 基下多项式的友矩阵，构造了一个特殊矩阵。同时，将用于表述子结式多项式的幂基行列式多项式概念推广到 Newton 基。文中证明，该特殊设计矩阵的广义行列式多项式给出了 Newton 基下子结式多项式的新公式，并且它等价于幂基下的子结式多项式。此外，作者展示了该新公式在设计保持基的方法以计算若干 Newton 多项式最大公因式中的应用。
英文摘要：
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.
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。
