Parametric"non-nested"discriminants for multiplicities of univariate polynomials

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外文摘要：We consider the problem of complex root classification,i.e.,finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots.It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients.Those polynomials in the coefficients are called discriminants for multiplicities.It is also known that discriminants can be obtained using repeated parametric greatest common divisors.The resulting discriminants are usually nested determinants,i.e.,determinants of matrices whose entries are determinants,and so on.In this paper,we give a new type of discriminant that is not based on repeated greatest common divisors.The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.

外文关键词：

parametric polynomialcomplex rootsdiscriminantmultiplicityresultant

作者：

Hoon Hong、Jing Yang

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作者单位：

Department of Mathematics,North Carolina State University,Raleigh,NC 27695,USA

SMS-HCIC-School of Mathematics and Physics,Center for Applied Mathematics of Guangxi,Guangxi Minzu University,Nanning 530006,China

基金：

National Science FoundationsNational Science FoundationsNational Natural Science Foundation of ChinaNational Natural Science Foundation of China

项目编号：

221246118133401226101011801101

出版年：

2024

DOI：

10.1007/s11425-023-2143-3

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(8)