Parametric“non-nested”discriminants for multiplicities of univariate polynomials

作     者：Hoon Hong Jing Yang 

作者机构：Department of MathematicsNorth Carolina State UniversityRaleighNC 27695USA SMS-HCIC-School of Mathematics and PhysicsCenter for Applied Mathematics of GuangxiGuangxi Minzu UniversityNanning 530006China 

出 版 物：《Science China Mathematics》 (中国科学（数学）（英文版）)

年 卷 期：2024年第67卷第8期

页      面：1911-1932页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by U.S.National Science Foundations(Grant Nos.2212461 and 1813340) supported by National Natural Science Foundation of China(Grant Nos.12261010 and 11801101) 

主　　题：parametric polynomial complex roots discriminant multiplicity resultant 

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 *** is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the *** polynomials in the coefficients are called discriminants for *** is also known that discriminants can be obtained using repeated parametric greatest common *** resulting discriminants are usually nested determinants,i.e.,determinants of matrices whose entries are determinants,and so *** this paper,we give a new type of discriminant that is not based on repeated greatest common *** new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.