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

作　　者：Hoon Hong Jing Yang 

机构地区：[1]Department of Mathematics,North Carolina State University,Raleigh,NC 27695,USA [2]SMS-HCIC-School of Mathematics and Physics,Center for Applied Mathematics of Guangxi,Guangxi Minzu University,Nanning 530006,China

出　　处：《Science China Mathematics》2024年第8期1911-1932,共22页中国科学（数学）（英文版）

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)。

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.

关 键 词：parametric polynomial complex roots DISCRIMINANT MULTIPLICITY RESULTANT 

分 类 号：O174.14[理学—数学]