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