The second discriminant of a univariate polynomial

作     者：Dongming Wang Jing Yang Dongrning Wang;Jing Yang

作者机构：BDBCLMIB and School of Mathematics and Systems ScienceBeihang UniversityBeijing 100191China SMSHCICGuangxi University for NationalitiesNanning 530006China Centre National de la Recherche ScientifiqueParis 75794France 

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

年 卷 期：2021年第64卷第6期

页      面：1157-1180页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61702025 and 11801101) the Special Fund for Guangxi Bagui Scholar Project Guangxi Science and Technology Program(Grant No.2017AD23056) the Startup Foundation for Advanced Talents in Guangxi University for Nationalities(Grant No.2015MDQD018) 

主　　题：determinant discriminant polynomial ideal resultant root configuration 

摘      要：We define the second discriminant D_(2)of a univariate polynomial f of degree greater than 2 as the product of the linear forms 2r_(k)-r_(i)-r_(j)for all triples of roots r_(i),r_(k),r_(j)of f with ij and j≠k,k≠i.D_(2)vanishes if and only if f has at least one root which is equal to the average of two other *** show that D_(2)can be expressed as the resultant of f and a determinant formed with the derivatives of f,establishing a new relation between the roots and the coefficients of *** prove several notable properties and present an application of D_(2).