The Second Discriminant of a Univariate Polynomial
副标题：
时间：2018-07-02 来源：数学机械化重点实验室
题目： The Second Discriminant of a Univariate Polynomial
报告人： 杨静 (广西民族大学)
时间地点： 2018.07.05 15:00pm N205
摘要： In this talk, we define the second discriminant D2D2 of a univariate polynomial ff of degree greater than 22 as the product of the linear forms 22 rk？ri？rjrk？ri？rj for all triples of roots ri,rk,rjri,rk,rj of ff with j>ij>i and j≠k,k≠ij≠k,k≠i. D2D2 vanishes if and only if ff has at least one root which is equal to the average of two other roots. We show that D2D2 can be expressed as the resultant of ff and a determinant formed with the derivatives of ff, establishing a new relation between the roots and the coefficients of ff. We prove several notable properties and present an application of D2D2.
This work is jointly done with Professor Dongming Wang.
