Multivariate Discriminant and Iterated Resultant  

作　　者：Jing Jun HAN 

机构地区：[1]School of Mathematical Sciences & Beijing International Center for Mathematical Research,Peking University

出　　处：《Acta Mathematica Sinica,English Series》2016年第6期659-667,共9页数学学报（英文版）

基　　金：Supported by China Scholarship Council

摘　　要：In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form f（xn） with even degree d, if the polynomial is squarefreed after each iteration, the multivariate discriminant A（f） is a factor of the squarefreed iterated resulrant. In fact, we find a factor Hp（f, [x1 , xn]） of the squarefreed iterated resultant, and prove that the multivariate discriminant A（f） is a factor of Hp（f,[x1,... ,xn]）. Moreover, we conjecture that Hp（f, [x1,..., xn]） =△（f） holds for generic form f, and show that it is true for generic trivariate form f（x, y, z）.In this paper, we study the relationship between iterated resultant and multivariate discriminant. We show that, for generic form f（xn） with even degree d, if the polynomial is squarefreed after each iteration, the multivariate discriminant A（f） is a factor of the squarefreed iterated resulrant. In fact, we find a factor Hp（f, [x1 , xn]） of the squarefreed iterated resultant, and prove that the multivariate discriminant A（f） is a factor of Hp（f,[x1,... ,xn]）. Moreover, we conjecture that Hp（f, [x1,..., xn]） =△（f） holds for generic form f, and show that it is true for generic trivariate form f（x, y, z）.

关 键 词：Cylindrical algebraic decomposition semi-definiteness polynomial RESULTANT multivariate discriminant 

分 类 号：O174.14[理学—数学]