A complete discrimination system for polynomials with complex coefficients and its automatic generation  

作　　者：梁松新 张景中 

机构地区：[1]Institute for Educational Softwares, Guangzhou Normal University

出　　处：《Science China(Technological Sciences)》1999年第2期113-128,共16页中国科学（技术科学英文版）

基　　金：Project supported by the "Scale" Plan and the "863" Plan of China.

摘　　要：By establishing a complete discrimination system for polynomials, the problem of complete root classification for polynomials with complex coefficients is utterly solved, furthermore, the algorithm obtained is made into a general program in Maple, which enables the complete discrimination system and complete root classification of a polynomial to be automatically generated by computer, without any human intervention. Besides, by using the automatic generation of root classification, a method to determine the positive definiteness of a polynomial in one or two indeterminates is automatically presented.By establishing a complete discrimination system for polynomials, the problem of complete root classification for polynomials with complex coefficients is utterly solved, furthermore, the algorithm obtained is made into a general program in Maple, which enables the complete discrimination system and complete root classification of a polynomial to be automatically generated by computer, without any human intervention. Besides, by using the automatic generation of root classification, a method to determine the positive definiteness of a polynomial in one or two indeterminates is automatically presented.

关 键 词：DISCRIMINANT sequence revised SIGN LIST root classification complete DISCRIMINATION system positive definiteness. 

分 类 号：O174.14[理学—数学]