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 in...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.展开更多
基金Project supported by the "Scale" Plan and the "863" Plan of China.
文摘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.
