摘要
利用参系数多项式正实根的判别序列，给出了多变元5次对称形式在畔上取非负值的显示判定方法．并以此为依据，导出了一个有效的算法，能够在变元数较多时也可以使用计算机来自动判定．
In this paper, based on the positive root discriminant sequence of polynomial with symbolic coefficients, an explicit criterion of positivity on R^n＋ is presented for symmetric quintic forms, and accordingly an efficient algorithm is derived from the criterion. By means of our algorithm, the positivity of symmetric quintic forms with much more variables can be determined automatically by computer.
出处
《系统科学与数学》
CSCD
北大核心
2008年第3期313-324,共12页
Journal of Systems Science and Mathematical Sciences
基金
国家973计划项目(2004CB318003)
中科院知识创新工程重要方向(KJCX-YW-S02)
国家自然科学基金(10771205)资助.
关键词
正根的判别序列
5次对称形式
机器证明
Positive root discriminant sequence, symmetric quintic forms, automated theorem proving.
