关于5次对称形式正性的机器判定  

AUTOMATED DECISION OF POSITIVITY OF SYMMETRIC QUINTIC FORMS

作　　者：姚勇[1] 冯勇[1] 

机构地区：[1]中国科学院成都计算机应用研究所,成都610041

出　　处：《系统科学与数学》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.

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.

关 键 词：正根的判别序列 5次对称形式 机器证明 

分 类 号：O178[理学—数学]