中文摘要：

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．

英文摘要：

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.