中文摘要：

研究了多元多项式系统的Sylvester结式、Dixon结式以及混合CayleySylvester结式之间是否存在特定关系的问题,利用构造混合结式矩阵的方法 证明了在满足一定的条件下,多元多项式系统的这些结式的绝对值都相等.而对于一般的多元多项式系统,也证实了上述这些结式之间仅仅相差一个因子,推广了两变元多项式系统的结论.

英文摘要：

The paper study the relationship among the Sylvester, Dixon and Mixed Cayley- Sylvester resultant. Based on the construction method of hybrid resultant matrix, we proves that the resultant of these three resultant are only up to a sign for a class of polynomial system, and for a general polynomial system, they only difference a factor, which extends the result of [17].