Sylvester's Double Sums：一般情况
Sylvester's Double Sums: the general case
摘要：
在1853年西尔维斯特介绍了一个家庭的双和表达式两个有限集的indeterminates和表明，一些成员的家庭基本上是多项式subresultants的首一多项式与这些集。一个问题自然出现了：家庭的其他成员是什么？本文对这一问题提供了一个完整的答案。我们为回答这个问题而开发的技术被证明是足够普遍的，可以描述家庭的所有成员，提供了一个统一的方法。
英文摘要：
In 1853 Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. A question naturally arises: What are the other members of the family? This paper provides a complete answer to this question. The technique that we developed to answer the question turns out to be general enough to charactise all members of the family, providing a uniform method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
