结式与围道积分
Resultants and Contour Integrals
摘要：
结式是描述非线性现象的重要特殊函数。结果式$R_{r_1, ..., r_n}$定义了$n$变量中$r_1, ..., r_n$次数的$n$齐次多项式系统的可解性条件，就像行列式对线性方程组所做的那样。不幸的是，当变量的数量很大时，缺乏方便的结式公式。本文利用柯西围道积分得到了一个结式的多项式公式，希望在应用中有所帮助。
英文摘要：
Resultants are important special functions used in description of non-linear phenomena. Resultant $R_{r_1, ..., r_n}$ defines a condition of solvability for a system of $n$ homogeneous polynomials of degrees $r_1, ..., r_n$ in $n$ variables, just in the same way as determinant does for a system of linear equations. Unfortunately, there is a lack of convenient formulas for resultants when the number of variables is large. In this paper we use Cauchy contour integrals to obtain a polynomial formula for resultants, which is expected to be useful in applications.
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。
