鉴别的确定Log Det =生成物的跟踪Log
Analogue of the identity Log Det = Trace Log for resultants
摘要：
结果式$R_{r_1, ..., r_n}$定义了一个以$n$为变量的次数为$r_1, ..., r_n$的$n$齐次多项式系统的可解性条件，就像行列式定义线性方程组一样。正因为如此，结式是即将到来的非线性物理学的重要特殊函数，并开始在与弦论相关的各种主题中发挥作用。不幸的是，当变量的数量很大时，缺乏方便的结式公式。为了解决这个问题，我们将著名的恒等式Log Det = Trace Log从行列式推广到结式。广义恒等式允许获得多维结式的显式多项式公式：对于任何数量的变量，结式由舒尔多项式给出。我们还给出了几个积分表示的结式，以及求和路径表示。
英文摘要：
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. Because of this, resultants are important special functions of upcoming non-linear physics and begin to play a role in various topics related to string theory. Unfortunately, there is a lack of convenient formulas for resultants when the number of variables is large. To cure this problem, we generalize the well-known identity Log Det = Trace Log from determinants to resultants. The generalized identity allows to obtain explicit polynomial formulas for multidimensional resultants: for any number of variables, resultant is given by a Schur polynomial. We also give several integral representations for resultants, as well as a sum-over-paths representation.
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