中文摘要：

那结果的消除是解决 multivariate 多项式方程的一个有效方法，是众所周知的。在这份报纸，而不是由可变消除经由变量计算目标 resultants ，作者联合 multivariate 含蓄的方程插值和 multivariate 计算减少的 resultants 的结果的消除，在哪个 multivariate 的技术含蓄的方程插值被一些高概率算法在 multivariate 多项式插值和 univariate 上完成合理函数插值。作为结果的消除的应用，作者在三个著名未解决的组合几何优化问题上说明建议算法。实验证明结果的消除的建议途径比某存在更有效这些困难的问题上的结果的消除方法。

英文摘要：

It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.