零维代数簇短系数有理单变量表示的可分元计算

针对零维多项式系统中Rouillier计算可分元的算法使其相应的有理单变量表示中整系数过长的问题, 提出一种改进的可分元选取算法, 新算法通过逐步确定坐标可分元得以实现. 结果表明, 较之Rouillier算法, 新算法选取可分元对应的有理单变量表示中整系数的长度更短, 且两算法具有几乎相同的平均复杂度.

Separating Element Computation for the Rational Univariate Representation with Short Coefficients in Zero-dimensional Algebraic Varieties

Since the separable element algorithm of the rational univariate representation(RUR) for solving zero-dimensional systems presented by Rouillier makes the size of the coefficients in this representation too long,an improved algorithm for finding separating elements is presented in this paper,which is implemented by confirming the separating element of the coordinates step by step.Results show that the size of the coefficients in the RUR corresponding to the separating element selected by the new algorithm i...