A Modular Method to Compute the Rational Univariate Representation of Zero-dimensional Ideals
A Modular Method to Compute the Rational Univariate Representation of Zero-dimensional Ideals
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DOI：
10.1006/jsco.1999.0275
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发表时间：
1999-07
期刊：
影响因子：
--
通讯作者：
M. Noro;K. Yokoyama
中科院分区：
文献类型：
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作者：
M. Noro;K. Yokoyama
为了给出零维理想I的零点的有效可计算表示，Rouillier（1996）引入了有理单变量表示（RUR）作为Alonso等人（1996）提出的广义形状引理（GSL）的扩展。在本文中，我们提出了一种新的方法来计算RUR的根式I，并报告其实际实施。在新的方法中，RUR的根的I的计算有效地应用模块技术来解决线性方程组。该方法的性能通过实际实验进行了检验。我们还讨论了它的理论效率。
To give an efficiently computable representation of the zeros of a zero-dimensional ideal I, Rouillier (1996) introduced the rational univariate representation (RUR) as an extension of the generalized shape lemma (GSL) proposed by Alonso et al. (1996). In this paper, we propose a new method to compute the RUR of the radical of I, and report on its practical implementation. In the new method, the RUR of the radical of I is computed efficiently by applying modular techniques to solving the systems of linear equations. The performance of the method is examined by practical experiments. We also discuss its theoretical efficiency.