Towards more accurate separation bounds of empirical polynomials
Towards more accurate separation bounds of empirical polynomials
复制标题
迈向更准确的经验多项式分离界限
DOI：
10.1145/1060328.1060330
复制
发表时间：
2004
期刊：
影响因子：
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通讯作者：
Kosaku Nagasaka
中科院分区：
文献类型：
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作者：
Kosaku Nagasaka
我们研究绝对不可约多项式的边界问题，远离非绝对不可约多项式。这些分离界限可用于测试经验多项式对于其系数的给定公差或误差界限是否绝对不可约。卡尔托芬和梅研究了一种方法，该方法使用鲁珀特提出的绝对不可约性准则来找到适用的分离界限。在本文中，我们研究了他们的方法的一些改进，通过这些改进，我们能够为二元多项式找到更准确的分离界限。
We study the problem of bounding a polynomial which is absolutely irreducible, away from polynomials which are not absolutely irreducible. These separation bounds are useful for testing whether an empirical polynomial is absolutely irreducible or not, for the given tolerance or error bound of its coefficients. Kaltofen and May studied a method which finds applicable separation bounds using an absolute irreducibility criterion due to Ruppert. In this paper, we study some improvements on their method, by which we are able to find more accurate separation bounds, for bivariate polynomials.