On Approximate Irreducibility of Polynomials in Several Variables

机译：关于多个变量的多项式的近似不可约性

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We study the problem of bounding a polynomial away from polynomials which are absolutely irreducible. Such separation bounds are useful for testing whether a numerical polynomial is absolutely irreducible, given a certain tolerance on its coefficients. Using an absolute irreducibility criterion due to Ruppert, we are able to find useful separation bounds, in several norms, for bivariate polynomials. We also use Rup-pert's criterion to derive new, more effective Noether forms for polynomials of arbitrarily many variables. These forms lead to small separation bounds for polynomials of arbitrarily many variables.

机译：我们研究了将多项式与绝对不可约的多项式定界的问题。在给定其系数一定的容忍度的情况下，这种分离界限可用于测试数值多项式是否绝对不可约。使用基于Ruppert的绝对不可约性准则，我们能够在几个范数中找到双变量多项式的有用分离界限。我们还使用Rup-pert准则为任意多个变量的多项式推导新的，更有效的Noether形式。这些形式导致任意多个变量的多项式的较小分隔界。

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来源
《International Symposium on Symbolic and Algebraic Computation Aug 3-6, 2003 Philadelphia, Pennsylvania, USA》|2003年|p.161-168|共8页
会议地点 Philadelphia PA(US);Philadelphia PA(US)
作者
Erich Kaltofen; John May;
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作者单位

Department of Mathematics North Carolina State University Raleigh, North Carolina 27695-8205 USA;

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会议组织
原文格式 PDF
正文语种 eng
中图分类 O2;
关键词
multivariate polynomial factorization; absolute irreducibility; radius of irreducibility; approximate factorization; symbolicumeric hybrid method; effective noether irreducibility forms;

机译：多元多项式分解;绝对不可约性;不可约半径;近似因式分解;符号/数值混合法;有效的Noether不可约形式;

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1. Irreducible Multivariate Polynomials Obtained from Polynomials in Fewer Variables, II [J] . Alexandru Zaharescu, Nicolae Ciprian Bonciocat Proceedings of the Indian Academy of Sciences. Mathematical sciences . 2011,第2期

机译：从较少变量的多项式中获得的不可约多元多项式，II
2. Number of irreducible polynomials and pairs of relatively prime polynomials in several variables over finite fields [J] . Xiang-dong Hou, Gary L. Mullen Finite fields and their applications . 2009,第3期

机译：有限域上几个变量中不可约多项式的数量和相对素多项式对
3. Irreducible multivariate polynomials obtained from polynomials in fewer variables [J] . Bonciocat NC, Zaharescu A Journal of pure and applied algebra . 2008,第10期

机译：从较少变量的多项式获得的不可约多元多项式
4. On approximate irreducibility of polynomials in several variables [C] . Erich Kaltofen, John May International symposium on Symbolic and algebraic computation . 2003

机译：关于多项式的多项式的近似不可约性
5. Approximate factorization of polynomials in many variables and other problems in approximate algebra via singular value decomposition methods. [D] . May, John P. 2005

机译：通过奇异值分解方法，可对多项式中多项式的近似因式分解以及近似代数中的其他问题。
6. On the Intersections of Irreducible Components in the Manifold of a Differential Polynomial [O] . J. F. Ritt 1940

机译：关于微分多项式流形中不可约成分的交点
7. On Approximate Irreducibility of Polynomials in Several Variables [O] . Erich Kaltofen, John May 100

机译：关于多个变量的多项式的近似不可约性

On Approximate Irreducibility of Polynomials in Several Variables

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