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Exact bivariate polynomial factorization over Q by approximation of roots
  • ISSN号：1009-6124
  • 期刊名称：Journal of Systems Science and Complexity
  • 时间：0
  • 页码：-
  • 分类：O241.6[理学—计算数学;理学—数学] O151.2[理学—数学;理学—基础数学]
  • 作者机构：[1]Chongqing Key Lab of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology ( CIGIT), Chinese Academy of Sciences, Chongqing 400714, China.
  • 相关基金：This work was partly supported by the National Natural Science Foundation of China under Grant Nos. 91118001 and 11170153, the National Key Basic Research Project of China under Grant No. 2011CB302400, and Chongqing Science and Technology Commission Project under Grant No. cstc2013jjys40001.
  • 相关项目：基于同伦方法的代数方程并行计算的理论、实现及其应用
作者： Yong Feng|Wenyuan Wu|Jinzhong Zhang|Jingwei Chen|
关键词： 二元多项式, 因式分解, 高级编程语言, 逼近, 根系, 符号计算, 数值方法, 数值计算, Factorization of multivariate polynomials, interpolation methods, minimal polynomial, numerical continuation.
中文摘要：

Factorization of polynomials is one of the foundations of symbolic computation.Its applications arise in numerous branches of mathematics and other sciences.However,the present advanced programming languages such as C++ and J++,do not support symbolic computation directly.Hence,it leads to difficulties in applying factorization in engineering fields.In this paper,the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients.The proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision Library.In addition,the numerical computation part often only requires double precision and is easily parallelizable.

英文摘要：

Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C＋＋ and J＋＋, do not support symbolic computation directly. Hence, it leads to difficulties in applying factorization in engineering fields. In this paper, the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with ratio- nal coefficients. The proposed method can be directly implemented in efficient programming language such C＋＋ together with the GNU Multiple-Precision Library. In addition, the numerical computation part often only requires double precision and is easily parallelizable.

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期刊信息
  • 《系统科学与复杂性学报：英文版》
  • 主管单位:中国科学院
  • 主办单位:中国科学院系统科学研究所
  • 主编：
  • 地址：北京东黄城根北街16号
  • 邮编：100080
  • 邮箱：
  • 电话：010-62541831 62541834
  • 国际标准刊号：ISSN：1009-6124
  • 国内统一刊号：ISSN：11-4543/O1
  • 邮发代号:82-545
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,美国工程索引,美国科学引文索引（扩展库）,英国科学文摘数据库
  • 被引量:125