Exact Bivariate Polynomial Factorization over Q by Approximation of Roots  

作　　者：FENG Yong WU Wenyuan ZHANG Jingzhong CHEN Jingwei 

机构地区：[1]Chongqing Key Lab of Automated Reasoning and Cognition,Chongqing Institute of Green and Intelligent Technology(CIGIT),Chinese Academy of Sciences

出　　处：《Journal of Systems Science & Complexity》2015年第1期243-260,共18页系统科学与复杂性学报（英文版）

基　　金：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;Chongqing Science and Technology Commission Project under Grant No.cstc2013jjys40001

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.

关 键 词：Factorization of multivariate polynomials interpolation methods minimal polynomial numerical continuation. 

分 类 号：O241.5[理学—计算数学]