High performance implementation of factoring multivariate polynomials based on NTL

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High performance implementation of factoring multivariate polynomials based on NTL

Received:2007-12-28 Revised:2008-02-22 Online:2008-06-01 Published:2008-06-01
Contact: Xiao-lin QIN

基于NTL算法库的多元多项式因式分解高效实现

秦小林冯勇李骏

中国科学院成都计算机应用研究所中国科学院成都计算机应用研究所中国科学院成都计算机应用研究所

通讯作者: 秦小林

Abstract

Abstract: Due to the difficulty of factoring multivariate polynomials, a new implementation of high performance named HPFMF was proposed based on NTL and the existence of factorization algorithms. The NTL was introduced and how to apply the library to implement the algorithms of number theory and computer algebra was discussed. The factoring multivariate polynomials was successfully designed and implemented. Experimental results show that the method is more efficient than factor in Maple 11 for multivariate polynomials.

Key words: multivariate, polynomial computation, factorization, NTL

摘要： 针对多元多项式因式分解困难问题，利用现有因式分解算法，提出了一种基于任意精度计算函数库NTL的高效多元多项式因式分解实现方法HPFMP。介绍了NTL算法库,讨论了如何运用该算法库实现高效的数论与计算代数计算；充分利用具备高效、任意精度大整数、实数的计算数论与计算代数的NTL算法库实现了多元多项式因式分解；与现有代数系统Maple11进行了对比测试，实验结果表明，该实现方法具有更高的效率。

关键词: 多变元, 多项式运算, 因式分解, NTL

Xiao-lin QIN Yong FENG Jun LI. High performance implementation of factoring multivariate polynomials based on NTL[J]. Journal of Computer Applications.

秦小林冯勇李骏. 基于NTL算法库的多元多项式因式分解高效实现[J]. 计算机应用.

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