| 整系数多元多项式快速分解（1）——初始化算法 |
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| 引用本文： | 黄文奇,陈亮.整系数多元多项式快速分解（1）——初始化算法[J].应用数学,1996,9(3):364-368. |
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| 作者姓名： | 黄文奇 陈亮 |
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| 作者单位： | 华中理工大学计算机系 |
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| 基金项目： | 国家自然科学基金,武汉大学软件工程国家重点实验室及国家“八六三”高科技部分资助 |
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| 摘 要： | 对于一般形式的整系数多元多项式Ｆ（ｘ１，ｘ２，…，ｘｔ）进行因式分解，通常总是首先选定一个变量，比如Ｘｔ，作为主变量，将下的因式分解转化为对关子Ｘｔ首１的，并使Ｆ＊（０，…，０，Ｘｔ）无重因式的多元多项式Ｆ＊进行分解．本文给出了这种转化的一个新算法．由此算法而得到的Ｆ＊之规模要明显地小于以前的方法的结果，从而使得进一步分解Ｆ＊以得到Ｆ的因式分解的计算时间复杂可以大大地降低．
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| 关 键 词： | 多元多项式 因式分解 算法 时间复杂度 |
A preprocessing algorithm for fast factoring multioariatepolynomials with integral coefficients |
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| Huang wenqi,Chen Liang and Yu Xinguo.A preprocessing algorithm for fast factoring multioariatepolynomials with integral coefficients[J].Mathematica Applicata,1996,9(3):364-368. |
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| Authors: | Huang wenqi Chen Liang and Yu Xinguo |
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| Institution: | Huajhong University of Scienceand Technology |
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| Abstract: | For factoring a multivariate polynomial F (x1, x2, .., xt), We usually select a avariable,Say xt, as the principal variable,and then translate the problem of factoring F into that of factoring a certain F*. The F * (x1,x2, ..',xt) satisfies that its first coefficient with respect to xt is 1 and F* (0, ..,0,xt) has no repeated factors. A new translating algorithm is proposed in this paper. The F* obtained is much Shorter than that obtained by previous methods. |
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| Keywords: | Multivariate Polynomial with integral coefficients Factorization Algorithm Complexity |
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