| 采用牛顿插值的多项式因式分解算法的设计与实现 |
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| 引用本文： | 李治强,龙法宁.采用牛顿插值的多项式因式分解算法的设计与实现[J].计算机时代,2009(11):9-11. |
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| 作者姓名： | 李治强 龙法宁 |
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| 作者单位： | 玉林师范学院数学与计算机科学系,广西,玉林,537000 |
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| 摘 要： | 基于Kronecker所提供的一元多项式因式分解的构造算法、一元整系数多项式在整数环上因式分解理论,利用牛顿向前差分插值算法代替拉格朗日插值算法,把有理域上一元高次多项式因式分解化为在整数环上的因式分解,得到了整数环上的一元多项式因式分解的构造性算法,给出了具体实现过程。
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| 关 键 词： | Newton插值 不可约多项式 因式构造 算法 |
Design and Implementation of Polynomial Factorization Algorithm Using Newton Interpolation |
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| LI Zhi-qiang,LONG Fa-ning.Design and Implementation of Polynomial Factorization Algorithm Using Newton Interpolation[J].Computer Era,2009(11):9-11. |
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| Authors: | LI Zhi-qiang LONG Fa-ning |
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| Affiliation: | (Dept. of Mathematics and Computer Science, Yulin Normal University, Yulin, Guangxi 537000, China) |
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| Abstract: | Based on the constructive algorithm of one-place polynomial factorization provided by Kronecker and the factorization theory of one-place integer coefficients polynomial over integer ring,replacing Lagrange interpolation algorithm with Newton forward difference interpolation algorithm,the factorization of one-place high order polynomial over rational number field is transformed into the factorization over integer ring,then the constructive algorithm and implementation procedure of one-place polynomial factorization over integer ring are obtained. |
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| Keywords: | Newton interpolation irreducible polynomial factor structure algorithm |
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