| 代数数极小多项式的近似重构 |
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| 引用本文： | 陈经纬,冯勇,秦小林,张景中.代数数极小多项式的近似重构[J].系统科学与数学,2011,31(8):903-912. |
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| 作者姓名： | 陈经纬 冯勇 秦小林 张景中 |
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| 作者单位： | 中国科学院重庆绿色智能技术研究院,重庆401122;中科院成都计算机应用研究所,成都610041;中国科学院研究生院,北京100049 |
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| 基金项目： | 国家973计划资助(2011CB302400); 国家自然科学基金资助(10771205); 中国科学院知识创新基金(KJCX2-YW-S02)资助;中国科学院西部之光项目资助 |
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| 摘 要： | 给出了代数数极小多项式近似重构的误差控制条件,进而基于同步整数关系探测算法SIRD,得到一个从代数数近似值重构其准确极小多项式的完备的新算法,从而将“采用近似计算获得准确值”这一思想的适用范围从有理数扩展到代数数.
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| 关 键 词： | 同步整数关系 代数数 极小多项式 |
RECONSTRUCTING MINIMAL POLYNOMIAL FROM APPROXIMATE ALGEBRAIC NUMBERS |
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| CHEN Jingwei
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FENG Yong
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QIN Xiaolin
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ZHANG Jingzhong.RECONSTRUCTING MINIMAL POLYNOMIAL FROM APPROXIMATE ALGEBRAIC NUMBERS[J].Journal of Systems Science and Mathematical Sciences,2011,31(8):903-912. |
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| Authors: | CHEN Jingwei FENG Yong QIN Xiaolin ZHANG Jingzhong |
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| Institution: | CHEN Jingwei,FENG Yong,QIN Xiaolin ZHANG Jingzhong (Chongqing Institute of Green and Intelligent Technology,Chinese Academy of Sciences,Chongqing 401122,Chengdu Institute of Computer Application,Chengdu 610041,Graduate University,Beijing 100049) |
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| Abstract: | This paper gives an error condition for reconstructing the minimal polynomial of an algebraic number from its approximation,and then present a newly complete algorithm to obtain the exact minimal polynomial from an approximate value by simultaneous integer relations detection.This work extends the applicable area ofobtaining exact value by approximate computationsfrom the rational to algebraic numbers. |
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| Keywords: | Simultaneous integer relation algebraic number minimal polynomial |
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