| 一类根式不等式的有理化算法与机器证明 |
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| 引用本文： | 徐嘉,姚勇. 一类根式不等式的有理化算法与机器证明[J]. 计算机学报, 2008, 31(1): 24-31 |
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| 作者姓名： | 徐嘉 姚勇 |
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| 作者单位： | 中国科学院成都计算机应用研究所,成都,610041;中国科学院成都计算机应用研究所,成都,610041 |
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| 基金项目： | 国家“九七三”重点基础研究发展规划项目基金(2004CB318003)，中国科学院知识创新工程重要方向项目(KJCX-YW-S02)资助 |
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| 摘 要： | 文中讨论了一类根式不等式的有理等价问题.证明了这类根式不等式可等价转化为一组有理不等式.建立了一个算法RFD,并用Maple编程实现.对一个给定的这类根式不等式,RFD可自动快速地产生一组有理等价不等式.将RFD算法和差分代换方法相结合,给出了一大类具有相当难度的几何不等式的机器证明.此前该课题仅有的工作是杨路关于二次根式的结果.
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| 关 键 词： | 根式不等式 有理化 不等式机器证明 差分代换 |
| 收稿时间： | 2006-10-19 |
| 修稿时间： | 2007-09-12 |
Rationalizing Algorithm and Automated Proving for a Class of Inequalities Involving Radicals |
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| XU Jia,YAO Yong. Rationalizing Algorithm and Automated Proving for a Class of Inequalities Involving Radicals[J]. Chinese Journal of Computers, 2008, 31(1): 24-31 |
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| Authors: | XU Jia YAO Yong |
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| Abstract: | A theory is developed to transform a class of inequalities involving radicals to a set of rational inequalities.And this theory is implemented by a Maple program named "RFD" which can efficiently produce a set of rational inequalities that equal to the original inequalities involving radicals.Combining RFD with SDS,the program can automatically prove an extensive class of geometric inequalities involving radicals. |
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| Keywords: | inequalities invomving radicals rationalization automated proving SDS |
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