| 一类半正定多项式的平方和分解及其表达式的自动生成 |
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| 引用本文： | 姚勇,冯勇.一类半正定多项式的平方和分解及其表达式的自动生成[J].计算机学报,2006,29(10):1862-1868. |
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| 作者姓名： | 姚勇 冯勇 |
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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 |
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| 基金项目： | 国家重点基础研究发展计划(973计划) |
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| 摘 要： | 建立了一个把半正定稀疏多项式表为多项式平方和的算法.这一算法依赖于Hilbert第17问题的一系列经典研究结果以及实闭域上量词消去的柱形代数剖分算法.该算法的机器实现为一类代数不等式可读性证明的自动生成提供了一种非常自然的途径.
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| 关 键 词： | 平方和分解 柱形代数剖分 Gram矩阵方法 Hilbert 17问题 |
| 收稿时间： | 2005-03-03 |
| 修稿时间： | 2005-03-032006-03-06 |
The Sum of Squares Decomposition and Automated Production for a Class of Positive Semi-Definite Polynomials |
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| YAO Yong,FENG Yong.The Sum of Squares Decomposition and Automated Production for a Class of Positive Semi-Definite Polynomials[J].Chinese Journal of Computers,2006,29(10):1862-1868. |
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| Authors: | YAO Yong FENG Yong |
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| Affiliation: | Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu 610041 |
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| Abstract: | In this paper, an algorithm is presented for a positive semi-definite sparse polynomials to be decomposed into sum of squares. The algorithm is based on a series of research results of Hilbert 17th problem and Cylindrical Algebraic Decomposition. Its implementation on computer provides a nature approach for the automated production of readable proof for a class of algebraic inequalities. |
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| Keywords: | sum of squares decomposition cylindrical algebraic decomposition Gram matrix method Hilbert 17th problem |
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