| IMPLICITIZATION OF PARTIAL DIFFERENTIAL RATIONAL PARAMETRIC EQUATIONS |
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| 引用本文： | Guangwei LI. IMPLICITIZATION OF PARTIAL DIFFERENTIAL RATIONAL PARAMETRIC EQUATIONS[J]. 系统科学与复杂性, 2006, 19(2): 256-265. DOI: 10.1007/s11424-006-0256-4 |
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| 作者姓名： | Guangwei LI |
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| 作者单位： | Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China. |
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| 基金项目： | Research supported by the Foundation of Mathematics Mechanization and Its Applications in Information Technology （65432A0） of China. |
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| 摘 要： | In this paper, we propose algorithms for the following problems in the implicitization of a set of partial differential rational parametric equations P. （1）To find a characteristic set for the implicit prime ideal of P; （2） To find a canonical representation for the image of P; （3）To decide whether the parameters of P are independent, and if not, to re-parameterize P so that the new parametric equations have independent parameters; （4） To compute the inversion maps of P, and as a consequence, to decide whether P is proper.
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| 关 键 词： | 偏微分 参数方程 算法 特征集 |
| 收稿时间： | 2005-03-09 |
| 修稿时间： | 2005-03-09 |
Implicitization of Partial Differential Rational Parametric Equations |
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| Guangwei Li. Implicitization of Partial Differential Rational Parametric Equations[J]. Journal of Systems Science and Complexity, 2006, 19(2): 256-265. DOI: 10.1007/s11424-006-0256-4 |
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| Authors: | Guangwei Li |
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| Affiliation: | (1) Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China |
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| Abstract: | In this paper,we propose algorithms for the following problems in the implicitization of a set of partial differential rational parametric equations P.(1)To find a characteristic set for the implicit prime ideal of P;(2)To find a canonical representation for the image of P;(3)To decide whether the parameters of P are independent,and if not,to re-parameterize P so that the new parametric equations have independent parameters;(4)To compute the inversion maps of P,and as a consequence,to decide whether P is proper. |
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| Keywords: | Implicitization partial differential rational parametric equations rational differential varieties unirational differential varieties. |
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