Implicitization of rational curves and polynomial surfaces
文献类型：期刊论文
| 作者 | Yu, Jian-ping1; Sun, Yong-li2,3 |
| 刊名 | BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
 |
| 出版日期 | 2007-02-01 |
| 卷号 | 44期号:1页码:13-29 |
| 关键词 | implicitization rational curve polynomial surface implicit curve(surface) Grobner bases characteristic set |
| ISSN号 | 1015-8634 |
| 英文摘要 | In this paper, we first present a method for finding the implicit equation of the curve given by rational parametric equations. The method is based on the computation of Grobner bases. Then, another method for implicitization of curve and surface is given. In the case of rational curves, the method proceeds via giving the implicit polynomial f with indeterminate coefficients, substituting the rational expressions for the given curve and surface into the implicit polynomial to yield a rational expression g/h in the parameters. Equating coefficients of g in terms of parameters to 0 to get a system of linear equations in the indeterminate coefficients of polynomial f, and finally solving the linear system, we get all the coefficients of f, and thus we obtain the corresponding implicit equation. In the case of polynomial surfaces, we can similarly as in the case of rational curves obtain its implicit equation. This method is based on characteristic set theory. Some examples will show that our methods are efficient. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000254932000002 |
| 出版者 | KOREAN MATHEMATICAL SOC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/4787]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Yu, Jian-ping |
| 作者单位 | 1.Univ Sci & Technol Beijing, Dept Math & Mech, Beijing 100083, Peoples R China 2.Acad Sinica, Key Lab Math Mechanizat, AMSS, Beijing 100080, Peoples R China 3.Beijing Univ Chem Technol, Dept Math & Comp Sci, Beijing 100029, Peoples R China |
| 推荐引用方式 GB/T 7714 | Yu, Jian-ping,Sun, Yong-li. Implicitization of rational curves and polynomial surfaces[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY,2007,44(1):13-29. |
| APA | Yu, Jian-ping,&Sun, Yong-li.(2007).Implicitization of rational curves and polynomial surfaces.BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY,44(1),13-29. |
| MLA | Yu, Jian-ping,et al."Implicitization of rational curves and polynomial surfaces".BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY 44.1(2007):13-29. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。