Implicitization of rational curves and polynomial surfaces

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	Implicitization of rational curves and polynomial surfaces
	Yu, Jian-ping 1; Sun, Yong-li 2,3
	2007-02-01
发表期刊	BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
ISSN	1015-8634
卷号	44 期号:1 页码:13-29
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.
关键词	implicitization rational curve polynomial surface implicit curve(surface) Grobner bases characteristic set
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000254932000002
出版者	KOREAN MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4788
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.