低維度代數曲線之Puiseux展開式之計算

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Title:	低維度代數曲線之Puiseux展開式之計算
Other Titles:	Computation of low dimensional Puiseux expansion of algebraic curves
Authors:	林士翔;Lin, Shi-Shung
Contributors:	淡江大學數學學系碩士班吳孟年;Wu, Meng-Nien
Keywords:	Puiseux 展開式;代數曲線;Puiseux expansion;algebraic curve
Date:	2011
Issue Date:	2011-12-28 18:13:43 (UTC+8)
Abstract:	若方程式 f(x,y) = a0(x)+a1(x)y+a2(x)y2+...+an(x)yn = 0, ai(x)∈C(x)∗, 我們要找出解 y(x) = x^{r1}(c1 + x^{r2}(c2 + x^{r3}(c3 + ...))), r2,r3,r4,...> 0, 並討論 y(x) 分支的情形以及何時會出現 {r1,r2,r3,...} 的最小公分母, 最後再算 y(x) 的收斂範圍。 If we have an equation that is f(x,y) = a0(x)+a1(x)y+a2(x)y2+...+an(x)yn = 0, ai(x)∈C(x)∗, we want to find solutions which are of the form x^{r1}(c1 + x^{r2}(c2 + x^{r3}(c3 + ...))), r2,r3,r4,...> 0, and we will discuss the bifurcation of y(x) and when the lowest common denominator of {r1,r2,r3,...} appears. Finally, we compute the range of convergence of y(x) expansion.
Appears in Collections:	[Graduate Institute & Department of Mathematics] Thesis

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