探討多項式的判別式及其圖形的關係

Discussion of several polynomial discriminants and their graphs

陳冠中(Guan-Zhong Chen)

指導教授 ： 王藹農

國立臺灣大學/理學院/應用數學科學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201703303

摘要

本篇論文主要是要探討多項式函數的判別式，與判別式的圖形，藉由其圖形來暸解多項式的根的分佈情形，並說明幾個求解多項式判別式的方法。

關鍵字

多項式 ； 判別式 ； 圖形

並列摘要

In this paper, we will be discussing discriminants of polynomials as well as their graphs, using graphs of other functions to understand root distributions of polynomial functions. We will also explain a few methods to solve for polynomial discriminants.

並列關鍵字

polynomial ； discriminants ； graph

參考文獻

[1] Takeshi Sasaki and Masaaki Yoshida, Surface Singularities Appeared in the Hyperbolic Schwarz Map for the Hypergeometric Equation, Vol. 283, 247-272 (2009).

[4] Oleg N. Kirillov1 and Michael L. Overton Robust stability at the Swallowtail singularity, published: 03 December 2013, doi:10.3389/fphy.2013.00024.

[2] 張海潮, 三次多項式圖形的基本探討, 數學傳播 32 卷 1 期, pp. 54-59.

[3] Viktor Prasolov and Yuri Solovyev, Elliptic Functions and Elliptic Integrals. ams, 1997.