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| Title: | 熱帶圓錐曲線之研究
On Tropical Conics |
| Authors: | 黃馨儀 |
| Contributors: | 蔡炎龍
黃馨儀 |
| Keywords: | 熱帶幾何
熱帶圓錐曲線
二元二次多項式
熱帶直線 |
| Date: | 2010 |
| Issue Date: | 2013-09-04 15:16:08 (UTC+8) |
| Abstract: | 本篇文章主要研究熱帶幾何之圓錐曲線，即二元二次多項式""根``的圖形。在文章中，我們以二元二次多項式係數關係做曲線的分類，歸納出20種熱帶圓錐曲線圖形，並證明此為完整的熱帶圓錐曲線之分類。然後，我們進一步討論如何調整二元二次多項式係數使圖形平移。最後，提出以熱帶直線輔助熱帶圓錐曲線快速作圖的方式。
The purpose of the present study is to investigate conics -the graphs of the ""roots`` of quadratic polynomial- in tropical geometry. First, we induct and classify twenty types of tropical conics based on the relation between the coefficients and roots in quadratic polynomial. Second, evidences are provided to prove the classification thorough and intact. Then, we further discuss how to modify the quadratic polynomial in order to translate the graphs. Finally, suggestion about how to use tropical line to assist the graphing of tropical conics more efficiently is provided. |
| Reference: | Kasie G.Farlow. Max-plus algebra. Master`s thesis,Blacksburg,Virginia,2009.
S. Gao and A. Lauder. Decomposition of polytopes and polynomials. Discrete and Computational Geometry,26:89-94,2001.
Andreas Gathmann. Tropical algebraic geometry. Jahresber. Deutsch. Math.-Verein.,108(1):3-32,2006.
Grigory Mikhalkin. Tropical geometry and its applications. In International Congress of Mathematicians. Vol. II,pages 827-852. Eur. Math. Soc.,Zurich,2006.
Jurgen Richter-Gebert, Brend Sturmfels,and Thorsten Theovald. First steps in tropical geometry. In Idempotent mathematics and mathematical physics,volume 377 of Contemp.Math.,pages 289-317. Amer. Math. Soc.,Providence,RI,2005. |
| Description: | 碩士
國立政治大學
應用數學系數學教學碩士在職專班
97972011
99 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0097972011 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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| 201101.pdf | | 4851Kb | Adobe PDF2 | 521 | View/Open |
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