政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/58973

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/58973

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/58973

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/58973

Title:	熱帶直線建構二次及三次熱帶曲線之研究 Constructing Tropical Curves of Degree Two and Three with Tropical Lines
Authors:	江泰緯
Contributors:	蔡炎龍江泰緯
Keywords:	熱帶多項式熱帶曲線熱帶直線 Tropical Polynomial Tropical Curve Tropical Line
Date:	2012
Issue Date:	2013-07-22 17:22:31 (UTC+8)
Abstract:	在這篇論文裡，我們找到了一個方法來反推出對應到某個熱帶曲線的熱帶多項式。在給定一個二次或三次的熱帶曲線之後，我們利用熱帶直線來找出此熱帶曲線的多項式。再來，若給定一個二次或三次的牛頓細分(Newton subdivision) ，我們也能找出能對應到它的熱帶多項式。 In this thesis, we develop an algorithm to recover tropical polynomials from plane tropical curves of degree two and three. We use tropical lines to approach a given tropical curve. Furthermore, we also give another algorithm to recover tropical polynomials from a (maximal) Newton subdivision of degree two and three.
Reference:	[1] Andreas Gathmann. Tropical algebraic geometry. Jahresber. Deutsch. Math.- Verein., 108(1):3–32, 2006. [2] Nathan Grigg. Factorization of tropical polynomials in one and several variables. Honor’s thesis, Brigham Young University, 2007. [3] Grigory Mikhalkin. Counting curves via lattice paths in polygons. C. R. Math. Acad. Sci. Paris, 336(8):629–634, 2003. [4] Grigory Mikhalkin. Enumerative tropical algebraic geometry in R2. J. Amer. Math. Soc., 18(2):313–377, 2005. [5] Jürgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald. 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. [6] Imre Simon. Recognizable sets with multiplicities in the tropical semiring. In Michal Chytil, Ladislav Janiga, and Václav Koubek, editors, MFCS, volume 324 of Lecture Notes in Computer Science, pages 107–120. Springer, 1988. [7] David Speyer. Tropical geometry. PhD thesis, UC Berkeley, 2005. [8] Yen-Lung Tsai. Working with tropical meromorphic functions of one variable. Taiwanese J. Math., 16(2):691–712, 2012.
Description:	碩士國立政治大學應用數學研究所 99751005 101
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0099751005
Data Type:	thesis
Appears in Collections:	[Department of Mathematical Sciences] Theses

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