Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/58973
題名: 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
作者: 江泰緯
貢獻者: 蔡炎龍
江泰緯
關鍵詞: 熱帶多項式
熱帶曲線
熱帶直線
Tropical Polynomial
Tropical Curve
Tropical Line
日期: 2012
上傳時間: 22-Jul-2013
摘要: 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.
參考文獻: [1] Andreas Gathmann. Tropical algebraic geometry. Jahresber. Deutsch. Math.- Verein., 108(1):3–32, 2006.\n[2] Nathan Grigg. Factorization of tropical polynomials in one and several variables. Honor’s thesis, Brigham Young University, 2007.\n[3] Grigory Mikhalkin. Counting curves via lattice paths in polygons. C. R. Math. Acad. Sci. Paris, 336(8):629–634, 2003.\n[4] Grigory Mikhalkin. Enumerative tropical algebraic geometry in R2. J. Amer. Math. Soc., 18(2):313–377, 2005.\n[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.\n[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.\n[7] David Speyer. Tropical geometry. PhD thesis, UC Berkeley, 2005.\n[8] Yen-Lung Tsai. Working with tropical meromorphic functions of one variable. Taiwanese J. Math., 16(2):691–712, 2012.
描述: 碩士
國立政治大學
應用數學研究所
99751005
101
資料來源: http://thesis.lib.nccu.edu.tw/record/#G0099751005
資料類型: thesis
Appears in Collections:學位論文

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