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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/58973
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dc.contributor.advisor蔡炎龍zh_TW
dc.contributor.author江泰緯zh_TW
dc.creator江泰緯zh_TW
dc.date2012en_US
dc.date.accessioned2013-07-22T09:22:31Z-
dc.date.available2013-07-22T09:22:31Z-
dc.date.issued2013-07-22T09:22:31Z-
dc.identifierG0099751005en_US
dc.identifier.urihttp://nccur.lib.nccu.edu.tw/handle/140.119/58973-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學研究所zh_TW
dc.description99751005zh_TW
dc.description101zh_TW
dc.description.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。zh_TW
dc.description.abstractIn 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.en_US
dc.description.tableofcontentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i\n中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii\nContent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv\n1 Introduction 1\n2 Tropical Algebraic Geometry 3\n2.1 Tropical polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . 3\n2.2 Tropical curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4\n2.3 Tropical factorization . . . . . . . . . . . . . . . . . . . . . . . . . . 15\n3 Recovering Tropical Polynomials from Tropical curves 19\n3.1 Tropical curves of degree two . . . . . . . . . . . . . . . . . . . . . 19\n3.2 Tropical curves of degree three . . . . . . . . . . . . . . . . . . . . . 29\n4 Recovering Tropical Polynomials from Newton Subdivisions 36\n4.1 Newton subdivisions of degree two . . . . . . . . . . . . . . . . . . 36\n4.2 Newton subdivisions of degree three . . . . . . . . . . . . . . . . . . 38\nA All types of maximal Newton subdivisions of degree three 51\nBibliography 55zh_TW
dc.format.extent1447497 bytes-
dc.format.mimetypeapplication/pdf-
dc.language.isoen_US-
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#G0099751005en_US
dc.subject熱帶多項式zh_TW
dc.subject熱帶曲線zh_TW
dc.subject熱帶直線zh_TW
dc.subjectTropical Polynomialen_US
dc.subjectTropical Curveen_US
dc.subjectTropical Lineen_US
dc.title熱帶直線建構二次及三次熱帶曲線之研究zh_TW
dc.titleConstructing Tropical Curves of Degree Two and Three with Tropical Linesen_US
dc.typethesisen
dc.relation.reference[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.zh_TW
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