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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 17:22:31 (UTC+8)
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.
[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.
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
dc.contributor.advisor 蔡炎龍zh_TW
dc.contributor.author (Authors) 江泰緯zh_TW
dc.creator (作者) 江泰緯zh_TW
dc.date (日期) 2012en_US
dc.date.accessioned 22-Jul-2013 17:22:31 (UTC+8)-
dc.date.available 22-Jul-2013 17:22:31 (UTC+8)-
dc.date.issued (上傳時間) 22-Jul-2013 17:22:31 (UTC+8)-
dc.identifier (Other Identifiers) G0099751005en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58973-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 99751005zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (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。zh_TW
dc.description.abstract (摘要) 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.en_US
dc.description.tableofcontents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
1 Introduction 1
2 Tropical Algebraic Geometry 3
2.1 Tropical polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Tropical curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Tropical factorization . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Recovering Tropical Polynomials from Tropical curves 19
3.1 Tropical curves of degree two . . . . . . . . . . . . . . . . . . . . . 19
3.2 Tropical curves of degree three . . . . . . . . . . . . . . . . . . . . . 29
4 Recovering Tropical Polynomials from Newton Subdivisions 36
4.1 Newton subdivisions of degree two . . . . . . . . . . . . . . . . . . 36
4.2 Newton subdivisions of degree three . . . . . . . . . . . . . . . . . . 38
A All types of maximal Newton subdivisions of degree three 51
Bibliography 55		zh_TW
dc.format.extent 1447497 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099751005en_US
dc.subject (關鍵詞) 熱帶多項式zh_TW
dc.subject (關鍵詞) 熱帶曲線zh_TW
dc.subject (關鍵詞) 熱帶直線zh_TW
dc.subject (關鍵詞) Tropical Polynomialen_US
dc.subject (關鍵詞) Tropical Curveen_US
dc.subject (關鍵詞) Tropical Lineen_US
dc.title (題名) 熱帶直線建構二次及三次熱帶曲線之研究zh_TW
dc.title (題名) Constructing Tropical Curves of Degree Two and Three with Tropical Linesen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [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.		zh_TW