| dc.contributor.advisor | 蔡炎龍 | zh_TW |
| dc.contributor.author (Authors) | 林如苹 | zh_TW |
| dc.creator (作者) | 林如苹 | zh_TW |
| dc.date (日期) | 2008 | en_US |
| dc.date.accessioned | 19-Sep-2009 12:08:25 (UTC+8) | - |
| dc.date.available | 19-Sep-2009 12:08:25 (UTC+8) | - |
| dc.date.issued (上傳時間) | 19-Sep-2009 12:08:25 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0095972002 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/37096 | - |
| 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) | 95972002 | zh_TW |
| dc.description (描述) | 97 | zh_TW |
| dc.description.abstract (摘要) | 熱帶幾何(tropical geometry)在近年來引起數學家的注意，因為它可以簡化許多數學難題。本篇論文主要在探討單變數熱帶多項式(single variable tropical polynomial)的因式分解。對於每個熱帶多項式，我們都可以定義其對應的最大係數熱帶多項式(largest-coefficient tropical polynomial )，而且此最大係數熱帶多項式可以因式分解為線性乘積。根據此結果，熱帶代數基本定理(Fundamental Theorem of Tropical Algebra)即成立。此外，可將單變數熱帶多項式因式分解的許多概念延伸至多變數的情形。 | zh_TW |
| dc.description.abstract (摘要) | Tropical geometry draw much attention recent years for it simplifies many difficult classical mathematics problems. The thesis mainly discuss factorization of single variable tropical polynomials. For every tropical polynomial, we define the corresponding largest-coefficient tropical polynomial. We show that each largest-coefficient tropical polynomial can be factorized into a product of linear terms. As a result, the Fundamental Theorem of Tropical Algebra holds. Furthermore, we observe that many notions of factorization of single variable tropical polynomial can be extended to multivariate cases. | en_US |
| dc.description.tableofcontents | 1 Introduction .....................................22 Background .....................................52.1 Arithmetic .....................................52.2 Tropical Polynomial in one variable ............63 Fundamental Theorem of Tropical Algebra ..........93.1 Tropical Polynomials and Tropical Functions ...103.2 The Fundamental Theorem of Tropical Algebra ...213.3 The Corner Locus of a Polynomial ..............234 Conclusion ......................................26 | zh_TW |
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| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
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| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0095972002 | en_US |
| dc.subject (關鍵詞) | 熱帶幾何 | zh_TW |
| dc.subject (關鍵詞) | 熱帶多項式 | zh_TW |
| dc.subject (關鍵詞) | 最大係數熱帶多項式 | zh_TW |
| dc.subject (關鍵詞) | 熱帶代數基本定理 | zh_TW |
| dc.title (題名) | 最大係數熱帶多項式及其應用 | zh_TW |
| dc.title (題名) | Largest-coefficient Tropical Polynomials and Their Applications | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | [1] Lucia Caporaso and Joe Harris. Counting plane curves of any genus. Inventiones Mathematicae, 131(2):345{392, 2 1998. | zh_TW |
| dc.relation.reference (參考文獻) | [2] Andreas Gathmann. Tropical algebraic geometry. Jahresber. Deutsch. Math.-Verein., 108(1):3{32, 2006. | zh_TW |
| dc.relation.reference (參考文獻) | [3] Nathan Grigg and Nathan Manwaring. An elementary proof | zh_TW |
| dc.relation.reference (參考文獻) | of the fundamental theorem of tropical algebra. Preprint at | zh_TW |
| dc.relation.reference (參考文獻) | arXiv:math.CO/0701.2591, February 2008. | zh_TW |
| dc.relation.reference (參考文獻) | [4] Nathan B. Grigg. Factorization of Tropical Polynomials in One and Several Variables. Honor`s thesis, Brigham Young University, June 2007. | zh_TW |
| dc.relation.reference (參考文獻) | [5] Grigory Mikhalkin. Counting curves via lattice paths in polygons. C.R. Math. Acad. Sci. Paris, 336(8):629{634, 2003. | zh_TW |
| dc.relation.reference (參考文獻) | [6] Grigory Mikhalkin. Enumerative tropical algebraic geometry in R2. J.Amer. Math. Soc., 18(2):313{377 (electronic), 2005. | zh_TW |
| dc.relation.reference (參考文獻) | [7] Grigory Mikhalkin. Tropical geometry and its applications. In Interna-tional Congress of Mathematicians. Vol. II, pages 827{852. Eur. Math. | zh_TW |
| dc.relation.reference (參考文獻) | Soc., Zurich, 2006. | zh_TW |
| dc.relation.reference (參考文獻) | [8] Jurgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald. First steps in tropical geometry. Contemporary Mathematics, 377:289{317,2005. | zh_TW |
| dc.relation.reference (參考文獻) | [9] David Speyer and Bernd Sturmfels. The tropical grassmannian. Ad-vances in Geometry, 4:389{411, 2004. | zh_TW |
| dc.relation.reference (參考文獻) | [10] David Speyer and Bernd Sturmfels. Tropical mathematics. Preprint at arXiv:math.CO/0408099, 2004. | zh_TW |
