| dc.contributor.advisor | 蔡炎龍 | zh_TW |
| dc.contributor.author (作者) | 林容溶 | zh_TW |
| dc.creator (作者) | 林容溶 | zh_TW |
| dc.date (日期) | 2012 | en_US |
| dc.date.accessioned | 1-二月-2013 16:53:23 (UTC+8) | - |
| dc.date.available | 1-二月-2013 16:53:23 (UTC+8) | - |
| dc.date.issued (上傳時間) | 1-二月-2013 16:53:23 (UTC+8) | - |
| dc.identifier (其他 識別碼) | G0099972013 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/56886 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系數學教學碩士在職專班 | zh_TW |
| dc.description (描述) | 99972013 | zh_TW |
| dc.description (描述) | 101 | zh_TW |
| dc.description.abstract (摘要) | 本篇主要討論快速計算最大係數熱帶多項式的方法。首先我們比較古典幾何和熱帶幾何中多項式的異同。為了讓熱帶多項式有如古典多項式的唯一表示，我們必須要定義最大係數多項式。接著我們討論一元二次最大係數多項式的性質，並更進一步找出任意次數最大係數多項式的判斷與計算方式。 | zh_TW |
| dc.description.abstract (摘要) | The goal of this thesis is to find fast computing methods of largest coefficient tropical polynomials. First, we compare the difference between classical polynomials and tropical polynomials. In order to have the unique representation for any tropical polynomials, we have to define so called the largest coefficient polynomial. We then discuss the propertyof the largest coefficient polynomials of degree two. Finally, we find different methods to determine of the largest coefficient polynomials with arbitrary degrees. | en_US |
| dc.description.tableofcontents | Abstract iii中文摘要iv1 緒論12 背景知識33 熱帶多項式54 比較一元二次多項式和一元二次熱帶多項式的不同84.1 討論二次項係數為0 時的熱帶多項式分解法. . . . . . . . . . . . . 84.2 討論二次項係數不為0 時的熱帶多項式分解法. . . . . . . . . . . 124.3 最大係數的判斷及利用最大係數做因式分解. . . . . . . . . . . . . 185 二元二次熱帶多項式的快速畫圖法325.1 一元二次的熱帶齊次多項式. . . . . . . . . . . . . . . . . . . . . . 325.2 xy 的係數不為0 所對應的三角形切割. . . . . . . . . . . . . . . . 386 結論44 | zh_TW |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0099972013 | en_US |
| dc.subject (關鍵詞) | 最大係數熱帶多項式 | zh_TW |
| dc.title (題名) | 最大係數多項式之快速計算法 | zh_TW |
| dc.title (題名) | Fast Computation of Largest Coefficient Polynomials | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | [1] 林如苹, Largest-coefficient Tropical Polynomials and Their Applications, PhDthesis, National Chengchi University, 2009.[2] 黃馨儀, On Tropical Conics, PhD thesis, National Chengchi University, 2010.[3] A. Gathmann, Tropical algebraic geometry, Jahresber. Deutsch. Math.-Verein.,108 (2006), pp. 3–32.[4] N. B. Grigg, Factorization of Tropical Polynomials in One and Several Variables,PhD thesis, Brigham Young University, 2007.[5] Y.-L. Tsai, Working with tropical meromorphic functions of one variable, TaiwaneseJ. Math., 16 (2012), pp. 691–712.46 | zh_TW |
