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題名 最大係數多項式之快速計算法
Fast Computation of Largest Coefficient Polynomials
作者 林容溶
貢獻者 蔡炎龍
林容溶
關鍵詞 最大係數熱帶多項式
日期 2012
上傳時間 1-二月-2013 16:53:23 (UTC+8)
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。
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 property
of the largest coefficient polynomials of degree two. Finally, we find different methods to determine of the largest coefficient polynomials with arbitrary degrees.
參考文獻 [1] 林如苹, Largest-coefficient Tropical Polynomials and Their Applications, PhD
thesis, 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, Taiwanese
J. Math., 16 (2012), pp. 691–712.
46
描述 碩士
國立政治大學
應用數學系數學教學碩士在職專班
99972013
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0099972013
資料類型 thesis
dc.contributor.advisor 蔡炎龍zh_TW
dc.contributor.author (Authors) 林容溶zh_TW
dc.creator (作者) 林容溶zh_TW
dc.date (日期) 2012en_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 (Other Identifiers) G0099972013en_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) 99972013zh_TW
dc.description (描述) 101zh_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 property
of 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iv
1 緒論1
2 背景知識3
3 熱帶多項式5
4 比較一元二次多項式和一元二次熱帶多項式的不同8
4.1 討論二次項係數為0 時的熱帶多項式分解法. . . . . . . . . . . . . 8
4.2 討論二次項係數不為0 時的熱帶多項式分解法. . . . . . . . . . . 12
4.3 最大係數的判斷及利用最大係數做因式分解. . . . . . . . . . . . . 18
5 二元二次熱帶多項式的快速畫圖法32
5.1 一元二次的熱帶齊次多項式. . . . . . . . . . . . . . . . . . . . . . 32
5.2 xy 的係數不為0 所對應的三角形切割. . . . . . . . . . . . . . . . 38
6 結論44		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0099972013en_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 Polynomialsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] 林如苹, Largest-coefficient Tropical Polynomials and Their Applications, PhD
thesis, 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, Taiwanese
J. Math., 16 (2012), pp. 691–712.
46		zh_TW