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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: 2013-02-01 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
    顯示於類別:[應用數學系] 學位論文

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