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| Title: | 熱帶導數與熱帶反導數
Tropical Derivatives and Anti-derivatives |
| Authors: | 王靜萍 |
| Contributors: | 蔡炎龍
王靜萍 |
| Keywords: | 熱帶導數
熱帶反導數
熱帶多項式
Tropical Derivatives
Tropical Anti-derivatives
Tropical Polynomials |
| Date: | 2012 |
| Issue Date: | 2013-02-01 16:53:20 (UTC+8) |
| Abstract: | 在這篇論文中,我們定義了熱帶導數和熱帶反導數.當我們對兩個相同的熱帶多項式求導數時,可能會得到不同的函數.為了克服此困難,我們限制在最大係數多項式下才求導數.熱帶導數的定義與古典導數相當不同.特別的是,我們有d/dxan⊙x^(⊙n)= an⊙x⊙n-1.將它線性化,我們得到d/dx[an⊙x^(⊙n)⊕an-1⊙x⊙n-1 ⊕…. a1⊙x⊕a0] = an⊙x⊙n-1 ⊕an-1⊙x⊙n-2⊕…⊕a1.我們將會解釋為什麼使用這種定義.導數對了解熱帶幾何很有幫助,它也引出了一些與古典導數相似的資訊.最後,我們討論如何定義及求熱帶多項式的熱帶反導數
In this thesis, we define the tropical derivatives and anti-derivatives. When we differ-
entiate two identical tropical polynomials, we might get two different functions. In order to overcome the diffculties, we restrict the polynomials to largest coeffcient polynomials to avoid unpredictable results when taking derivatives. The definitiion of the tropical derivatives is quite diffrent from the definition of classical derivatives. In particular, we have d/dxan⊙x^(⊙n)= an⊙x⊙n-1 . To extend it linearly, we obtain d/dx[an⊙x^(⊙n)⊕
a n-1⊙x⊙n-1 ⊕…. a1⊙x⊕a0] = an⊙x⊙n-1 ⊕a n-1⊙x⊙n-2⊕…⊕a1. We will explain why we use this kind of definition. The derivatives are helpful in understanding more about tropical geometry, and it carries out some information similar to classical derivatives. Finally, we discuss how to define and find tropical anti-derivatives for tropical polynomials.
Keywords : Tropical derivatives, tropical anti-derivatives, tropical polynomials. |
| Reference: | [1] I.Simon, Recognizable sets with multiplicities in the tropical semiring. Mathematical foundations of computer science, (Carlsbad, 1988), 107-120, Lecture Notes in
Comput, Sci., 324, Springer, Berlin, 1988.
[2] Julian Tay, Tropical Derivatives And Duality. Honor`s thesis, Brigham Young University, 2007.
[3] Yen-Lung Tsai, Working With Tropical Meromorphic Functions Of One Variable. Taiwanese J. Math., 16(2), 2012.
[4] David Speyer and Bernd Sturmfels, Tropical Mathematics. Math. Mag. 82(3), 2009.
[5] Gen-Wei Huang, Visualization of Tropical Curves. Master`s thesis, National Chengchi University, Taipei Taiwan, 2009.
[6] Jurgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald. First steps in tropical geometry. Contemp. Math., 377, 2005. |
| Description: | 碩士
國立政治大學
應用數學系數學教學碩士在職專班
99972004
101 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0099972004 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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| 200401.pdf | 833Kb | Adobe PDF2 | 802 | View/Open |
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