最大係數多項式之快速計算法

Abstract

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\n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\n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\n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\n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\nof the largest coefficient polynomials of degree two. Finally, we find different methods to determine of the largest coefficient polynomials with arbitrary degrees.