臺灣博碩士論文加值系統

本篇論文主要是以個人電腦為工具達到分解第七個費馬數為目的。基於分解三次方型整數的因數分解方法，我們利用 Mathematica 3.0版，將演算法的每個步驟轉換成程式。在有理整數系的處理過程中，我們遇到的困難主要在於 Mathematica對於迴圈的計算上佔用太多的記憶體及虛擬記憶體，造成電腦運算時速度變慢，於是我們採用三部電腦分工處理的方式，解決這一方面的困擾。而在處理代數整數環的過程中，將代數轉換成程式時遇到較多的問題，我們在細分成數個程式之後仍不夠完美，在這一方面仍有改進的空間。

The aim of the thesis is to factor the seventh Fermat number by personal computers. We use Mathematica 3.0 to translate each step into programs on the base of the factoring cubic integers method. In the process of dealingwith the rational integers, the main problem is that we use too much memoriesand pseudo memories on the computation of loops on Mathematica, which causes the speed to slow down. Therefore, we adopt division of labor by three computersto resolve the problem. In the process of dealing with the algebraic integers,we encounter more difficulties translating Algebra into programs. After dividingseveral programs it is still rough. There should be room for improvement.-1 -aCryptography And Factorization