從先前研究計畫的成果中我們發現 restricted Nagata’s pairwise algorithm 和Euclidean algorithm 有非常密切的內在關係，相關結果所寫成的論文 “The restricted Nagata’s pairwise algorithm and the Euclidean Algorithm” 已經在2007年10月被 Osaka Journal of Mathematics 所接受。我們目前對restricted Nagata’s pairwise algorithm 的內涵知道的非常有限。在這個新提出的計畫裡，我們希望藉由學習代數數論中一些algorithm 的理論再回頭來對 restricted Nagata’s pairwise algorithm 作內在深層的探討。在研究與代數數論有關的algorithms 的過程中，我們也會整理收集合適的研究題目。 ; In the paper entitled “The restricted Nagata’s pairwise algorithm and the Euclidean Algorithm”, accepted by Osaka Journal of Mathematics (2007), we build an unexpected genetic relation between these two types of algorithms. But, at this moment, we do not know much about the role played by the restricted Nagata’s pairwise algorithm. In this project we like to study the theory of algorithms in algebraic number theory. Then we will take a close look at the restricted Nagata’s pairwise algorithm. We expect to gain more internal knowledge of the restricted Nagata’s pairwise algorithm. As a byproduct we will collect new research problems for future study. ; 研究期間 9708 ~ 9807
