p-adic Root Isolation

Abstract

Root isolation is a very crucial problem in mathematics. There are various types of algorithms that are used to isolate real roots. The real number field and the p-adic number field are similar in many ways. Both fields are completion of Q with respect to their multiplicative norm. Here, our main concern is the isolation of the p-adic roots. Therefore, I tried to summarize the paper titled “p-adic Root Isolation”[3] published by T Sturm and V Weispfenning, (2004) where we focused on “isolation of p-adic roots”. Before moving on to the paper, we try to cover the basics of p-adic numbers. This thesis project is divided into two parts, where the first part is for background building, and in the second part, we discuss the paper.