Algebraic algorithms using p-adic constructions

Abstract

Machine computation of many algebraic operations of interest and utility to mathematicians and scientists has received increasing attention in the recent years. A variety of terminology has been used to describe this area of mathematical computation. Among these are symbolic manipulation, computer algebra, algebraic methods, constructive algebra, and seminumerical algorithms. Whatever name is chosen for the field currently known as symbolic and algebraic manipulation, the most fundamental part of any symbolic computer software system for the actual computing is always the workhorse subpackage that deals with polynomial and rational functions.