Set Theory and Logic

The N-th Root Algorithm

Authors: Daniel Cordero Grau
Comments: 2 Pages.

In this paper we give the N-th root algorithm in completions of fraction semfields of normed euclidean semialgebras for every natural N > 1. The algorithm starts with a nonzero element of arbitrary length n in terms of its p-adic expansion for a nonunit p of nonzero degree of a normed euclidean semialgebra, thereafter, for a nonzero natural m = O(n), writes O(m) elements of length O(1) to go through O(m) steps in each of which compares, calculates and writes O(1) elements of length O(m^(N-1)), and so, in time O(n^N).
Category: Set Theory and Logic