A stream processing approach to distance measurement of integers in p-adic metric space

Abstract

This paper takes the p-adic representation of integers as the research object to realize the distance measurement of integers in the p-adic metric space. The authors firstly apply the Euclidean algorithm to infer the coefficients of a positive integer in polynomial representation, whose corresponding negative integer can be obtained with the help of the similar solution method of binary complement; secondly, the coefficients are respectively mapped into from mod p to mod the n-th power of p layers, where n can be 0 to approaching infinite integer; lastly, the distance measurement method and the data storage structure based on multi-way tree are achieved by Java 8 programming and the library Javaslang. The research results can be applied in p-adic numbers representation and non-Euclidean space task solutions based on p-adic metrics.