Analysis Of Exact Solution Of Linear Equation Systems Over Rational Numbers By Parallel p-adic Arithmetic

We study and investigate the p-adic arithmetic along with analysis of exact solution of linear equation systems over rational numbers. Initially we study the basic concepts involving the p-adic numbers and why they form a better representation. After that we describe a parallel implementation of an algorithm for solving systems of linear equations over the field of rational number based on the Gaussian elimination.The rationals are represented ny truncated p-adic expansion. The approach leads to error free computations directly over the rationals without converting the system to an equivalent one over integers. The parallelization is based on multiple homomorphic image technique and the result is recovered by parallel version of Chinese Remainder Algorithm.