p-adic Arithmetic and Parallel Symbolic Computation: An Implementation for Solving Linear Systems Over Rationals

In this work we describe the use of truncated p adic expansion for handling rational numbers by parallel algorithms for symbolic computation As a case study we propose a parallel implementation for solving linear systems over the rationals The parallelization is based on a multiple homomorphic image technique and the result is recovered by a parallel version of the Chinese remainder algorithm Using a MIMD machine we compare the proposed implementation with the classical modular arithmetic showing that truncated p adic arithmetic is a feasible tool for solving systems of linear equations working directly over rational numbers A safe algorithm for computing the p adic division operation is proposed The implementation leads to a speedup up to seven by ten processors with respect to the sequential implementation