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.

Limongelli, C., & R., P. (1996). p-adic Arithmetic and Parallel Symbolic Computation: an Implementation for Solving Linear Systems over the Rationals. COMPUTERS AND ARTIFICIAL INTELLIGENCE, 14 n. 1, 35-62.

p-adic Arithmetic and Parallel Symbolic Computation: an Implementation for Solving Linear Systems over the Rationals

LIMONGELLI, Carla;
1996

Abstract

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.
Limongelli, C., & R., P. (1996). p-adic Arithmetic and Parallel Symbolic Computation: an Implementation for Solving Linear Systems over the Rationals. COMPUTERS AND ARTIFICIAL INTELLIGENCE, 14 n. 1, 35-62.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/144351
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