Factorization of Polynomials over the Field of Rational Numbers

TL;DR

This paper introduces a randomized algorithm for factoring and testing the irreducibility of polynomials over the rational numbers by converting to integer coefficients and reducing modulo large primes, avoiding lifting methods.

Contribution

It presents a novel randomized approach for polynomial factorization over rationals that simplifies the process by avoiding lifting, using modular reduction techniques.

Findings

Algorithm effectively determines irreducibility.

Polynomial factorization over rationals achieved without lifting.

Method applicable to a wide class of polynomials.

Abstract

In this paper, a randomized algorithm for deciding the irreducibility of an irreducible polynomial and factoring a reducible polynomial over the field of rational numbers is presented. The main idea underlying the algorithm is based on conversion of a given polynomial into a polynomial with integer coefficients and reduction to mod p, for several large prime numbers p, without applying a lifting method.