Multivariate Polynomial Factorization

Abstract

This paper describes algorithms for factoring a polynomial in one or more variables, with integer coefficients, into factors which are irreducible over the integers These algorithms are based on the use of factorIzatmns over finite fields and "Hensel's lemma constructions " "Abstract algorithm" descripttons are used m the presentation of the underlying algebra:c theory Included ~s a new generahzatmn of Hensel's p-adlc constructmn which leads to a practical algorithm for factor- lng multivariate polynommls The univarmte case algorithm is also specified m greater deta:l than in the prewous literature, with attentmn to a number of improvements wh:ch the author has de- veloped based OR theoretical computing time analyses and experience with actual implementatmns