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Factoring larger multivariate polynomials

An improved algorithm for factoring multivariate polynomials over the integers has been developed. For larger polynomials, it is generally faster and requires less storage than the original algorithm as described by Wang and Rothschild [2]. The new algorithm has improved strategy to deal with the known problems of the original algorithm. namely, the leading coefficient problem, the bad-zero problem and the combinatorial search for true factors. It features a linearly convergent variable-by-variable p-adic construction procedure for parallel lifting of all factors at once. This procedure is very efficient and it relies on i) distributing the factors of the leading coefficient correctly, and ii) solving the equation αf+βg = h, with multivariate f, g and h, efficiently. Details of these and other aspects of this algorithm together with its generalization to factoring over algebraic number fields will be forthcoming. Obviously, the EZ-GCD algorithm [1] can be similarly improved if its lifting procedure is replaced.