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A heuristic factorization scheme that uses learning and other heuristic programming techniques to improve the efficiency of determining the symbolic factorization of multivariate polynomials with integer coefficients and an arbitrary number of variables and terms is described. This factorization scheme is implemented in the learning program POLYFACT and is applied only to multivariate polynomials. The factorization scheme cannot be considered to be a completely general factorization algorithm for there are some instances where the scheme can fail to factor a reducible polynomial. The practical utility of this scheme lies in trying to employ some of the heuristic techniques in an algorithm such as Wang's to reduce the combinatorial searching that must be done to obtain the truefactors of a multivariate polynomial over the integers. Wang's algorithm uses a bottom-up approach for determining the truefactors; whereas, the heuristic scheme in POLYFACT uses a top-down approach.

Extended abstract of "a new approach to the symbolic factorization of multivariate polynomials"