An Artificial Intelligence Approach to the Symbolic Factorization of Multivariable Polynomials. Technical Report No. CS74019-R.

A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and automatic classification) in an attempt to reduce the amount of searching for the irreducible factors of the polynomial. The approach taken to polynomial factorization is quite different from previous attempts because: (1) it is distinct from numerical techniques; (2) possibilities for terms in a factor are generated from the terms in the polynomial; and (3) a reclassification technique is used to allow the application of different sets of heuristics to a polynomial during factorization attempts on it. Data presented show the importance of learning to the efficiency of operation of the scheme. Factorization times of polynomials factored by both the scheme described in this paper and Wang's implementation of Berlekamp's algorithm are given and compared, and an analysis of avariance experiment provides an indication of the significant sources of variation influencing the factorization time. (Author/DGC)