A remark on factorisation
John Abbott, Russell Bradford, James H. Davenport · ACM SIGSAM Bulletin · 1985
We are concerned with factoring polynomials over algebraic extensions of the rationals, and have implemented a variant of Trager's [1976] algorithm, which reduces this problem to that of factoring polynomials over the integers, for which we use Wang's [1978] algorithm (as implemented in REDUCE [Hearn 82] by Moore and Norman [1981]). However, Trager's method often produces a norm polynomial which factors profusely modulo every prime, leading to a combinatorial explosion of trial divisions in Wang's algorithm. We present some simple divisibility tests for polynomials to help combat the cost of this explosion.