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I would like to try to implement a factorization method for polynomials with integer coefficients which returns the irreducible factors. I read about Zassenhaus, LLL, van Hoeij algorithms but they all seem to be an overkill for what I try to do (which is learning the basics).

Could someone please suggest a simpler alternative? Preferably one without lifting, modular arithmetic, lattices, ... Ideally, I would be interested in the literature describing it or another implementation.

Faaf
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  • The things to which you refer are ways of reducing polynomials factorisations to a finite problem, and to reduce the search space for factors so that the algorithms are more efficient. Some of the issues are discussed in this paper https://arxiv.org/pdf/0904.3057v1.pdf (you don't have to read all the proofs to get an idea of what is going on). The problem in the general case has not been found to be simple. – Mark Bennet Jun 10 '18 at 20:33
  • A very simple method is given here – Count Iblis Jun 10 '18 at 20:33
  • @CountIblis That finds linear factors, but these need not exist in general. – Mark Bennet Jun 10 '18 at 20:34
  • @MarkBennet In that question I find quadratic factors, it can be generalized to find factors of any degree, however, it becomes rather unwieldy to find factors of high degrees. – Count Iblis Jun 10 '18 at 20:40

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