Factoring in Fp[x] and in ℤ[x]
We describe methods for factoring polynomials over F p = ℤ/pℤ and over ℤ. In the first section we present Berlekamp’s algorithm for factoring a polynomial over ℤ/pℤ. In subsequent sections we show how to lift such a factorization to one over ℤ/p2ℤ, then over ℤ/p4ℤ, etc., and eventually to a unique possible factorization over ℤ.
KeywordsNull Space Great Common Divisor Irreducible Polynomial Monic Polynomial Irreducible Factor
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