A Fast Algorithm for Polynomial Factorization over ℚp
Résumé
We present an algorithm that returns a proper factorization of a polynomial Φ(x) over the p-adic integers ℤp (if Φ(x) is reducible over ℚp) or returns a power basis of the ring of integers of ℚp[x]/Φ(x)ℚp[x] (if Φ(x) is irreducible over ℚp). Our algorithm is based on the Round Four maximal order algorithm. Experimental results show that the new algorithm is considerably faster than the Round Four algorithm.
Domaines
Théorie des nombres [math.NT]
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