A fast algorithm for polynomial factorization over $\mathbb {Q}_p$

Abstract

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Factoring Polynomials Over Local Fields

“…• The improved Round Four algorithm by Ford et al (2000) is considerably faster than the original Round Four algorithm. Formulated as an algorithm for factoring a polynomial Φ(x) over Q p , it returns a local integral basis (in fact, a power basis) for…”

“…The following result from Ford and Letard (1994) (also see Ford et al, 2000) provides a method for approximating the greatest common divisor to a given precision.…”

Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields

“…There are several efficient methods for this problem, most of them based on variants of the Round 2 and Round 4 routines [15], [16], [3], [4], [1], [5].…”

Single-factor lifting and factorization of polynomials over local fields

“…Different authors (Cohen, 2000;Ford et al, 2002) have provided such benchmarks for different problems in computational algebraic number theory. These lists of polynomials have been of great use, but the new algorithms and the fast evolution of hardware have left it out of date.…”