Single-factor lifting and factorization of polynomials over local fields
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Let f (x) be a separable polynomial over a local field. The Montes algorithm computes certain approximations to the different irreducible factors of f (x), with strong arithmetic properties. In this paper, we develop an algorithm to improve any one of these approximations, till a prescribed precision is attained. The most natural application of this ‘‘single-factor lifting’’ routine is to combine it with the Montes algorithm to provide a fast polynomial factorization algorithm. Moreover, the single-factor lifting algorithm may be applied as well to accelerate the computational resolution of several global arithmetic problems in which the improvement of an approximation to a single local irreducible factor of a polynomial is required
CitacióGuardia, J.; Nart, E.; Pauli, S. Single-factor lifting and factorization of polynomials over local fields. "Journal of symbolic computation", Novembre 2012, vol. 47, núm. 11, p. 1318-1346.