Author:
Bauch Jens-Dietrich,Nart Enric,Stainsby Hayden D.
Abstract
AbstractLet $k$ be a locally compact complete field with respect to a discrete valuation $v$. Let $ \mathcal{O} $ be the valuation ring, $\mathfrak{m}$ the maximal ideal and $F(x)\in \mathcal{O} [x] $ a monic separable polynomial of degree $n$. Let $\delta = v(\mathrm{Disc} (F))$. The Montes algorithm computes an OM factorization of $F$. The single-factor lifting algorithm derives from this data a factorization of $F(\mathrm{mod~} {\mathfrak{m}}^{\nu } )$, for a prescribed precision $\nu $. In this paper we find a new estimate for the complexity of the Montes algorithm, leading to an estimation of $O({n}^{2+ \epsilon } + {n}^{1+ \epsilon } {\delta }^{2+ \epsilon } + {n}^{2} {\nu }^{1+ \epsilon } )$ word operations for the complexity of the computation of a factorization of $F(\mathrm{mod~} {\mathfrak{m}}^{\nu } )$, assuming that the residue field of $k$ is small.
Subject
Computational Theory and Mathematics,General Mathematics
Reference19 articles.
1. Schnelle Multiplikation großer Zahlen
2. 13. E. Nart , ‘Local computation of differents and discriminants’, Math. Comput., to appear, arXiv:1205.1340v1 [math.NT].
3. Newtonsche Polygone in der Theorie der algebraischen K�rper
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