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- W4284688093 abstract "We improve significantly the Nart-Montes algorithm for factoring polynomials over a complete discrete valuation ring A. Our first contribution is to extend the Hensel lemma in the context of generalised Newton polygons, from which we derive a new divide and conquer strategy. Also, if A has residual characteristic zero or high enough, we prove that approximate roots are convenient representatives of types, leading finally to an almost optimal complexity both for irreducibility and factorisation issues, plus the cost of factorisations above the residue field. For instance, to compute an OM-factorisation of F∈A[x], we improve the complexity results of [3] by a factor δ, the discriminant valuation of F." @default.
- W4284688093 created "2022-07-08" @default.
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- W4284688093 date "2022-07-04" @default.
- W4284688093 modified "2023-09-25" @default.
- W4284688093 title "Local Polynomial Factorisation" @default.
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- W4284688093 doi "https://doi.org/10.1145/3476446.3535487" @default.
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