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On the complexity of computing integral bases of function fields

Abstract : Let $\mathcal{C}$ be a plane curve given by an equation $f(x, y) = 0$ with $f ∈ K[x][y]$ a monic squarefree polynomial. We study the problem of computing an integral basis of the algebraic function field $K(\mathcal{C})$ and give new complexity bounds for three known algorithms dealing with this problem. For each algorithm, we study its subroutines and, when it is possible, we modify or replace them so as to take advantage of faster primitives. Then, we combine complexity results to derive an overall complexity estimate for each algorithm. In particular, we modify an algorithm due to Böhm et al. and achieve a quasi-optimal runtime.
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https://hal.inria.fr/hal-02568086
Contributor : Simon Abelard <>
Submitted on : Friday, November 27, 2020 - 2:12:24 PM
Last modification on : Saturday, November 28, 2020 - 3:29:26 AM

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Simon Abelard. On the complexity of computing integral bases of function fields. CASC 2020 - Computer Algebra in Scientific Computing, Sep 2020, Linz / Virtual, Austria. pp.42-62, ⟨10.1007/978-3-030-60026-6_3⟩. ⟨hal-02568086v2⟩

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