A quasi-linear time algorithm for computing modular polynomials in dimension 2

Enea Milio 1, 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We propose to generalize the work of Régis Dupont for computing modular polynomials in dimension 2 to new invariants. We describe an algorithm to compute modular polynomials for invariants derived from theta constants and prove under some heuristics that this algorithm is quasi-linear in its output size. Some properties of the modular polynomials defined from quotients of theta constants are analyzed. We report on experiments with our implementation.
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Enea Milio. A quasi-linear time algorithm for computing modular polynomials in dimension 2. LMS Journal of Computation and Mathematics, London Mathematical Society, 2015, 18, pp.603-632. ⟨hal-01080462v3⟩

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