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A quasi-linear 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 any invariants derived from theta constants and prove that this algorithm is quasi-linear.Some properties of the modular polynomials with the quotient of theta constants are analyzed.We report on experiments with our implementation.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01080462
Contributor : Enea Milio <>
Submitted on : Wednesday, November 26, 2014 - 9:46:57 AM
Last modification on : Thursday, January 11, 2018 - 6:22:36 AM
Long-term archiving on: : Friday, February 27, 2015 - 10:58:26 AM

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  • HAL Id : hal-01080462, version 2

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Enea Milio. A quasi-linear algorithm for computing modular polynomials in dimension 2. 2014. ⟨hal-01080462v2⟩

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