# A quasi-linear algorithm for computing modular polynomials in dimension 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.
Document type :
Preprints, Working Papers, ...
Domain :

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

### File

QuasiLinAlgModPol.pdf
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### Identifiers

• HAL Id : hal-01080462, version 2

### Citation

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

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