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




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1 LFANT - Lithe and fast algorithmic number theory IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest 2 IMB - Institut de Mathématiques de Bordeaux

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-linearin its output size. Some properties of the modular polynomials defined from quotients of theta constants are analyzed.We report on experiments with our implementation.





Author: Enea Milio -

Source: https://hal.archives-ouvertes.fr/



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