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

Published online by Cambridge University Press:  01 September 2015

Enea Milio*
INRIA Bordeaux Sud-Ouest, 33405 Talence, France email


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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 heuristically 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.

Research Article
© The Author 2015 


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