Computing Hilbert Class Polynomials
Number Theory
2008-02-08 v1
Abstract
We present and analyze two algorithms for computing the Hilbert class polynomial . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing , and we show that all methods have comparable run times.
Cite
@article{arxiv.0802.0979,
title = {Computing Hilbert Class Polynomials},
author = {Juliana Belding and Reinier Bröker and Andreas Enge and Kristin Lauter},
journal= {arXiv preprint arXiv:0802.0979},
year = {2008}
}