On the complexity of class group computations for large degree number fields
Number Theory
2018-10-29 v1 Symbolic Computation
Abstract
In this paper, we examine the general algorithm for class group computations, when we do not have a small defining polynomial for the number field. Based on a result of Biasse and Fieker, we simplify their algorithm, improve the complexity analysis and identify the optimal parameters to reduce the runtime. We make use of the classes defined in [GJ16] for classifying the fields according to the size of the extension degree and prove that they enable to describe all the number fields.
Cite
@article{arxiv.1810.11396,
title = {On the complexity of class group computations for large degree number fields},
author = {Alexandre Gélin},
journal= {arXiv preprint arXiv:1810.11396},
year = {2018}
}