English

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 D\mathcal D 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.

Keywords

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}
}
R2 v1 2026-06-23T04:53:52.090Z