English

Computing class groups and unit groups in Magma

Number Theory 2025-10-08 v1

Abstract

We describe the computation of class groups and unit groups of number fields as implemented in Magma (V2.29). After quickly reviewing the main algorithms based on factor bases, relation collection, and analytic class number evaluation, we distinguish their behavior across formalizable, rigorous, GRH-conditional, and heuristic regimes.

Cite

@article{arxiv.2510.05501,
  title  = {Computing class groups and unit groups in Magma},
  author = {Andreas-Stephan Elsenhans and John Voight},
  journal= {arXiv preprint arXiv:2510.05501},
  year   = {2025}
}

Comments

18 pages, 2 figures