Computing class groups and unit groups in Magma

2025/10/07 by Elsenhans, Andreas-Stephan, Voight, John · 1 citation
#11Y40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.05501

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.

Citations

• Generalized Pohst inequality and small regulators
• Computing the residue of the Dedekind zeta function

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• Formally certifying number field invariants

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