Computing class groups and unit groups in Magma

Andreas-Stephan Elsenhans; John Voight

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arXiv · 2510.05501

Computing class groups and unit groups in Magma

Andreas-Stephan Elsenhans·John Voight

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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.

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Andreas-Stephan Elsenhans, John Voight. 2025-10-07. Computing class groups and unit groups in Magma. https://arxiv.org/abs/2510.05501

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