Computing class groups and unit groups in Magma
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914078978473984 |
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| author | Elsenhans, Andreas-Stephan Voight, John |
| author_facet | Elsenhans, Andreas-Stephan Voight, John |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing class groups and unit groups in Magma Elsenhans, Andreas-Stephan Voight, John Number Theory 11Y40 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. |
| title | Computing class groups and unit groups in Magma |
| topic | Number Theory 11Y40 |
| url | https://arxiv.org/abs/2510.05501 |