Calculating generators of power integral bases in sextic fields with a real quadratic subfield
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915276167053312 |
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| author | Gaál, István |
| author_facet | Gaál, István |
| contents | We discuss the problem of calculating generators of power integral bases in sextic fields, especially focusing on the case of sextic fields with real quadratic subfields. Our main purpose is to describe an efficient algorithm for calculating generators of power integral bases. We show that appropriately using integer arithmetics speeds up the calculations considerably. Our experiences lead to some interesting general statements on generators of power integral bases in number fields generated by a unit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Calculating generators of power integral bases in sextic fields with a real quadratic subfield Gaál, István Number Theory 11Y50, 11R04, 11D25 We discuss the problem of calculating generators of power integral bases in sextic fields, especially focusing on the case of sextic fields with real quadratic subfields. Our main purpose is to describe an efficient algorithm for calculating generators of power integral bases. We show that appropriately using integer arithmetics speeds up the calculations considerably. Our experiences lead to some interesting general statements on generators of power integral bases in number fields generated by a unit. |
| title | Calculating generators of power integral bases in sextic fields with a real quadratic subfield |
| topic | Number Theory 11Y50, 11R04, 11D25 |
| url | https://arxiv.org/abs/2505.04293 |