Computing the Determinant of a Dense Matrix over Z
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913311471173632 |
|---|---|
| author | Abbott, John Fieker, Claus |
| author_facet | Abbott, John Fieker, Claus |
| contents | We present a new, practical algorithm for computing the determinant of a non-singular dense, uniform matrix over Z; the aim is to achieve better practical efficiency, which is always at least as good as currently known methods. The algorithm uses randomness internally, but the result is guaranteed correct. The main new idea is to use a modular HNF in cases where the Pauderis--Storjohann HCOL method performs poorly. The algorithm is implemented in OSCAR~1.0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08358 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing the Determinant of a Dense Matrix over Z Abbott, John Fieker, Claus Number Theory 15B36 (Primary), 11C20 (Secondary), 15-04, 15A15 We present a new, practical algorithm for computing the determinant of a non-singular dense, uniform matrix over Z; the aim is to achieve better practical efficiency, which is always at least as good as currently known methods. The algorithm uses randomness internally, but the result is guaranteed correct. The main new idea is to use a modular HNF in cases where the Pauderis--Storjohann HCOL method performs poorly. The algorithm is implemented in OSCAR~1.0. |
| title | Computing the Determinant of a Dense Matrix over Z |
| topic | Number Theory 15B36 (Primary), 11C20 (Secondary), 15-04, 15A15 |
| url | https://arxiv.org/abs/2404.08358 |