Efficient enumeration of quadratic lattices
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915768300470272 |
|---|---|
| author | Assaf, Eran Chen, Victor Garg, Rohan Wang, Benny |
| author_facet | Assaf, Eran Chen, Victor Garg, Rohan Wang, Benny |
| contents | We present an algorithm to enumerate isometry classes of integral quadratic lattices of a given rank and determinant, and analyze its running time by giving bounds on the number of genus symbols for a fixed rank and determinant. We build on previous work of Kirschmer, Brandhorst, Hanke, and Dubey and Holenstein. We analyze the running times of their respective algorithms and compare the practical performance of their implementations with our own. Our implementations are publicly available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18990 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient enumeration of quadratic lattices Assaf, Eran Chen, Victor Garg, Rohan Wang, Benny Number Theory 11E12, 11E39, 11E41 We present an algorithm to enumerate isometry classes of integral quadratic lattices of a given rank and determinant, and analyze its running time by giving bounds on the number of genus symbols for a fixed rank and determinant. We build on previous work of Kirschmer, Brandhorst, Hanke, and Dubey and Holenstein. We analyze the running times of their respective algorithms and compare the practical performance of their implementations with our own. Our implementations are publicly available. |
| title | Efficient enumeration of quadratic lattices |
| topic | Number Theory 11E12, 11E39, 11E41 |
| url | https://arxiv.org/abs/2601.18990 |