Efficient enumeration of quadratic lattices

Fuente: arXiv
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Main Authors: Assaf, Eran, Chen, Victor, Garg, Rohan, Wang, Benny
Format: Preprint
Published: 2026
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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