PreprintarXiv licencearXiv
Automorphisms and canonical forms of integer lattices
Abstract
We improve the Plesken--Souvignier algorithm for computing automorphism groups and isometries of positive definite integer quadratic lattices by exploiting characteristic sublattices and refining vector enumeration. For lattices with roots, we also use the Weyl group to accelerate the computation of canonical forms. Experiments with concrete implementations demonstrate substantial speedups and show that canonical forms can be computed at a cost comparable to that of computing automorphism groups.
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BibTeX
@misc{brandhorst2026automorphisms,
title = {{Automorphisms and canonical forms of integer lattices}},
author = {Simon Brandhorst and Tommy Hofmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16753},
eprint = {2610.16753},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16753},
}
RIS
TY - UNPB
TI - Automorphisms and canonical forms of integer lattices
AU - Simon Brandhorst
AU - Tommy Hofmann
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16753
UR - https://arxiv.org/abs/2610.16753
AB - We improve the Plesken--Souvignier algorithm for computing automorphism groups and isometries of positive definite integer quadratic lattices by exploiting characteristic sublattices and refining vector enumeration. For lattices with roots, we also use the Weyl group to accelerate the computation of canonical forms. Experiments with concrete implementations demonstrate substantial speedups and show that canonical forms can be computed at a cost comparable to that of computing automorphism groups.
ER -