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math.NT2026
Automorphisms and canonical forms of integer lattices
Simon Brandhorst, Tommy Hofmann
We improve the Plesken--Souvignier algorithm for computing automorphism groups and isometries of positive definite integer quadratic lattices by exploiting characteristic sublattic…
math.NT2023★ 2 cited
Hensel lifting algorithms for quadratic forms
Simon Brandhorst, Davide Cesare Veniani
We provide an algorithm to compute generators of the orthogonal group of the discriminant group associated to an integral quadratic lattice over the integers. We give a closed form…
math.NT2021★ 2 cited
Generation of Local Unitary Groups
Simon Brandhorst, Tommy Hofmann, Sven Manthe
Let be a two-dimensional étale algebra over a non-Archimedean local field of characteristic zero. We show that the unitary group of a non-degenerate hermitian lattice over…