Automorphisms and canonical forms of integer lattices

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.