Magma code for the paper: Moduli of elliptic K3 surfaces: monodromy and root lattice strata

The results and tables in the appendix of the paper
K. Hulek and M. Lönne, Moduli of elliptic K3 surfaces: monodromy and root lattice strata
where obtained with the help of the computer algebra system Magma.

The computations can be done as follows:

Download the file K3.zip.
Unzip the downloaded file.
Run "magma K3.m".

Magma will then start computing the lattices T and certain subgroups of O(T). It will print out several group indices and genera as it proceeds. This information was used to create the two tables in the appendix.

The above code uses an algorithm for computing automorphism groups of hyperbolic lattices by M. H. Mertens [1].
This algorithm has been extended by S. Schönnenbeck to output a presentation of these automorphism groups, following the ideas of [2].
The algorithm and its extension are contained in the file "AutHyp.m" provided by the archive "K3.zip".

[1] M. H. Mertens, Automorphism Groups of Hyperbolic Lattices, Journal of Algebra 408 (2014), pp. 147-165, DOI.
[2] O. Braun, R. Coulagon, G. Nebe and S. Schönnenbeck, Computing in arithmetic groups with Voronoi's algorithm, Journal of Algebra 435 (2015), pp. 263-285, DOI.