swMATH ID: 22773
Software Authors: Mertens, Michael H.
Description: Automorphism groups of hyperbolic lattices. Based on the concept of dual cones introduced by J. Opgenorth [Exp. Math. 10, No.4, 599–608 (2001; Zbl 1007.20046)] we give an algorithm to compute a generating system of the group of automorphisms of an integral lattice endowed with a hyperbolic bilinear form. The paper will be organized as follows: In Section 2 we recall the basic definitions and key results about dual cones from the paper cited above which give a general method to determine generating systems of discontinuous groups acting on dual cones. The application of the results in Section 2 on hyperbolic lattices as well as a quite powerful way to shorten the calculation time is given in Section 3. In Section 4 we analyse the scope and running time of our algorithm and give some examples. These were calculated using the computer algebra system Magma. The source code for the necessary Magma-package AutHyp.m as well as a short description of the included intrinsics is available via the author’s homepage http://www.mi.uni-koeln.de/ mmertens.
Homepage: http://www.mi.uni-koeln.de/~mmertens/AutHypDocu.html
Keywords: hyperbolic lattices; Lorentzian lattices; automorphism group; Voronoi algorithm
Related Software: CARAT; Magma
Referenced in: 1 Publication

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Automorphism groups of hyperbolic lattices. Zbl 1377.11079
Mertens, Michael H.

Referenced by 1 Author

1 Mertens, Michael Helmut

Referenced in 1 Serial

1 Journal of Algebra

Referenced in 1 Field

1 Number theory (11-XX)

Referencing Publications by Year