Abstract We present the main ideas for an algorithm to calculate the group of automorphisms of a Euclidean lattice. This algorithm can be applied to related problems, e.g. to compute Bravais groups, to calculate automorphisms of lattices over number fields or, in a slightly modified version, to find isometries between lattices. An implementation of the algorithm by the second author has been successfully applied to lattices up to dimension 40 and allows, for example, obtaining of generators for the automorphism group of the Leech lattice in less than 30 min on a HP 9000/730 workstation.
[1]
Bernd Souvignier,et al.
Irreducible finite integral matrix groups of degree 8 and 10
,
1994
.
[2]
W. Plesken,et al.
Constructing integral lattices with prescribed minimum. II
,
1985
.
[3]
Rudolf Scharlau,et al.
Unimodular lattices over real quadratic fields
,
1994
.
[4]
Rudolf Scharlau,et al.
The genus of the Barnes-Wall lattice
,
1994
.
[5]
Wilhelm Plesken,et al.
Finite Rational Matrix Groups
,
1995
.
[6]
Constructing integral lattices with prescribed minimum. II
,
1985
.