Program Aut_grp

Usage

Aut_grp 'file' [-d=n] [-s=n] [-b] [-b=n] [-B=n] [-v] [-g] [-p]

Description

Computes a generating set for the (finite) group of all g in GL_N(Z) with g^Tr * F * g = F for all F in file.

NOTE: if all F are symmetric, this is a Bravais group, otherwise a generalised Bravais group (relevant for Bravais groups in families like 2-1',2-1' etc.).

Options

-d=n    : Depth up to which scalar products are calculated. The value
          should be small. Usefull if the automorphism group is expected
          to be small.
-s=n    : The n-point stabilizer with respect to different basis will be
          calculated.
-b=n    : Use Bacher polynomials up to deepth n.
-B=n    : Use Bacher polynomials with vectors having scalar product n
-v,-g   : Read additional data from 'file'. If -v is given the program
          assumes that the short vectors of the first form in 'file'
          are given below the forms.
          If -g is given, the program assumes known generators for
          the automorphism group to be given below any other information in
          'file'.
-p      : Write additional output to the file AUTO.tmp

Remarks

Examples

1. Find all Bravaisgroups of degree 6 consisting of permutation matrices and their negatives only.
2. Find the stabilizer of a sublattice in the Bravais group of the unit form F=I₆.