## Program Aut_grp

### Usage

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

file: matrix_TYP containing a set of integral NxN-matrices, the first
of which is symmetric and positive definite.
### 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

See also for Short and Shortest.
### Examples

- Find all Bravaisgroups of degree 6 consisting of permutation
matrices and their negatives only.
- Find the stabilizer of a sublattice in the Bravais
group of the unit form F=I
_{6}.