CARAT Introduction / Programs / Aut_grp

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## 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 gTr * 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

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.

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