CARAT Introduction / Programs / Sublattices

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## Program Sublattices

### Usage

    Sublattices 'file1'  ['file2'] [-b] [-g] [-h] [-l=<#level>]
                [-m] [-n=<#number>] [-p] [-q] [-r] [-s] [-t=out] [-u]

file1: bravais_TYP containing a finite unimodular group G, ending with the order of G.
file2: (OPTIONAL) matrix_TYP containing the Gram matrix of a symmetric positive definite G-invariant bilinear form. This form is used for reduction purposes only. If this file is not given, the program computes such a form. In particular the forms possibly given in 'file1' are ignored.

### Description

Calculates the the G-sublattices of the natural lattice Zn of finite index, the prime divisors of which divide the order of G as given in 'file1'. Sublattices of proper multiples of Zn are ignored.

### Options

    -b      : Print only the matrices of change of base and their inverse.
    -g      : Do not compute elementary divisors of the gram matrix.
    -l=#    : Stop after reaching level #level (default #=500).
    -n=#    : Stop after computation of #number "sublattices" (default #=1000).
    -q      : Quiet mode. Suppress any messages to stderr.
    -r      : With LLL-reduction for the bases, cf. 'file2'.
    -s      : Print less information.
    -t='out': Create an output file with additional information. The name
              of the output file defaults to stdout. Specifying "none"
              disables writing to the output file
    -u      : Do not compute elementary divisors of the basis
              transformations.

Options for experts:

    -p<N>/<d1>/<d2>...<dN> : treat the lattice as a direct sum of <N>
                             sublattices of dimensions <d1>, <d2> etc.
                             (1 <= N, di <= 6) and compute only those
                             sublattices that have surjective projections
                             onto each of the N component lattices.

### Remarks

Sublattices is a synomym for ZZprog.

See also for Order, QtoZ and Z_equiv.

### Examples

1. Find all space groups with a given point group and decide for which superlattices each extension splits.

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