## 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 Z^{n} of
finite index, the prime divisors of which divide the order of G
as given in 'file1'. Sublattices of proper multiples of Z^{n} 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

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