CARAT Introduction / Programs / Bravais_inclusions

Previous Program | Introduction | Next Program

## Program Bravais_inclusions

### Usage

    Bravais_inclusions 'file' [-S] [-G]

file: bravais_TYP containing a Bravais group G.

### Description

Lists representatives of the Bravais subgroups (resp. Bravais supergroups with option -S) of the BRAVAIS GROUP G under the conjugation action of the normalizer of G in GL_n(Z).
Remark: Without option -G only the symbols of the Bravais groups are given.

### Options

    -S:   Search for all supergroups
    -G:   Calculate generators for the groups as well

### Remarks

See also for Bravais_catalog/Datei and Bravais_type/Symbol

### Examples

1. List all names of Bravais groups of degree 4.
2. Determine the maximal finite subgroups of GL5(Z)
3. Find the dual pairs of Bravais groups in family 1;1;1;1
4. Find all Bravaisgroups of degree 6 consisting of permutation matrices and their negatives only.
5. Do two given groups have Z-equivalent copies which lie in a finite unimodular group?

Previous Program | Introduction | Next Program