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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?
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