The GAP 4 package `images’

This package provides functionality to compute minimal and canonical representatives of objects under group actions in GAP: sets, tuples, sets of sets, transformations, permutations and partial permutations up to conjugacy, and general combinatorial structures.

gap> LoadPackage("images", false);;
gap> G := Group((1,2,3)(4,5,6)(7,8,9), (1,4,7)(2,5,8)(3,6,9));;
gap> MinimalImage(G, [2,3,5,7], OnSets);
[ 1, 2, 4, 9 ]
gap> CanonicalImage(G, [2,3,5,7], OnSets) = CanonicalImage(G, [1,6,7,8], OnSets);
true

Requirements

The package requires GAP >= 4.13 and the Digraphs and Datastructures packages (both in the standard GAP package distribution). The ferret and vole packages are optional: ferret greatly speeds up stabilizer computations for transformations, permutations, partial permutations and sets of sets, and vole provides an alternative canonicalisation engine and is required for canonicalising fundamental structures under groups which are not direct products of symmetric groups.

Documentation

Full information and documentation can be found in the manual, available on the package homepage at

https://gap-packages.github.io/images/

or built locally into doc/ by running gap makedoc.g.

Citing

If this package is useful in your research, please cite the paper it implements: C. Jefferson, E. Jonauskyte, M. Pfeiffer and R. Waldecker, Minimal and canonical images, Journal of Algebra 521 (2019), 481-506.

Bug reports and feature requests

Please submit bug reports and feature requests via our GitHub issue tracker:

https://github.com/gap-packages/images/issues

License

images is free software; you can redistribute it and/or modify it under the terms of the Mozilla Public Licence, Version 2.

History

For newer versions see CHANGES.md.

1.3.3

• More internal improvements (improving CI and compatibility with future GAP versions)

1.3.2

• Internal improvements (improving CI and compatibility with future GAP versions)

1.3.1

• Minor cleanups (including removing global variables with names like ‘orbit’)

1.3.0

• Add IsMinimalImageLessThan

1.2.0

• Improve testing (no new bugs found)
• Change license to MPL-v2

1.1.0

• Add OnTuplesSets support

1.0.0

• First Stable Release