permgroups package

Python implementation of permutation groups is presented. Two classes are introduced: Perm for permutations, Group for permutation groups (everal versions).

The class Perm from the perms module is based on Python dictionaries and utilize cycle notation. The methods of calculation for the perm order, parity, ranking and unranking are given. A random permutation generation is also shown.

The class Group from the groups module is very simple and it is also based on dictionaries. It is mainly the presentation of the permutation groups interface with methods for the group order, subgroups (normalizer, centralizer, center, stabilizer), orbits, and several tests.

The class Group from the setgroups module is also simple and it is based on sets.

The class Group from the simsgroups module is advanced and it is bases on the Sims theory.

The project is moved from Google Code.

Download

To install an official release do

python3 -m pip install permgroups

To get the git version do

git clone https://github.com/ufkapano/permgroups.git

Usage

>>> from permgroups.perms import Perm
>>> from permgroups.groups import Group
>>> p = Perm()(0, 1, 2, 4)(3, 5)
>>> ~p
Perm()(0, 4, 2, 1)(3, 5)
>>> p.is_identity(), p.parity(), p.is_even(), p.sign()
(False, 0, True, 1)
>>> p.order(), pow(p, 4)
(4, Perm())
>>> Perm.random(10)
Perm()(0, 1, 4, 2, 7)(3, 9, 8)(5, 6)
>>> G = Group()
>>> G.insert(p)
>>> G.order()
4
>>> list(G.iterperms())
[Perm(), Perm()(0, 1, 2, 4)(3, 5), Perm()(0, 2)(1, 4), Perm()(0, 4, 2, 1)(3, 5)]
>>> Perm()(1, 4)(0, 2) in G, Perm()(0, 1, 2, 3) in G
(True, False)
>>> G.is_abelian()
True

References

[1] A. Kapanowski, Python for education: permutations. http://arxiv.org/abs/1307.7042 [draft]

[2] A. Kapanowski, The Python Papers 9, 3 (2014). Python for education: permutations. [final version] http://ojs.pythonpapers.org/index.php/tpp/article/view/258

Contributors

Andrzej Kapanowski (project leader)

Tomasz Gądek

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