Python for education: permutations

TL;DR

This paper introduces Python classes for permutations and permutation groups, providing methods for calculation, error reporting, and group analysis, with implementations in Python modules.

Contribution

It presents new Python classes Perm and Group for permutations and groups, with comprehensive methods and error handling, based on dictionaries and cycle notation.

Findings

Perm class supports order, parity, ranking, unranking, and random permutations.

Group class offers subgroup analysis, orbits, and group properties.

Python modules perms and groups implement these classes and methods.

Abstract

Python implementation of permutations is presented. Three classes are introduced: Perm for permutations, Group for permutation groups, and PermError to report any errors for both classes. The class Perm 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 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 corresponding Python code is contained in the modules perms and groups.