Permutations of finitely many positive integers
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permutation provides a Permutation class for representing permutations of finitely many positive integers in Python. Supported operations & properties include inverses, (group theoretic) order, parity, composition/multiplication, cycle decomposition, cycle notation, word representation, Lehmer codes, and, of course, use as a callable on integers.
Installation
permutation requires Python 3.7 or higher. Just use pip for Python 3 (You have pip, right?) to install:
python3 m pip install permutation
Examples
>>> from permutation import Permutation >>> p = Permutation(2, 1, 4, 5, 3) >>> p.to_cycles() [(1, 2), (3, 4, 5)] >>> print(p) (1 2)(3 4 5) >>> print(p.inverse()) (1 2)(3 5 4) >>> p.degree 5 >>> p.order 6 >>> p.is_even False >>> p.lehmer(5) 27 >>> q = Permutation.cycle(1,2,3) >>> print(p * q) (2 4 5 3) >>> print(q * p) (1 3 4 5) >>> for p in Permutation.group(3): ... print(p) ... 1 (1 2) (2 3) (1 3 2) (1 2 3) (1 3)
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