symmetria 0.0.1

Symmetria provides an intuitive, thorough, and comprehensive framework for interacting with the symmetric group and its elements.

Welcome to symmetria

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Symmetria provides an intuitive, thorough, and comprehensive framework for interacting with the symmetric group and its elements.

• 📦 - installable via pip
• 🐍 - compatible with Python 3.9, 3.10, 3.11 and 3.12
• 👍 - intuitive API
• 🔢 - mathematically corrected
• ✅ - 100% of test coverage

You can give a look at how to work with symmetria in the section quickstart, or you can check (almost) all the functionality implemented here.

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change, and give a look to the contribution guidelines.

Installation

Symmetria can be comfortably installed from PyPI using the command

pip install symmetria

or directly from the source GitHub code with

pip install git+https://github.com/VascoSch92/symmetria@xxx

where xxx is the name of the branch or the tag you would like to install.

You can check that symmetria was successfully installed by typing the command

symmetria --version

Quickstart

Let's get started with symmetria. First and foremost, we can import the Permutation class from symmetria. The Permutation class serves as the fundamental class for working with elements of the symmetric group, representing permutations as bijective maps. Additionally, you can utilize the Cycle class and CycleDecomposition class to work with cycle permutations and permutations represented as cycle decompositions, respectively.

from symmetria import Permutation

permutation = Permutation(1, 3, 4, 5, 2, 6)

You can now represent your permutation in various formats:

print(permutation)                      # (1, 3, 4, 5, 2, 6)
print(permutation.cycle_notation())     # (1)(2 3 4 5)(6)
print(permutation.one_line_notation()   # 134526

Permutations can be compared between them and are easy to manipulate.

if permutation:
    print("The permutation is different from the identity.")
if permutation == Permutation(1, 2, 3, 4, 5, 6):
    print("The permutation is equal to the identity.")
if len(permutation) == 6:
    print("The permutation acts on 6 elements.")
print(permutation * permutation)

Furthermore, we can decompose a permutation into its cycle decomposition (CycleDecomposition) and compute its order and support.

permuttation.cycle_decomposition()
# returns CycleDecomposition(Cycle(1), Cycle(2, 3, 4, 5), Cycle(6))
permutation.order()  # 4
permutation.support()  # {2, 3, 4, 5}
permutation.is_derangement()  # True

List of implemented functionality

A list of (some) of the functionality implemented for the various classes representing permutation. Here, P is for Permutation, Cfor Cycle, and CD for CycleDecomposition.

Feature	Description	P	C	CD
__call__	Call a permutation on an object	✅	✅	✅
__mul__	Multiplication (composition) between permutations	✅	❌	✅
cycle_decomposition	Cycle decomposition of the permutation	✅	✅	✅
cycle_notation	Return the cycle notation of the permutation	✅	✅	✅
is_derangement	Check if the permutation is a derangement	✅	✅	✅
map	Return the map defining the permutation	✅	✅	✅
one_line_notation	Return the one line notation of the permutation	✅	❌	❌
support	Return the support of the permutation	✅	✅	✅
orbit	Compute image of a given element under the permutation	✅	✅	✅
order	Return the order of the permutation	✅	✅	✅