GroupsMath – v0.4.0

GroupsMath is a Python module for constructing, studying, and manipulating finite groups.

The project aims to provide a simple and intuitive interface for working with finite groups and their algebraic properties.

Note: GroupsMath is currently under active development. Its API is still evolving and may change before version 1.0.0.

Installation

GroupsMath is currently distributed through GitHub and has not yet been published on PyPI.

To install the latest released version from PyPI, run:

pip install groupsmath

Alternatively, you can install the latest development version directly from GitHub:

pip install git+https://github.com/MarioSultan/GroupsMath.git

Alternatively, you can visit https://github.com/MarioSultan/GroupsMath and download all the files.

Examples

Cayley table of $S_3$

Cayley table of $A_5\times C_4$

Cayley table of $U_{1200}$

Features

GroupsMath is designed to provide tools for working with finite groups, including:

GROUPS:

• Construction of finite groups.
• Determination of the order of a group and its elements.
• Operation with group elements (multiplication, inverse, powers, ...)
• Computation of Cayley tables with matplotlib.pyplot.
• Detection of algebraic properties such as cyclicity and commutativity.
• Computation and exploration of other structural properties of finite groups.
• Predefined group families in the library groupsmath.precooked, such as $C_n$, $S_n$, $A_n$, $D_n$, $V_4$, $Q_8$, ...

SUBGROUPS:

• Study of subgroups (order, cosets, normal subgroups, quotients, ...).
• Normal subgroups.
• Quotient groups $Q=G/H$.

AUTOMORPHISMS:

• Class Automorphism and automorphism functions.
• Automorphism groups $\text{Aut}(G)$.

PRODUCTS:

• Direct product of two groups $G\times H$.
• Semidirect product of two groups $G\rtimes H$.

The available functionality will expand as the project develops.

Coming soon

The GroupsMath team is currently working on theese ideas:

• Presentation of groups and generators.
• Groups generated by matrices ($GL$, $O$,...).
• Optimization of actual features.

Documentation

Detailed documentation is available in the docs directory of GitHub. The documentation is developed alongside the library.

Project status

GroupsMath is currently under active development.

The project has successfully transitioned to an object-oriented interface centered around the Group class. The legacy function-based interface is being removed for future versions.

The API should therefore be considered unstable until the 1.0.0 release, and breaking changes may occur between development versions.

Contributing

Contributions, suggestions, and bug reports are welcome. If you find a bug or have an idea for improving GroupsMath, please open an issue in the GitHub repository.