NoetherPy

A python library for computational abstract algebra designed to make it easy to learn, test conjectures and ideas in a python notebook.

Features

Most of basic (finite) group theory has been implemented:

• Simple and intuitive ways to define groups, subgroups, homomorphisms, etc.
• Symmetric/alternating groups, matrix groups over finite fields, cyclic groups and groups of units of (implemented) rings, finite abelian groups, dihedral groups, quasidihedral groups, and the Klein 4 group are all implemented.
  • Many of the above groups can be instantiated as matrix groups, or permutation groups.
• Most well-known operations on groups/subgroups are supported:
  • Cartesian products, quotient groups, and semidirect products
  • centers, centralizers, normalizers, normal cores, etc.
  • basic Sylow theory
  • automorphism groups (along with inner and outer automorphism groups)
  • subgroup series (derived, lower and upper central)
• Group actions can be defined on anything of Iterable type
• Utilizes the galois package for finite field / number theory support

Getting Started

First, clone this repo:

git clone https://github.com/CCain67/noetherpy.git

then, for now it is recommended to work in a python 3.11 virtual environment:

conda create -n venv_name python=3.11

and install the package by running the following command in the project's root directory:

pip install .

Now, inside of a Jupyter Notebook, the package can be imported:

import noetherpy as ntr

Showcase

For a getting a general idea of what one can do with this library, check the showcase here: Showcase

Future plans:

• better documentation + wiki
• representation and character theory of finite groups
• group (co)homology

You know GAP/Magma/Sage/etc. exists right??

Of course! Those tools are certainly better/faster, this is just for fun.