groups is a basic Computer Algebra System to study various finite group structures from Group Theory.
Definition (Group). A group is a non-empty set in Mathematics, elements of which follow 4 properties namely Closure, Associativity, Existence of Identity and Existence of Inverses under a certain operation.
Study finite group structures easily with python! This library contains various modules related to select group structures in Mathematics. This is a work in continuous progress, and I hope to continue working on this and add many more groups gradually. This README file walks you through the available modules.
To install the library, run
pip install git+"https://github.com/zplus11/groups"
groups offers the following Groups:
| Group | Class | Description |
|---|---|---|
| Dihedral | D(sides = 3) |
Dn is the group of symmetries of a regular polygon. See [1] below. |
| Addition modulo n | Z(n = 1) |
Zn is the group {0, 1, ..., n-1} formed under addition modulo n. |
| Multiplication modulo n | U(n = 1) |
Un is the group {1 <= x < n : gcd(n, x) = 1} formed under multiplication modulo n. |
| K4 | K4() |
Klein's 4 group. |
| Q8 | Q8() |
Quaternion group. |
| EDP | EDP(G1, G2, ..., Gn) |
External Direct Product of groups. |
[1] The symmetries\dihedral.py module implements the idea of polygon symmetries using permutations. See this page for more details.
See this file to get a tour through the available modules in this package.
groups is licensed under the MIT License. See License for more details.