algorithms-to-solve-the-word-and-conjugacy-problem-in-free-groups-of-finite-rank
I coded these algorithms as part of my thesis work for the King's College London module 6CCM345A Third Year Project to decide the word and conjugacy problems in free groups.
Science Score: 44.0%
This score indicates how likely this project is to be science-related based on various indicators:
-
✓CITATION.cff file
Found CITATION.cff file -
✓codemeta.json file
Found codemeta.json file -
✓.zenodo.json file
Found .zenodo.json file -
○DOI references
-
○Academic publication links
-
○Academic email domains
-
○Institutional organization owner
-
○JOSS paper metadata
-
○Scientific vocabulary similarity
Low similarity (4.7%) to scientific vocabulary
Repository
I coded these algorithms as part of my thesis work for the King's College London module 6CCM345A Third Year Project to decide the word and conjugacy problems in free groups.
Basic Info
- Host: GitHub
- Owner: FrankieNC
- License: cc0-1.0
- Language: Python
- Default Branch: main
- Size: 26.4 KB
Statistics
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 0
Metadata Files
README.md
Algorithms to solve the word and conjugacy problem in free groups of finite rank
I coded these algorithms as part of my thesis work for the King's College London module 6CCM345A Third Year Project to decide the word and conjugacy problems in free groups.
In our algorithms, we adopt a specific representation for words. A word is expressed in the form: $$w = x{i1}^{\varepsilon1}x{i2}^{\varepsilon2}\cdots x{ik}^{\varepsilonk}$$ where $x{ij}$ is an element of the set $X \cup {x^{-1} : x\in X}$ and $\varepsilonh \in { -1,1}.$ We represent this word using an array: $$w = [[i1, \varepsilon1], [i2, \varepsilon2], \ldots, [ik, \varepsilonk]].$$ We have opted for this representation in Python because utilising letters from the alphabet would impose limitations on the number of generators permitted in our group.
In this coding scheme, uppercase letters represent the inverse elements. For instance, the inverse of $xi$ is denoted as $Xi$. When prompted to input words using this code, each letter must be separated by whitespace. For example, if we wish to input the word $w=x1^{-1} x2 x3^{-1} x4$, it should be written as: X1 x2 X3 x4.
Owner
- Login: FrankieNC
- Kind: user
- Repositories: 1
- Profile: https://github.com/FrankieNC
Citation (CITATION.cff)
# This CITATION.cff file was generated with cffinit.
# Visit https://bit.ly/cffinit to generate yours today!
cff-version: 1.2.0
title: Algorithms for word and conjugacy problems in free groups
message: >-
If you use this software, please cite it using the
metadata from this file.
type: software
authors:
- given-names: Francesco Nishanil
family-names: Chotuck
email: fchotuck@gmail.com
identifiers:
- type: url
value: >-
https://github.com/FrankieNC/Algorithms-to-solve-the-word-and-conjugacy-problem-in-free-groups
description: GitHub repository
repository-code: >-
https://github.com/FrankieNC/Algorithms-to-solve-the-word-and-conjugacy-problem-in-free-groups
version: '1.0'
date-released: '2024-03-19'