Gromov’s Approximating Tree .ipynb
Research Tool / Demonstration
Included in this repository is a Jupyter Notebook file containing an implementation of the algorithm discussed in Gromov’s Approximating Tree and the All-Pairs Bottleneck Paths Problem by Anders Cornect (myself) and Dr. Eduardo Martinez-Pedroza of Memorial University of Newfoundland.
Current Features:
- Jupyter Notebook containing code that demonstrates the connection between Gromov’s Approximating Tree and the All-Pairs Bottleneck Paths problem, as discussed in the above paper.
- Included is an example of a graph being approximated by this method, with each graph drawn using the NetworkX package for Python.
Thompson’s Group F Python Package
Research Tool
This package implements Thompson’s Group \(F\), from this point simply referred to as \(F\), as a Python class. For the necessary background information, please see José Burillo’s Introduction to Thompson’s Group \(F\), available from his page on the Universitat Politècnica de Catalunya website. This book assumes basic knowledge of group theory and graph theory.
Elements of \(F\) are implemented using the following infinite presentation by generators and relations:
\[F = \left\langle x_0, x_1, x_2, \ldots, x_n, \ldots \mid x_i^{-1}x_jx_i = x_{j+i}, \text{ for } i < j \right\rangle.\]Each element is represented as a product of the above generators \(x_i\). Much of the theory behind certain features, most notably the representation of elements by “forest diagrams”, as well as calculating the word length of elements, come from the paper Forest Diagrams for Elements of Thompson’s Group \(F\) (2005) by James M. Belk and Kenneth S. Brown of Cornell University, available on arXiv.
Documentation is hosted on ReadTheDocs.
Current Features:
- Multiplication and division of abstract elements in \(F\).
- Finding normal forms of elements.
- Representing elements by forest diagrams (in the form of strings and Python Turtle drawings).
- Calculating the word length of elements in terms of generators \(x_0\) and \(x_1\).
Planned Features:
- Representing of elements as pairs of binary trees.
Requirements:
- Python 3.10 or newer.
ForPeanuts (4PN) Small Inventory Manager
Personal Project
ForPeanuts is a small inventory manager, designed with a focus on simplicity and ease of use. This was originally designed for use by vendors at a local farmer’s market, but ended up becoming more of a personal coding project. Designed with PyQt6.
Current Features:
- Tracking of inventory by item, with categories that can comprise a number of similar items.
- Order and revenue tracking, with built-in profit calculator (i.e., profit after taking production costs into account).
- Built-in sales feature, i.e., automatic tracing & price calculation for BOGO-style and bulk offerings.
- Order logging, allows inventory and sales data to be saved locally for later use.
- Graphing of customer count and profit over time.