chipfiring 0.0.1

This is an Pythonic API for visualization and analysis of chip firing games and corresponding algorithms.

chipfiring

Unified interface for visualization and analysis of chip firing games and related algorithms.

A Python implementation of the chip-firing game (also known as the dollar game) on graphs. This package provides a mathematical framework for studying and experimenting with chip-firing games, with a focus on the dollar game variant.

Documentation

Visit Read the Docs for the full documentation, including overviews and several examples.

Overview

The chip-firing game is a mathematical model that can be used to study various phenomena in graph theory, algebraic geometry, and other areas of mathematics. In the dollar game variant, we consider a graph where:

• Vertices represent people
• Edges represent relationships between people
• Each vertex has an integer value representing wealth (negative values indicate debt)
• Players can perform lending/borrowing moves by sending money across edges

The goal is to find a sequence of moves that makes everyone debt-free. If such a sequence exists, the game is said to be winnable.

Installation

pip install chipfiring

Usage

Here's a simple example of how to use the package:

from chipfiring.graph import Graph, Vertex
from chipfiring.divisor import Divisor
from chipfiring.dollar_game import DollarGame

# Create vertices
alice = Vertex("Alice")
bob = Vertex("Bob")
charlie = Vertex("Charlie")
elise = Vertex("Elise")

# Create graph
G = Graph()
G.add_vertex(alice)
G.add_vertex(bob)
G.add_vertex(charlie)
G.add_vertex(elise)

# Add edges
G.add_edge(alice, bob)
G.add_edge(alice, charlie)
G.add_edge(alice, elise)
G.add_edge(bob, charlie)
G.add_edge(charlie, elise)

# Create initial wealth distribution
initial_divisor = Divisor(G, {
    alice: 2,
    bob: -3,
    charlie: 4,
    elise: -1
})

# Create and play the game
game = DollarGame(G, initial_divisor)

# Check if game is winnable
print(f"Is winnable? {game.is_winnable()}")

# Try some moves
game.fire_vertex(charlie)  # Charlie lends
game.borrow_vertex(bob)    # Bob borrows
game.fire_set({alice, elise, charlie})  # Set-firing move

# Check current state
print(f"Current wealth: {game.get_current_state()}")
print(f"Is effective? {game.is_effective()}")

Mathematical Background

The implementation follows the mathematical formalization described in the LaTeX writeup, which includes:

1. Graph Structure: Finite, connected, undirected multigraphs without loop edges
2. Divisors: Elements of the free abelian group on vertices
3. Laplacian Matrix: Matrix representation of lending moves
4. Linear Equivalence: Equivalence relation on divisors
5. Effective Divisors: Divisors with non-negative values
6. Winnability: Property of being linearly equivalent to an effective divisor

Features

• Mathematical graph implementation with support for multigraphs
• Divisor class with operations for lending and borrowing
• Laplacian matrix computations
• Linear equivalence checking
• Set-firing moves
• Comprehensive type hints and documentation

Development

To set up the development environment:

# Clone the repository
git clone https://github.com/yourusername/chipfiring.git
cd chipfiring

# Create and activate virtual environment
python -m venv venv
source venv/bin/activate  # On Windows: venv\Scripts\activate

# Install development dependencies
pip install -r requirements.txt
pip install -r requirements.docs.txt

# Run tests
pytest

# Build documentation
cd docs
make html

License

This project is licensed under the MIT License - see the LICENSE file for details.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.