Latin Square Tools

A Python module offering a suite of tools to work with Latin squares, including Hamiltonicity checks, isotopy operations, generation algorithms, and additional validation utilities.

Features

• Hamiltonicity Tools:
  • Check if a graph is a Hamiltonian cycle.
  • Verify CE-hamiltonian, CR-hamiltonian, and symbol-hamiltonian Latin squares.
  • Assess anti-row-hamiltonicity.
• Isotopy Tools:
  • Apply isotopies to Latin squares.
  • Check isotopy between two Latin squares (brute-force approach).
• Generation Tools:
  • Generate a random Latin square using backtracking.
  • Create the $Z_n$ Latin square.
  • Create a Latin square from a strong starter.
• Other Tools:
  • Validate Latin squares.
  • Verify orthogonality and idempotency.
  • Construct magic squares from orthogonal Latin squares.
  • Utilities for pretty printing matrices.

Installation

No external dependencies are required. Simply clone or download the module into your project:

git clone https://github.com/GanschowJosh/LatinSquareTools.git

Usage

Import the module and call the functions as needed. For example:

from latin_square_tools import generate_latin_square, is_magic_square, print_latin_square

# Generate a Latin square of order 5
square = generate_latin_square(5)
print("Generated Latin Square:")
print_latin_square(square)

# Check if the generated square is magic
if is_magic_square(square):
    print("The square is a magic square!")
else:
    print("The square is not a magic square.")

Contributions/Suggestions

Feel free to fork and add your own tools or send some suggestions for any utilities or functionality you'd like to see!