latinsq 0.2.3

A package for manipulating latin squares

Latin Squares

This is a small package for generating and manipulating Latin Squares. It was created to support games an other applications for the Callysto Project. It hasn't been particularly widely tested or optimized so use at your own risk.

Getting Started

This package implements a LatinSquare object with various methods to initialize, generate new squares, check validity and things like that.

>>> import numpy as np
>>> # from src.latinsq import LatinSquare
>>> from latinsq import LatinSquare


>>> # Initialize from values
>>> square = np.array([
[1, 2, 3],
[3, 1, 2],
[2, 3, 1]
])
>>> ls = LatinSquare(square)
array([[1, 2, 3],
       [3, 1, 2],
       [2, 3, 1]])

>>> square.valid()
True

>>> # Generate a random square
>>> LatinSquare.random(n=3)
array([[2, 1, 3],
       [3, 2, 1],
       [1, 3, 2]])

The random generator attempts to implement an algorithm described by Jacobson and Matthews draw a random latin square uniformly from the space of valid latin squares.

References

1. Wikipedia article: Latin Squares
2. Generating Uniformly distributed random latin squares - Jacobson & Matthews doi:10.1002/(sici)1520-6610(1996)4:6<405::aid-jcd3>3.0.co;2-j
3. susansmathgames.ca has an article on latin and euler squares with good exposition on teaching with squares.
4. Knuth, The Art of Computer Programming Volume 4A supposedly has a discussion. I haven't seen it yet, but will probably be interesting.
5. Wolfram.com latin squares.
6. Enclopedia of Mathematics.
7. Blog article with go implementation. This is probably closest to the version implemented here.
8. SageMath Latin Square Implementation - A recent find, but if we can split out the dependencies might be very useful.