https://github.com/dvberkel/picture-hanging

Provide primitives to construct words over free groups to solve picture-hanging puzzles
https://github.com/dvberkel/picture-hanging

Last synced: 3 months ago
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Provide primitives to construct words over free groups to solve picture-hanging puzzles

• Host: GitHub
• URL: https://github.com/dvberkel/picture-hanging
• Owner: dvberkel
• Created: 2012-03-22T07:05:37.000Z (about 13 years ago)
• Default Branch: master
• Last Pushed: 2012-03-23T07:21:29.000Z (about 13 years ago)
• Last Synced: 2025-02-07T23:32:46.067Z (4 months ago)
• Language: Python
• Homepage: http://arxiv.org/abs/1203.3602
• Size: 117 KB
• Stars: 1
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
Picture-Hanging

===============

[![Build Status](https://secure.travis-ci.org/dvberkel/picture-hanging.png?branch=master)](http://travis-ci.org/dvberkel/picture-hanging)

In [Picture-Hanging Puzzles](http://arxiv.org/abs/1203.3602 "ArXiv page for 'Picture-Hanging Puzzles'")

a famous puzzle, and some of its generalisations are solved using a

words over a free group.

This project offers primitives which enable a developer to express

words over free groups and operate on these words in similiar ways as

expressed in the article.

Free Group

----------

Wikipedia has a nice [article](http://en.wikipedia.org/wiki/Free_group "Wikipedia on Free Groups")

on free groups.

> In mathematics, a group *G* is called **free** if there is a subset *S* of *G*

> such that any element of *G* can be written in one and only one way as

> a product of finitely many elements of *S* and their inverses

> (disregarding trivial variations). Apart from the existence of

> inverses no other relation exists between the generators of a free

> group.

Environment

-----------

Python is used in this project. Make sure that python is able to find

the project. I usually add the current directory to the `PYTHONPATH`

with the following command.

    > export PYTHONPATH=.

### Tests

Execute the following command to run all tests in the project

    > python picture/test/test_all.py

### Executables

To solve a picture hanging puzzle with *n* pins run

    > bin/picture-hanging n