Math::Discrete

A library and DSL for discrete mathematical structures and algorithms

Installation

Add this line to your application's Gemfile:

gem 'discrete'

And then execute:

$ bundle

Or install it yourself as:

$ gem install discrete

To-do

This project is a work in progress and more structures and algorithms will be implemented:

Structures:

• Sets (finite and infinite)
• Set Comprehensions (for sets of all other constructs)
• Logic Propositions (first-order and second-order)
• Graphs
• Graph Constructs (paths)
• Natural numbers and Integer numbers
• Mappings (injections, surjections, bijections between two sets)

Algorithms:

• Graph algorithms:
  • Deterministic algorithms:
    • Breadth-first search
    • Depth-first search
    • Shortest path
    • Minimum spanning tree
    • Maximum flow
    • More TBD
  • Aproximation algorithms
    • Graph Colouring
    • Traveling salesman

Design:

• Extract a Math::Discrete::Structure namespace that contains cross-structure methods and logic
• Document every algorithm and property with relevant Wikipedia articles and papers

Usage

Graphs

# Initializing vertices and edges
first_vertex = Vertex['a'] # Or Node['a']
second_vertex = Vertex['b']
edge = Edge[first_vertex, second_vertex]

vertex_set = Vertex::Set['a', 'b', 'c', 'd'] # Or Node::Set['a', 'b', 'c', 'd']
a, b, c, d = *vertex_set
edge_set = Edge::Set[[a, b], [a, c], [a, d], [b, d], [c, d]]

# Initializing graphs
graph = Graph[]
graph << a
graph << b
graph << Edge[a,b]

# You can initialize a graph with a vertex set and an edge set
graph = Graph[vertex_set, edge_set]
# Or directly with labels
graph = Graph[['a', 'b', 'c', 'd'], ['a', 'b'], ['a', 'c'], ['a', 'd'], ['b', 'd'], ['c', 'd']]

# Weighted graphs are supported as well, by adding a third argument to the edge constructor
montreal, toronto = *Vertex::Set['Montreal', 'Toronto']
edge = Edge[montreal, toronto, 506] # The distance between MTL and the 6IX is 506 kms

map = Graph[
  ['Montreal', 'Toronto', 'Boston'],
  [
    ['Montreal', 'Toronto', 506],
    ['Toronto', 'Boston', 885],
    ['Boston', 'Montreal', 405]
  ]
]

Development

After checking out the repo, run bin/setup to install dependencies. Then, run rake spec to run the tests. You can also run bin/console for an interactive prompt that will allow you to experiment.

To install this gem onto your local machine, run bundle exec rake install. To release a new version, update the version number in version.rb, and then run bundle exec rake release, which will create a git tag for the version, push git commits and tags, and push the .gem file to rubygems.org.

Contributing

Bug reports and pull requests are welcome on GitHub at https://github.com/moechaieb/discrete. This project is intended to be a safe, welcoming space for collaboration, and contributors are expected to adhere to the Contributor Covenant code of conduct.

License

The gem is available as open source under the terms of the MIT License.