Silicium

Ruby Math Library written as exercise by MMCS students.

Installation

Add this line to your application's Gemfile:

gem 'silicium'

And then execute:

$ bundle

Or install it yourself as:

$ gem install silicium

Usage

• Graph Section:

  Oriented Graph Initialization example:

  g = OrientedGraph.new([{v: 0, i: [:one]}, {v: :one, i: [0, 'two']}, {v: 'two', i: [0, 'two']}])

  Unoriented Graph Initialization example:

  g = UnorientedGraph.new([{v: 0, i: [:one]}, {v: :one, i: [0, 'two']}, {v: 'two', i: [0, 'two']}])

  Graph Methods:

  Add vertex: add_vertex!(Vertex)

  Add edge: add_edge!(vertex_from, vertex_to)

  Get vertices adjacted with vertex: adjacted_with(vertex)

  Set label for edge: label_edge!(vertex_from, vertex_to, label)

  Get label for edge: get_edge_label(vertex_from, vertex_to)

  Set label for vertex: label_vertex!(vertex, label)

  Get label for vertex: get_vertex_label(vertex)

  Get number of vertices: vertex_number

  Get number of edges: edge_number

  Get number of vertex labels: vertex_label_number

  Get number of vertex edges:edge_label_number

  Check if graph contains vertex: has_vertex?(vertex)

  Check if graph contains edge: has_edge?(vertex_from, vertex_to)

  Delete vertex: delete_vertex!(vertex)

  Delete edge: delete_edge!(vertex_from, vertex_to)

  Get array of vertices: vertices

  Algorithms for graphs:

  Check if graph is connected: connected?(graph)

  BFS: breadth_first_search?(graph, starting_vertex, searching_vertex)

  Algorithm of Dijkstra: dijkstra_algorythm!(graph, starting_vertex)

Plotter

Determine your function

def fn(x)
  x**2
end

Set scale

# 1 unit is equal 40 pixels
set_scale(40)

Draw you function

draw_fn(-20, 20) {|args| fn(args)}

Show your plot

show_window

Result

Numerical integration

Library Numerical integration includes methods for numerical integration of functions, such as 3/8 method, Simpson method, left, right and middle rectangle methods and trapezoid method.

Each function accepts 4 parameters, such as left and right integration boundaries, default accuracy of 0.0001 and the function itself. Example: three_eights_integration(4, 5, 0.01) { |x| 1 / x } or three_eights_integration(4, 5) { |x| 1 / x }

For example, to integrate 1 / x in between [4, 5] using the 3/8 method, you need to use: NumericalIntegration.three_eights_integration(4, 5) { |x| 1 / x }

using the Simpson's method: NumericalIntegration.simpson_integration(4, 5) { |x| 1 / x }

using the left rectangle method: NumericalIntegration.left_rect_integration(4, 5) { |x| 1 / x }

using the right rectangle method: NumericalIntegration.right_rect_integration(4, 5) { |x| 1 / x }

using the middle rectangle method: NumericalIntegration.middle_rectangles(4, 5) { |x| 1 / x }

using the trapezoid method: NumericalIntegration.trapezoid(4, 5) { |x| 1 / x }

Theory of probability

Combinatorics

Module with usual combinatorics formulas

    factorial(5) # 5! = 120
    combination(n, k) # C(n, k) = n! / (k! * (n-k)!)
    arrangement(n, k) # A(n, k) = n! / (n - k)!

Module Dice

Module describing both ordinary and unique dices

You can initialize a Polyhedron by two ways

first: by number - Polyhedron.new(6) - creates polyhedron with 6 sides [1,2,3,4,5,6]

second: by array - Polyhedron.new([1,3,5]) - creates polyhedron with 3 sides [1,3,5]

class Polyhedron
    csides # sides number
    sides  # array of sides
    throw # method of random getting on of the Polyhedron's sides

Example

d = Polyhedron.new(8)
d.csides # 8
d.sides # [1,2,3,4,5,6,7,8]
d.throw # getting random side (from 1 to 8)

d1 = Polyhedron.new([1,3,5,6])
d1.csides # 4
d1.sides # [1,3,5,6]
d1.throw # getting random side (from 1 or 3 or 5 or 8)

Class PolyhedronSet

You can initialize PolyhedronSet by array of:

Polyhedrons

Number of Polyhedron's sides

Array of sides

class PolyhedronSet
    percentage # hash with chances of getting definite score
    throw   # method of getting points from throwing polyhedrons
    make_graph_by_plotter # creating graph introducing chances of getting score

Example

s = PolyhedronSet.new([6, [1,2,3,4,5,6], Polyhedron.new(6)]) 

s.percentage # {3=>0.004629629629629629, 4=>0.013888888888888888, 5=>0.027777777777777776, 6=>0.046296296296296294, 
              # 7=>0.06944444444444445, 8=>0.09722222222222222, 9=>0.11574074074074074, 
              # 10=>0.125, 11=>0.125, 12=>0.11574074074074074, 13=>0.09722222222222222, 14=>0.06944444444444445, 
              # 15=>0.046296296296296294, 16=>0.027777777777777776, 17=>0.013888888888888888, 18=>0.004629629629629629}    

s.throw   # getting random score (from 3 to 18)

s.make_graph_by_plotter(xsize, ysize) # creates a graph in 'tmp/percentage.png'

Development

After checking out the repo, run bin/setup to install dependencies. Then, run rake test 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/mmcs-ruby/silicium. 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.

Code of Conduct

Everyone interacting in the Silicium project’s codebases, issue trackers, chat rooms and mailing lists is expected to follow the code of conduct.