Ruby Math Library written as exercise by MMCS students.

Add this line to your application's Gemfile:

gem 'silicium'

And then execute:

$ bundle

Or install it yourself as:

$ gem install silicium

To create an empty graph just initialize an object:

    g = OrientedGraph.new
    g = UnorientedGraph.new

Of course, you can determine vertices (name them whatever you want!). To do that, write something like:

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

You have to pass an Array of Hashes, each hash consists of pair of keys:

• v: vertex name;
• i: Array of adjacent vertices

Same goes for the case with unoriented graph (note that missing edges will be added automatically):

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

• Add vertex to your graph:

    g.add_vertex!(Vertex)

• Add edge to your graph:

    g.add_edge!(vertex_from, vertex_to)

• Get vertices adjacted with vertex:

    g.adjacted_with(vertex)

• Set label for the edge:

    g.label_edge!(vertex_from, vertex_to, label)

• Get label for the edge:

    g.get_edge_label(vertex_from, vertex_to)

• Set label for the vertex:

    g.label_vertex!(vertex, label)

• Get label for the vertex:

    g.get_vertex_label(vertex)

• Get number of vertices:

    g.vertex_number

• Get number of edges:

    g.edge_number

• Get number of vertex labels:

    g.vertex_label_number

• Get number of vertex edges:

    g.edge_label_number

• Check whether graph contains vertex:

    g.has_vertex?(vertex)

• Check whether graph contains edge:

    g.has_edge?(vertex_from, vertex_to)

• Delete vertex:

    g.delete_vertex!(vertex)

• Delete edge:

    g.delete_edge!(vertex_from, vertex_to)

• Get array of vertices:

    g.vertices

• Check whether graph is connected:

    g.connected?(graph)

• Breadth-First Search:

    g.breadth_first_search?(graph, starting_vertex, searching_vertex)

• Algorithm of Dijkstra:

     g.dijkstra_algorythm!(graph, starting_vertex)

• Find Strongly Connected Components:

     g.find_strongly_connected_components

def fn(x)
  x**2
end

# 1 unit is equal 40 pixels
set_scale(40)

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

show_window

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 }

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 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)

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'

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.

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.

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

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