Symbo

A simple symbolic computation library in Ruby

Numerical calculations using computers are approximate. For example, if you calculate the square root of 2 on a computer, the result is an approximation with numbers omitted, despite √2 being an infinitely irrational number.

irb> Math.sqrt(2)
=> 1.4142135623730951

What happens if we further calculate (1/√2)^2? If we calculate it by hand, it should be 0.5 because it is equal to 1/2. However, in practice, a different value is returned.

irb> (1 / Math.sqrt(2))**2
=> 0.4999999999999999

If you use symbolic computation, you can do error-free calculations. Symbolic operations transform mathematical formulas in the same way as human calculations and find the answer. Symbo is a symbolic computation library for Ruby that can calculate the above expression correctly.

Open the Symbo console with the following command and calculate (1/√2)^2.

% ./bin/console
irb> ((1/√(2))**2).simplify.to_s
=> "1/2"

#simplify is a method that transforms a mathematical expression as simple as possible. Using this method, you can transform not only numerical calculations but also expressions with variables into simple forms.

# ((x·y)^(1/2) * z^2)^2 # => x·y·z^4
irb> (((:x * :y)**(1/2) * :z**2)**2).simplify.to_s
=> "x*y*z^4"

Add this line to your application's Gemfile:

gem 'symbo'

And then execute:

$ bundle

Or install it yourself as:

$ gem install symbo

Here is a simple sample code that uses Symbo. Load the required libraries with require 'symbo'. include Symbo allows operations and constants such as √ and π to be used. using Symbo replaces subsequent operations with symbolic operations by Symbo.

require 'symbo'

class MyClass
  include Symbo
  using Symbo

  # Your code goes here
  # ...

end

• +, -, *, /, **, TensorProduct
• Integers, fractions, complex numbers, variables, e (the base of the natural logarithm) and π
• Trigonometric functions (cos(x) and sin(x)) and anonymous functions (e.g. f(x), g(x))
• Matrices and vectors
• Qubit and bra-ket vectors

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/yasuhito/symbo.

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