NumericInverse

This gem provides a method Numeric#inverse to get a (usual/modular) multiplicative inverse of a number readily.

Installation

Add this line to your application's Gemfile:

gem 'numeric_inverse'

And then execute:

$ bundle

Or install it yourself as:

$ gem install numeric_inverse

Usage

The module NumericInverse uses "refinements" to define #inverse (alias #inv) locally. You should activate them with Module#using or main.using.

If you want to define them globally (without refinements), please require numeric_inverse/ext instead.

require "numeric_inverse"
p Rational(7, 22).inv   #=> NoMethodError

using NumericInverse
p Rational(7, 22).inv   #=> (22/7)
p Integer(16).inv       #=> (1/16)
p Float(16).inv         #=> 0.0625
p Complex(3, 4).inv     #=> ((3/25)-(4/25)*i)

# arithmetic mean and harmonic mean
a = [9, 10, 15, 18]
p a.sum.quo(a.size)           #=> (13/1)
p a.sum(&:inv).inv * a.size   #=> (12/1)

In addition, Integer#inverse returns its modular multiplicative inverse when a modulus is given.

require "numeric_inverse"
using NumericInverse

# multiplicative inverse of integers
p 63.inv        #=> (1/63)
p 63.inv * 63   #=> (1/1)

# modular multiplicative inverse
p 63.inv(100)              #=> 27
p 63.inv(100) * 63         #=> 1701
p 63.inv(100) * 63 % 100   #=> 1

p 64.inv(100)   #=> ArgumentError: modulus is not coprime to the receiver

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/hmmnrst/numeric_inverse.

License

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