README.md

# Ratio


[![hex.pm version](https://img.shields.io/hexpm/v/ratio.svg)](https://hex.pm/packages/ratio)
[![Build Status](https://travis-ci.org/Qqwy/elixir-rational.svg?branch=master)](https://travis-ci.org/Qqwy/elixir-rational)


This library allows you to use Rational numbers in Elixir, to enable exact calculations with all numbers big and small.

Ratio follows the Numeric behaviour from [Numbers](https://github.com/Qqwy/elixir_number), and can therefore be used in combination with any data type that uses Numbers (such as [Tensor](https://hex.pm/packages/tensor) and [ComplexNum](https://github.com/Qqwy/elixir_complex_num)).


## Some Examples

Rationals are constructed using `numerator <|> denomerator` (or, if you don't like the infix operator, using `Ratio.new(numerator, denomerator)`)

Notice that Rationals are automaically simplified, and coerced to integers whenever possible.

      iex> use Ratio
      nil
      iex> 1 <|> 2
      1 <|> 2
      iex> 2 <|> 1
      2
      iex> 100 <|> 300
      1 <|> 3
      iex> 1.5 <|> 4
      3 <|> 8

The normal arithmetic-operators are overloaded by Ratio to allow arithmetic with Rationals (as well as normal ints and floats). (If you do not like to overload the infix operators, there are also longhand variants available.)

      iex> 2 + (2 <|> 3)
      5 <|> 5
      iex> 2.3 + 0.3
      13 <|> 5
      iex> (2 <|> 3) - (1 <|> 5)
      7 <|> 15
      iex> (1 <|> 3) / 2
      1 <|> 6
      iex> (2 <|> 3) / (8 <|> 5)
      5 <|> 12

Floats are converted to Rational numbers before performing arithmetic. This allows for more precise results.

      iex> Kernel.-(2.3, 0.3)
      1.9999999999999998
      iex> Kernel.-(2.3, 0.1)
      2.1999999999999997
      iex> use Ratio
      nil
      iex> 2.3 - 0.3
      2
      iex> 2.3 - 0.1
      11 <|> 5

*(Of course, when possible, working with integers from the get-go is always more precise than converting floats)*




## Installation

  The package can be installed from hex, by adding `:ratio` to your list of dependencies in `mix.exs`:

        def deps do
          [
            {:ratio, "~> 1.2.0"}
          ]
        end


  To use the module, use `use Ratio` where you need it.

  If you do not want to override the Kernel's built-in math operators, use 

      # Does not override *, /, -, +, div, abs
      use Ratio, override_math: false

  If you just do not want to override the Kernel's built-in *inline* math operators, use `use Ratio, inline_math: false`

      # Does not override *, /, -, +
      use Ratio, override_math: false

  If you do not want the new operator `<|>` to be imported, use

      use Ratio, operator: false

  These options can be combined (with `override_math` taking precedence over `inline_math` )


## Changelog
- 1.2.3 Upgraded version of the `Numbers` dependency to 2.0.
- 1.2.2 Added default argument to `Ratio.new/2`, to follow the Numeric behaviour fully, and added `Ratio.minus/1` as alias for `Ratio.negate/1` for the same reason.
- 1.2.0 Changed name of `Ratio.mul/2` to `Ratio.mult/2`, to avoid ambiguety, and to allow incorporation with `Numbers`. Deprecation Warning was added to using `Ratio.mul/2`.
- 1.1.1 Negative floats are now converted correctly.
- 1.1.0 Elixir 1.3 compliance (Statefree if/else/catch clauses, etc.)
- 1.0.0 Proper `__using__` macro, with more readable option names. Stable release. 
- 0.6.0 First public release
- 0.0.1 First features


## Difference with the 'rational' library

Observant readers might notice that there also is a '[rational](https://hex.pm/packages/rational)' library in Hex.pm. The design idea between that library vs. this one is a bit different: `Ratio` hides the internal data representation as much as possible, and numbers are therefore created using `Rational.<|>/2` or `Ratio.new/2`. This has as mayor advantage that the internal representation is always correct and simplified.

The Ratio library also (optionally) overrides the built-in math operations `+, -, *, /, div, abs` so they work with combinations of integers, floats and rationals.

Finally, Ratio follows the Numeric behaviour, which means that it can be used with any data types that follow [Numbers](https://github.com/Qqwy/elixir_number).