Type:
Class
When mathn is required Rational is changed to simplify the use of Rational operations.
Normal behaviour:
1 2 | Rational.new!(1,3) ** 2 # => Rational(1, 9)(1 / 3) ** 2 # => 0 |
require 'mathn' behaviour:
1 | (1 / 3) ** 2 # => 1/9 |
A rational number can be represented as a paired integer number; a/b (b>0). Where a is numerator and b is denominator. Integer a equals rational a/1 mathematically.
In ruby, you can create rational object with Rational, #to_r or rationalize method. The return values will be irreducible.
1 2 3 4 | Rational(1) #=> (1/1)Rational(2, 3) #=> (2/3)Rational(4, -6) #=> (-2/3)3.to_r #=> (3/1) |
You can also create rational object from floating-point numbers or strings.
1 2 3 4 5 6 7 8 | Rational(0.3) #=> (5404319552844595/18014398509481984)Rational('0.3') #=> (3/10)Rational('2/3') #=> (2/3)0.3.to_r #=> (5404319552844595/18014398509481984)'0.3'.to_r #=> (3/10)'2/3'.to_r #=> (2/3)0.3.rationalize #=> (3/10) |
A rational object is an exact number, which helps you to write program without any rounding errors.
1 2 | 10.times.inject(0){|t,| t + 0.1} #=> 0.999999999999999910.times.inject(0){|t,| t + Rational('0.1')} #=> (1/1) |
However, when an expression has inexact factor (numerical value or operation), will produce an inexact result.
1 2 3 4 5 | Rational(10) / 3 #=> (10/3)Rational(10) / 3.0 #=> 3.3333333333333335Rational(-8) ** Rational(1, 3) #=> (1.0000000000000002+1.7320508075688772i) |