Type:
Class
When mathn is required Rational is changed to simplify the use of Rational operations.
Normal behaviour:
Rational.new!(1,3) ** 2 # => Rational(1, 9) (1 / 3) ** 2 # => 0
require 'mathn' behaviour:
(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.
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.
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.
10.times.inject(0){|t,| t + 0.1} #=> 0.9999999999999999
10.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.
Rational(10) / 3 #=> (10/3)
Rational(10) / 3.0 #=> 3.3333333333333335
Rational(-8) ** Rational(1, 3)
#=> (1.0000000000000002+1.7320508075688772i)