Class | Rational |
In: |
lib/rational.rb
|
Parent: | Numeric |
Rational implements a rational class for numbers.
A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q != 0. A rational number p/q is said to have numerator p and denominator q. Numbers that are not rational are called irrational numbers. (mathworld.wolfram.com/RationalNumber.html)
To create a Rational Number:
Rational(a,b) # -> a/b Rational.new!(a,b) # -> a/b
Examples:
Rational(5,6) # -> 5/6 Rational(5) # -> 5/1
Rational numbers are reduced to their lowest terms:
Rational(6,10) # -> 3/5
But not if you use the unusual method "new!":
Rational.new!(6,10) # -> 6/10
Division by zero is obviously not allowed:
Rational(3,0) # -> ZeroDivisionError
denominator | [R] | |
numerator | [R] |
Implements the constructor. This method does not reduce to lowest terms or check for division by zero. Therefore Rational() should be preferred in normal use.
Reduces the given numerator and denominator to their lowest terms. Use Rational() instead.
Returns the remainder when this value is divided by other.
Examples:
r = Rational(7,4) # -> Rational(7,4) r % Rational(1,2) # -> Rational(1,4) r % 1 # -> Rational(3,4) r % Rational(1,7) # -> Rational(1,28) r % 0.26 # -> 0.19
Returns the product of this value and a.
Examples:
r = Rational(3,4) # -> Rational(3,4) r * 2 # -> Rational(3,2) r * 4 # -> Rational(3,1) r * 0.5 # -> 0.375 r * Rational(1,2) # -> Rational(3,8)
Returns this value raised to the given power.
Examples:
r = Rational(3,4) # -> Rational(3,4) r ** 2 # -> Rational(9,16) r ** 2.0 # -> 0.5625 r ** Rational(1,2) # -> 0.866025403784439
Returns the addition of this value and a.
Examples:
r = Rational(3,4) # -> Rational(3,4) r + 1 # -> Rational(7,4) r + 0.5 # -> 1.25
Returns the difference of this value and a. subtracted.
Examples:
r = Rational(3,4) # -> Rational(3,4) r - 1 # -> Rational(-1,4) r - 0.5 # -> 0.25
Returns the quotient of this value and a.
r = Rational(3,4) # -> Rational(3,4) r / 2 # -> Rational(3,8) r / 2.0 # -> 0.375 r / Rational(1,2) # -> Rational(3,2)
Returns true iff this value is numerically equal to other.
But beware:
Rational(1,2) == Rational(4,8) # -> true Rational(1,2) == Rational.new!(4,8) # -> false
Don‘t use Rational.new!
Returns the quotient and remainder.
Examples:
r = Rational(7,4) # -> Rational(7,4) r.divmod Rational(1,2) # -> [3, Rational(1,4)]
Converts the rational to an Integer. Not the nearest integer, the truncated integer. Study the following example carefully:
Rational(+7,4).to_i # -> 1 Rational(-7,4).to_i # -> -2 (-1.75).to_i # -> -1
In other words:
Rational(-7,4) == -1.75 # -> true Rational(-7,4).to_i == (-1.75).to_i # false