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Rational

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

Attributes

denominator[R]
numerator[R]

Public Class Methods

new(num, den) click to toggle source

This method is actually private.

 
               # File rational.rb, line 102
def initialize(num, den)
  if den < 0
    num = -num
    den = -den
  end
  if num.kind_of?(Integer) and den.kind_of?(Integer)
    @numerator = num
    @denominator = den
  else
    @numerator = num.to_i
    @denominator = den.to_i
  end
end
            
new!(num, den = 1) click to toggle source

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.

 
               # File rational.rb, line 93
def Rational.new!(num, den = 1)
  new(num, den)
end
            
reduce(num, den = 1) click to toggle source

Reduces the given numerator and denominator to their lowest terms. Use Rational() instead.

 
               # File rational.rb, line 71
def Rational.reduce(num, den = 1)
  raise ZeroDivisionError, "denominator is zero" if den == 0

  if den < 0
    num = -num
    den = -den
  end
  gcd = num.gcd(den)
  num = num.div(gcd)
  den = den.div(gcd)
  if den == 1 && defined?(Unify)
    num
  else
    new!(num, den)
  end
end
            

Public Instance Methods

%(other) click to toggle source

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
 
               # File rational.rb, line 257
def % (other)
  value = (self / other).floor
  return self - other * value
end
            
*(a) click to toggle source

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)
 
               # File rational.rb, line 173
def * (a)
  if a.kind_of?(Rational)
    num = @numerator * a.numerator
    den = @denominator * a.denominator
    Rational(num, den)
  elsif a.kind_of?(Integer)
    self * Rational.new!(a, 1)
  elsif a.kind_of?(Float)
    Float(self) * a
  else
    x, y = a.coerce(self)
    x * y
  end
end
            
**(other) click to toggle source

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
 
               # File rational.rb, line 220
def ** (other)
  if other.kind_of?(Rational)
    Float(self) ** other
  elsif other.kind_of?(Integer)
    if other > 0
      num = @numerator ** other
      den = @denominator ** other
    elsif other < 0
      num = @denominator ** -other
      den = @numerator ** -other
    elsif other == 0
      num = 1
      den = 1
    end
    Rational.new!(num, den)
  elsif other.kind_of?(Float)
    Float(self) ** other
  else
    x, y = other.coerce(self)
    x ** y
  end
end
            
+(a) click to toggle source

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
 
               # File rational.rb, line 124
def + (a)
  if a.kind_of?(Rational)
    num = @numerator * a.denominator
    num_a = a.numerator * @denominator
    Rational(num + num_a, @denominator * a.denominator)
  elsif a.kind_of?(Integer)
    self + Rational.new!(a, 1)
  elsif a.kind_of?(Float)
    Float(self) + a
  else
    x, y = a.coerce(self)
    x + y
  end
end
            
-(a) click to toggle source

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
 
               # File rational.rb, line 148
def - (a)
  if a.kind_of?(Rational)
    num = @numerator * a.denominator
    num_a = a.numerator * @denominator
    Rational(num - num_a, @denominator*a.denominator)
  elsif a.kind_of?(Integer)
    self - Rational.new!(a, 1)
  elsif a.kind_of?(Float)
    Float(self) - a
  else
    x, y = a.coerce(self)
    x - y
  end
end
            
/(a) click to toggle source

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)
 
               # File rational.rb, line 195
def / (a)
  if a.kind_of?(Rational)
    num = @numerator * a.denominator
    den = @denominator * a.numerator
    Rational(num, den)
  elsif a.kind_of?(Integer)
    raise ZeroDivisionError, "division by zero" if a == 0
    self / Rational.new!(a, 1)
  elsif a.kind_of?(Float)
    Float(self) / a
  else
    x, y = a.coerce(self)
    x / y
  end
end
            
<=>(other) click to toggle source

Standard comparison operator.

 
               # File rational.rb, line 309
def <=> (other)
  if other.kind_of?(Rational)
    num = @numerator * other.denominator
    num_a = other.numerator * @denominator
    v = num - num_a
    if v > 0
      return 1
    elsif v < 0
      return  -1
    else
      return 0
    end
  elsif other.kind_of?(Integer)
    return self <=> Rational.new!(other, 1)
  elsif other.kind_of?(Float)
    return Float(self) <=> other
  elsif defined? other.coerce
    x, y = other.coerce(self)
    return x <=> y
  else
    return nil
  end
end
            
==(other) click to toggle source

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 ::new!

 
               # File rational.rb, line 294
def == (other)
  if other.kind_of?(Rational)
    @numerator == other.numerator and @denominator == other.denominator
  elsif other.kind_of?(Integer)
    self == Rational.new!(other, 1)
  elsif other.kind_of?(Float)
    Float(self) == other
  else
    other == self
  end
end
            
abs() click to toggle source

Returns the absolute value.

 
               # File rational.rb, line 277
def abs
  if @numerator > 0
    self
  else
    Rational.new!(-@numerator, @denominator)
  end
end
            
ceil() click to toggle source
 
               # File rational.rb, line 360
def ceil()
  -((-@numerator).div(@denominator))
end
            
coerce(other) click to toggle source
 
               # File rational.rb, line 333
def coerce(other)
  if other.kind_of?(Float)
    return other, self.to_f
  elsif other.kind_of?(Integer)
    return Rational.new!(other, 1), self
  else
    super
  end
end
            
div(other) click to toggle source
 
               # File rational.rb, line 243
def div(other)
  (self / other).floor
end
            
divmod(other) click to toggle source

Returns the quotient and remainder.

Examples:

r = Rational(7,4)        # -> Rational(7,4)
r.divmod Rational(1,2)   # -> [3, Rational(1,4)]
 
               # File rational.rb, line 269
def divmod(other)
  value = (self / other).floor
  return value, self - other * value
end
            
floor() click to toggle source

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             # -> -1
(-1.75).to_i                    # -> -1

In other words:

Rational(-7,4) == -1.75                 # -> true
Rational(-7,4).to_i == (-1.75).to_i     # -> true
 
               # File rational.rb, line 356
def floor()
  @numerator.div(@denominator)
end
            
hash() click to toggle source

Returns a hash code for the object.

 
               # File rational.rb, line 427
def hash
  @numerator.hash ^ @denominator.hash
end
            
inspect() click to toggle source

Returns a reconstructable string representation:

Rational(5,8).inspect     # -> "Rational(5, 8)"
 
               # File rational.rb, line 420
def inspect
  sprintf("Rational(%s, %s)", @numerator.inspect, @denominator.inspect)
end
            
round() click to toggle source
 
               # File rational.rb, line 373
def round()
  if @numerator < 0
    num = -@numerator
    num = num * 2 + @denominator
    den = @denominator * 2
    -(num.div(den))
  else
    num = @numerator * 2 + @denominator
    den = @denominator * 2
    num.div(den)
  end
end
            
to_f() click to toggle source

Converts the rational to a Float.

 
               # File rational.rb, line 389
def to_f
  @numerator.fdiv(@denominator)
end
            
to_i() click to toggle source
Alias for: truncate
to_r() click to toggle source

Returns self.

 
               # File rational.rb, line 411
def to_r
  self
end
            
to_s() click to toggle source

Returns a string representation of the rational number.

Example:

Rational(3,4).to_s          #  "3/4"
Rational(8).to_s            #  "8"
 
               # File rational.rb, line 400
def to_s
  if @denominator == 1
    @numerator.to_s
  else
    @numerator.to_s+"/"+@denominator.to_s
  end
end
            
truncate() click to toggle source
 
               # File rational.rb, line 364
def truncate()
  if @numerator < 0
    return -((-@numerator).div(@denominator))
  end
  @numerator.div(@denominator)
end
            
Also aliased as: to_i