Class Rational
In: 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

Methods

%   *   **   +   -   /   <=>   ==   abs   coerce   divmod   hash   inspect   new   new!   reduce   to_f   to_i   to_r   to_s  

Attributes

denominator  [R] 
numerator  [R] 

Public Class methods

This method is actually private.

[Source]

# 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

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.

[Source]

# File rational.rb, line 93
  def Rational.new!(num, den = 1)
    new(num, den)
  end

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

[Source]

# 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

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

[Source]

# File rational.rb, line 253
  def % (other)
    value = (self / other).to_i
    return self - other * value
  end

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)

[Source]

# 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

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

[Source]

# 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

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

[Source]

# 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

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

[Source]

# 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

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)

[Source]

# 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

Standard comparison operator.

[Source]

# File rational.rb, line 305
  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

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!

[Source]

# File rational.rb, line 290
  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

Returns the absolute value.

[Source]

# File rational.rb, line 273
  def abs
    if @numerator > 0
      Rational.new!(@numerator, @denominator)
    else
      Rational.new!(-@numerator, @denominator)
    end
  end

[Source]

# File rational.rb, line 329
  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

Returns the quotient and remainder.

Examples:

  r = Rational(7,4)        # -> Rational(7,4)
  r.divmod Rational(1,2)   # -> [3, Rational(1,4)]

[Source]

# File rational.rb, line 265
  def divmod(other)
    value = (self / other).to_i
    return value, self - other * value
  end

Returns a hash code for the object.

[Source]

# File rational.rb, line 395
  def hash
    @numerator.hash ^ @denominator.hash
  end

Returns a reconstructable string representation:

  Rational(5,8).inspect     # -> "Rational(5, 8)"

[Source]

# File rational.rb, line 388
  def inspect
    sprintf("Rational(%s, %s)", @numerator.inspect, @denominator.inspect)
  end

Converts the rational to a Float.

[Source]

# File rational.rb, line 357
  def to_f
    @numerator.to_f/@denominator.to_f
  end

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

[Source]

# File rational.rb, line 350
  def to_i
    Integer(@numerator.div(@denominator))
  end

Returns self.

[Source]

# File rational.rb, line 379
  def to_r
    self
  end

Returns a string representation of the rational number.

Example:

  Rational(3,4).to_s          #  "3/4"
  Rational(8).to_s            #  "8"

[Source]

# File rational.rb, line 368
  def to_s
    if @denominator == 1
      @numerator.to_s
    else
      @numerator.to_s+"/"+@denominator.to_s
    end
  end

[Validate]