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
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
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
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
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 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)
# 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
# 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
# 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
# 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)
# 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.
# 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 ::new!
# 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.
# File rational.rb, line 273 def abs if @numerator > 0 Rational.new!(@numerator, @denominator) else Rational.new!(-@numerator, @denominator) end end
# 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)]
# 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.
# File rational.rb, line 395 def hash @numerator.hash ^ @denominator.hash end
Returns a reconstructable string representation:
Rational(5,8).inspect # -> "Rational(5, 8)"
# File rational.rb, line 388 def inspect sprintf("Rational(%s, %s)", @numerator.inspect, @denominator.inspect) end
Converts the rational to a Float.
# 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
# File rational.rb, line 350 def to_i Integer(@numerator.div(@denominator)) end