Complex

The complex number class. See complex.rb for an overview.

Constants

I: I is the imaginary number. It exists at point (0,1) on the complex plane.

Attributes

imag[R]

The imaginary part of a complex number.

image[R]

The imaginary part of a complex number.

real[R]

The real part of a complex number.

Public Class Methods

new(a, b) click to toggle source

 
               # File complex.rb, line 128
def initialize(a, b)
  raise TypeError, "non numeric 1st arg `#{a.inspect}'" if !a.kind_of? Numeric
  raise TypeError, "`#{a.inspect}' for 1st arg" if a.kind_of? Complex
  raise TypeError, "non numeric 2nd arg `#{b.inspect}'" if !b.kind_of? Numeric
  raise TypeError, "`#{b.inspect}' for 2nd arg" if b.kind_of? Complex
  @real = a
  @image = b
end

new!(a, b=0) click to toggle source

Creates a Complex number a+bi.

 
               # File complex.rb, line 124
def Complex.new!(a, b=0)
  new(a,b)
end

polar(r, theta) click to toggle source

Creates a Complex number in terms of r (radius) and theta (angle).

 
               # File complex.rb, line 117
def Complex.polar(r, theta)
  Complex(r*Math.cos(theta), r*Math.sin(theta))
end

Public Instance Methods

%(other) click to toggle source

Remainder after division by a real or complex number.

 
               # File complex.rb, line 247
def % (other)
  if other.kind_of?(Complex)
    Complex(@real % other.real, @image % other.image)
  elsif Complex.generic?(other)
    Complex(@real % other, @image % other)
  else
    x , y = other.coerce(self)
    x % y
  end
end

*(other) click to toggle source

Multiplication with real or complex number.

 
               # File complex.rb, line 172
def * (other)
  if other.kind_of?(Complex)
    re = @real*other.real - @image*other.image
    im = @real*other.image + @image*other.real
    Complex(re, im)
  elsif Complex.generic?(other)
    Complex(@real * other, @image * other)
  else
    x , y = other.coerce(self)
    x * y
  end
end

**(other) click to toggle source

Raise this complex number to the given (real or complex) power.

 
               # File complex.rb, line 202
def ** (other)
  if other == 0
    return Complex(1)
  end
  if other.kind_of?(Complex)
    r, theta = polar
    ore = other.real
    oim = other.image
    nr = Math.exp!(ore*Math.log!(r) - oim * theta)
    ntheta = theta*ore + oim*Math.log!(r)
    Complex.polar(nr, ntheta)
  elsif other.kind_of?(Integer)
    if other > 0
      x = self
      z = x
      n = other - 1
      while n != 0
        while (div, mod = n.divmod(2)
               mod == 0)
          x = Complex(x.real*x.real - x.image*x.image, 2*x.real*x.image)
          n = div
        end
        z *= x
        n -= 1
      end
      z
    else
      if defined? Rational
        (Rational(1) / self) ** -other
      else
        self ** Float(other)
      end
    end
  elsif Complex.generic?(other)
    r, theta = polar
    Complex.polar(r**other, theta*other)
  else
    x, y = other.coerce(self)
    x**y
  end
end

+(other) click to toggle source

Addition with real or complex number.

 
               # File complex.rb, line 140
def + (other)
  if other.kind_of?(Complex)
    re = @real + other.real
    im = @image + other.image
    Complex(re, im)
  elsif Complex.generic?(other)
    Complex(@real + other, @image)
  else
    x , y = other.coerce(self)
    x + y
  end
end

-(other) click to toggle source

Subtraction with real or complex number.

 
               # File complex.rb, line 156
def - (other)
  if other.kind_of?(Complex)
    re = @real - other.real
    im = @image - other.image
    Complex(re, im)
  elsif Complex.generic?(other)
    Complex(@real - other, @image)
  else
    x , y = other.coerce(self)
    x - y
  end
end

/(other) click to toggle source

Division by real or complex number.

 
               # File complex.rb, line 188
def / (other)
  if other.kind_of?(Complex)
    self*other.conjugate/other.abs2
  elsif Complex.generic?(other)
    Complex(@real/other, @image/other)
  else
    x, y = other.coerce(self)
    x/y
  end
end

<=>(other) click to toggle source

Compares the absolute values of the two numbers.

 
               # File complex.rb, line 314
def <=> (other)
  self.abs <=> other.abs
end

==(other) click to toggle source

Test for numerical equality (a == a + 0i).

 
               # File complex.rb, line 321
def == (other)
  if other.kind_of?(Complex)
    @real == other.real and @image == other.image
  elsif Complex.generic?(other)
    @real == other and @image == 0
  else
    other == self
  end
end

abs() click to toggle source

Absolute value (aka modulus): distance from the zero point on the complex plane.

 
               # File complex.rb, line 277
def abs
  Math.hypot(@real, @image)
end

abs2() click to toggle source

Square of the absolute value.

 
               # File complex.rb, line 284
def abs2
  @real*@real + @image*@image
end

angle() click to toggle source

Alias for: arg

arg() click to toggle source

Argument (angle from (1,0) on the complex plane).

 
               # File complex.rb, line 291
def arg
  Math.atan2!(@image, @real)
end

Also aliased as: angle

coerce(other) click to toggle source

Attempts to coerce other to a Complex number.

 
               # File complex.rb, line 334
def coerce(other)
  if Complex.generic?(other)
    return Complex.new!(other), self
  else
    super
  end
end

conj() click to toggle source

Alias for: conjugate

conjugate() click to toggle source

Complex conjugate (z + z.conjugate = 2 * z.real).

 
               # File complex.rb, line 306
def conjugate
  Complex(@real, -@image)
end

Also aliased as: conj

denominator() click to toggle source

FIXME

 
               # File complex.rb, line 345
def denominator
  @real.denominator.lcm(@image.denominator)
end

hash() click to toggle source

Returns a hash code for the complex number.

 
               # File complex.rb, line 388
def hash
  @real.hash ^ @image.hash
end

inspect() click to toggle source

Returns “Complex(real, image)”.

 
               # File complex.rb, line 395
def inspect
  sprintf("Complex(%s, %s)", @real.inspect, @image.inspect)
end

numerator() click to toggle source

FIXME

 
               # File complex.rb, line 352
def numerator
  cd = denominator
  Complex(@real.numerator*(cd/@real.denominator),
          @image.numerator*(cd/@image.denominator))
end

polar() click to toggle source

Returns the absolute value and the argument.

 
               # File complex.rb, line 299
def polar
  return abs, arg
end

to_s() click to toggle source

Standard string representation of the complex number.

 
               # File complex.rb, line 361
def to_s
  if @real != 0
    if defined?(Rational) and @image.kind_of?(Rational) and @image.denominator != 1
      if @image >= 0
        @real.to_s+"+("+@image.to_s+")i"
      else
        @real.to_s+"-("+(-@image).to_s+")i"
      end
    else
      if @image >= 0
        @real.to_s+"+"+@image.to_s+"i"
      else
        @real.to_s+"-"+(-@image).to_s+"i"
      end
    end
  else
    if defined?(Rational) and @image.kind_of?(Rational) and @image.denominator != 1
      "("+@image.to_s+")i"
    else
      @image.to_s+"i"
    end
  end
end

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