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class Complex < Numeric
def initialize(real, imaginary)
real = real.to_f unless real.is_a? Numeric
imaginary = imaginary.to_f unless imaginary.is_a? Numeric
@real = real
@imaginary = imaginary
end
def self.polar(abs, arg = 0)
Complex(abs * Math.cos(arg), abs * Math.sin(arg))
end
def self.rectangular(real, imaginary = 0)
_new(real, imaginary)
end
def inspect
"(#{to_s})"
end
def to_s
"#{real}#{'+' unless imaginary.negative?}#{imaginary}i"
end
def +@
Complex(real, imaginary)
end
def -@
Complex(-real, -imaginary)
end
def +(rhs)
if rhs.is_a? Complex
Complex(real + rhs.real, imaginary + rhs.imaginary)
elsif rhs.is_a? Numeric
Complex(real + rhs, imaginary)
end
end
def -(rhs)
if rhs.is_a? Complex
Complex(real - rhs.real, imaginary - rhs.imaginary)
elsif rhs.is_a? Numeric
Complex(real - rhs, imaginary)
end
end
def *(rhs)
if rhs.is_a? Complex
Complex(real * rhs.real - imaginary * rhs.imaginary, real * rhs.imaginary + rhs.real * imaginary)
elsif rhs.is_a? Numeric
Complex(real * rhs, imaginary * rhs)
end
end
def /(rhs)
if rhs.is_a? Complex
div = rhs.real * rhs.real + rhs.imaginary * rhs.imaginary
Complex((real * rhs.real + imaginary * rhs.imaginary) / div, (rhs.real * imaginary - real * rhs.imaginary) / div)
elsif rhs.is_a? Numeric
Complex(real / rhs, imaginary / rhs)
end
end
alias_method :quo, :/
def ==(rhs)
if rhs.is_a? Complex
real == rhs.real && imaginary == rhs.imaginary
elsif rhs.is_a? Numeric
imaginary.zero? && real == rhs
end
end
def abs
Math.sqrt(abs2)
end
alias_method :magnitude, :abs
def abs2
real * real + imaginary * imaginary
end
def arg
Math.atan2 imaginary, real
end
alias_method :angle, :arg
alias_method :phase, :arg
def conjugate
Complex(real, -imaginary)
end
alias_method :conj, :conjugate
def numerator
self
end
def denominator
1
end
def fdiv(numeric)
Complex(real.to_f / numeric, imaginary.to_f / numeric)
end
def polar
[abs, arg]
end
def real?
false
end
def rectangular
[real, imaginary]
end
alias_method :rect, :rectangular
def to_c
self
end
def to_f
raise RangeError.new "can't convert #{to_s} into Float" unless imaginary.zero?
real.to_f
end
def to_i
raise RangeError.new "can't convert #{to_s} into Integer" unless imaginary.zero?
real.to_i
end
def to_r
raise RangeError.new "can't convert #{to_s} into Rational" unless imaginary.zero?
Rational(real, 1)
end
attr_reader :real, :imaginary
alias_method :imag, :imaginary
end
class << Complex
alias_method :_new, :new
undef_method :new
alias_method :rect, :rectangular
end
def Complex(real, imaginary = 0)
Complex.rectangular(real, imaginary)
end
[Fixnum, Float].each do |cls|
[:+, :-, :*, :/, :==].each do |op|
cls.instance_exec do
original_operator_name = "__original_operator_#{op}_complex"
alias_method original_operator_name, op
define_method op do |rhs|
if rhs.is_a? Complex
Complex(self).send(op, rhs)
else
send(original_operator_name, rhs)
end
end
end
end
end
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