[ ruby-Bugs-7759 ] Complex Number exp() function incorrect

Bugs item #7759, was opened at 2007-01-11 15:27
You can respond by visiting: 
http://rubyforge.org/tracker/?func=detail&atid=1698&aid=7759&group_id=426

Category: Standard Library
Group: 1.8.x
Status: Open
Resolution: None
Priority: 3
Submitted By: Kevin Olbrich (olbrich)
Assigned to: Nobody (None)
Summary: Complex Number exp() function incorrect

Initial Comment:
The implementation of the exp() function in Complex currently looks like this..
(for ruby 1.8.4)

 def exp(z)
    if Complex.generic?(z)
      exp!(z)
    else
      Complex(exp!(z.real) * cos!(z.image), exp!(z.real) * sin!(z.image))
    end
  end

However, the Euler function (which this uses) is defined in terms of the polar notation, so it should really be something like this..

 def exp(z)
    if Complex.generic?(z)
      exp!(z)
    else
      Complex(exp!(z.abs) * cos!(z.angle), exp!(z.abs) * sin!(z.angle))
    end
  end

Using the old function, this fails..

(-1)**(1/3) #=> Complex(0.5, 0.866025403784439)

but (-1)**(1/3) is really -1

the fixed code returns

(-1)**(1/3) #=> Complex(-1.0, 1.22460635382238e-16)

Which is essentially -1

_Kevin
[e-mail]

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You can respond by visiting: 
http://rubyforge.org/tracker/?func=detail&atid=1698&aid=7759&group_id=426