[Haskell-cafe] Complex numbers and (**)

[Paul Sargent]

On Sat, Aug 8, 2009 at 18:17, Henning Thielemann <
lemming at henning-thielemann.de> wrote:

>
> On Sat, 8 Aug 2009, Paul Sargent wrote:
>
>  First post to the cafe, so "Hello everybody!".
>> Hope this is reasonable subject matter and not too long.
>>
>> I've been working on some algorithms that involved taking the n-th root of
>> complex numbers.
>> In my code I've implemented this as raising the complex number ('z') to
>> 1/n using the (**)
>> operator. Obviously, there are n roots, but I only need one of them so
>> this is fine.
>>
>
> I have written something on that topic:
>  http://haskell.org/haskellwiki/Power_function
>
> I think the problem cannot be fully solved, especially not within the
> Haskell 98 numeric type classes. There is no satisfying implementation of
> (**) even for Float and Double.
>

Well, I'm an engineer rather than a mathematician, so I'm not 100% sure I
followed everything on that page, but you seem to be saying that nth-root
can't be done because we're using floating point, and floating point isn't
accurate enough to represent 1/n.

I basically agree with this, which was why I asked about nth-root functions,
but for my uses (**) is good enough as long as complex zero works.

(To be honest I'd expect any complex nth-root function to work with the
polar form, there-by getting around some of the issues I think you're
referring to.)
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