Bill Allombert on Sun, 29 Jun 2008 23:49:44 +0200

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Re: complex powers

On Fri, Jun 27, 2008 at 02:37:04AM +0200, Robert Gerbicz wrote:
> Hi!
> It's interesting that Pari gives a concrete value for example I^I, because
> it has got infinite many values:
> log(I)=1/2*Pi*I+2*k*Pi*I and using this
> I^I=exp(I*(Pi/2*I+2*k*Pi*I))=exp(-Pi*(1/2+2*k))
> where k is an integer.

So does log(2). In both case PARI/GP use the principal branch of the
logarithm which is uniquely defined.

> The major computer algebra softwares, Maple and Mathematica returns by the
> input if I type I^I this should be done by Pari-Gp also. But it's
> interesting that both of them gives 0 for I^I-I^I, what is wrong.

So what benefit would there be to return a symbolic value with no
meaning attached to it ?