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 ? Cheers, Bill.