[GiNaC-list] conjugates of power objects

[Alexei Sheplyakov]

Hello,

On Tue, Apr 27, 2010 at 03:16:00AM +0200, Burcin Erocal wrote:

> For conjugation, power objects just compute the conjugate of the basis
> and the exponent, and construct a new power object from these.

Proof:

(a^b)* = exp(b log(a))* = exp((b log(a))*) = exp(b* (log(a))*) 

(log(a))* = ( log |a| + i arg(a))* = log |a| - i arg(a) 
           = log |a*| + i arg(a*) = log(a*)

So (a^b)* = exp(b* log(a*)) = (a*)^(b*)

> > conjugate(sqrt(-3));
> sqrt(-3)

You are trying to compute the value of the function on the branch cut
(which is ill defined), so you get the nonsense result.


Please note: it's a midnight now (here in Ukraine), and I had a busy day, so
the above might be a total nonsense. Feel free to point out mistakes (if any). 

Best regards,
	Alexei