[GiNaC-list] conjugates of power objects
Alexei Sheplyakov
alexei.sheplyakov at gmail.com
Tue Apr 27 22:48:57 CEST 2010
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
More information about the GiNaC-list
mailing list