# [GiNaC-list] conjugates of power objects

Alexei Sheplyakov alexei.sheplyakov at gmail.com
Fri Apr 30 23:43:02 CEST 2010

```Hello,

On Fri, Apr 30, 2010 at 09:06:03AM +0200, Richard B. Kreckel wrote:

> Trying to argue that sqrt(-1) is ill-defined is going to rise an
> eyebrow or two, I guess.  ;-)

I agree. Let's put it another way: unfortunately GiNaC gives no way to
figure out if sqrt(-1) really stands for sqrt(-1 + I 0) or sqrt(-1 - I 0),
so we don't really know the if it's +I or -I.

Does this explanation make any sense?

> Alas, I think that automatic evaluation of conjugation is too
> aggressive in GiNaC. It just keeps giving incorrect results on
> branch cuts. Here are some examples, using ginsh:
>
> > conjugate(sqrt(x));
> sqrt(conjugate(x))
> > conjugate(sqrt(x))-sqrt(conjugate(x));
> 0
> > conjugate(sqrt(-1))-sqrt(conjugate(-1));
> -2*I
> > conjugate(log(x));
> log(conjugate(x))
> > conjugate(log(x))-log(conjugate(x));
> 0
> > conjugate(log(-1))-log(conjugate(-1));
> -(2*I)*Pi

> I suggest to disable automatic evaluateion of conjugation where
> these kinds of problems can appear.

> Opinions?

Should we stop evaluating x/x to 1, too? It gives incorrect result if x is zero.

Best regards,
Alexei

```