[GiNaC-list] conjugates of power objects

[Burcin Erocal]

Hi,

Sorry for the slow response. I'm on a research visit and I need to spend
my time on real work these days. :)

On Fri, 30 Apr 2010 09:06:03 +0200
"Richard B. Kreckel" <kreckel at ginac.de> wrote:

> Alexei Sheplyakov wrote:
> > On Tue, Apr 27, 2010 at 03:16:00AM +0200, Burcin Erocal wrote:
> >>> 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.
> 
> Trying to argue that sqrt(-1) is ill-defined is going to rise an
> eyebrow or two, I guess.  ;-)
> 
> Some background: GiNaC has been following the convention of counter 
> clockwise continuity (CCC) ever since. Functions are continuous as
> the cut is approached coming around the finite endpoint of the cut in
> a counter clockwise direction. GiNaC has inherited this from CLN,
> which has followed Steele's CLTL2 in this respect. Later, the same
> convention was adopted by C99 and C++. Most CAS follow it, too. (I
> haven't checked yet, but I suppose this convention is also adopted by
> the LIA-3 standard.)
> 
> A popular extension due to this is the one advocated by W. Kahan and 
> standardized in IEEE754, where a distinction is made betweenn +0 and
> -0. This is not a panacea because it opens the problem that one has
> to agree on what an unqualified 0 is supposed to be. CLN/GiNaC (and
> all CASs I am aware of) has no signed zero.
> 
> I heartily recommend the article "Function evaluation on branch cuts"
> by Albert Rich and David Jeffrey. It is a short but very inspiring
> read!

Wow! Thanks for this explanation. This should be put in the
documentation somewhere.

> 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?

I agree that the automatic evaluation should be disabled for most
cases. I don't immediately see a good definition for these cases
though, but then I am not knowledgeable in this area at all.

Maple seems to convert sqrt(-3) to sqrt(3)*I automatically:

> sqrt(-3);
                                     1/2
                                    3    I

Perhaps adding this automatic evaluation rule for power objects would
simplify the conditions we need to consider for automatic evaluation of
conjugation.

Comments? 


Thank you.

Burcin