Mirror symmetry and realpart/imagpart of functions

> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu]On Behalf Of Dieter Kaiser
> 
> -----Urspr?ngliche Nachricht-----
> Von: macrakis at gmail.com [mailto:macrakis at gmail.com] Im 
> Auftrag von Stavros
> Macrakis
> 
> I have checked in the handling of realpart/imagpart for 
> function with mirror
> symmetry and have added some tests to show how it works for 
> the functions
> expintegral_e, expintegral_ei and expintegral_si.
> 
> > These are nice transformations, which have the good property of
> > eliminating realpart/imagpart/abs/carg nouns, which means further
> > simplifications are possible.  However, I am not sure that a user
> > would always prefer to see
> >
> >         sqrt(gamma(1-%i))*sqrt(gamma(%i+1))
> >
> > than
> >
> >         abs(gamma(1+%i))
> >
> > I do not actually have an opinion on this, but I think the 
> question is
> > worth thinking about....
> 
> I hope it will be not too unusual to get the results in terms 
> of the sqrt
> function if we take the absolute value of a function with 
> mirror symmetry and a
> complex argument. But the starting point for me was to get a correct
> realpart/imagpart.
> 
> If it is necessary to modify this simplification it, we could 
> have a look into
> the code of the abs function. 
> 
> Remark: 
> 
> Because the conjugate function handles complex and imaginary 
> symbols and
> expressions carefully, Maxima gets correct results for much 
> more general
> arguments too.
> 
> Dieter Kaiser
> 

I would prefer the approach. The first and probably most important point is
to get realpart and imagepart RIGHT - by default, they are not today. The
second point is to allow for further simplifications and in general I would
call products of sqrt more easy to simplify than abs(). But I admit that it
will probably never be possible to display any result in a way  "a user
would always prefer to see"...

So, please go on.

Rolf Schirmacher