# [Maxima] Mirror symmetry and realpart/imagpart of functions

Schirmacher, Rolf Rolf.Schirmacher at MuellerBBM.de
Fri Feb 6 11:15:53 CST 2009

```> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu]On Behalf Of Dieter Kaiser
>
> -----Ursprüngliche 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
>
> 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