Mirror symmetry and realpart/imagpart of functions

-----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