Happy new year.



>
> >/
> />/       About computing the sum of rational functions by polygamma functions:
> />/ first this needs to compute the roots of the denominator --> a numerical method,
> />/ so the obtained precision is not that os polygamma but that of the numerical
> />/ method for computing the roots of the denominator.
> />/
> />/
> />/   
> /Maxima can work with algebraic integers!  tellrat is the command.
>
>   

And a common subcase would be where the roots are half integers. In that
case Maxima can use
simplication to obtain the symbolic result in terms of the zeta function.

Michel