Using taylor() for Laurent series



>From the documentation I expected both of the following two to
generate the 1/(x-...) term:

,----
| (%i1) taylor(coth(x), x, %i*%pi, -1);
| (%o1)/T/                           0 + . . .
| (%i2) taylor(coth(x), x, %i*%pi, 0);
| 
| `quotient' by `zero'
|  -- an error.  To debug this try debugmode(true);
`----

Could it be that you need a positive expansion power to even start
looking for the singular part?  This works as expected:

,----
| (%i3) taylor(coth(x), x, %i*%pi, 1);
|                             1        x - %i %pi
| (%o3)/T/                ---------- + ---------- + . . .
|                         x - %i %pi       3
`----

The simplest work-around for getting just the singular part I have
found is to use:

,----
| (%i4) taylor(taylor(coth(x), x, %i*%pi, 1), x, %i*%pi, 0);
|                                   1
| (%o4)/T/                      ---------- + . . .
|                               x - %i %pi
`----


This is with Maxima 5.11.0 on both Windows/GCL and Linux/CMUCL.

Regards,

Albert.