diff(psi(1,x),x);
diff(psi(n,x),x);
As everybody knows we don't have inert differentiation like Maple has for instance (lprint(diff(f(x),x)); returns diff(f(x),x) there), we are always applying the full chain rule, end of story. :-/ If a function does not know how to be differentiated it may throw an exception instead, this is acceptable. However, when trying to implement differentiation for the polygamma functions psi(n,x) I ran into a problem with that policy since differentiating wrt the first argument doesn't make much sense there (it's normally just an integer parameter). But when one differentiates wrt x, what happens is this (function::pdiff is the partial differentiation): psi(n,x).diff(x) -> pdiff(psi,0)*n.diff(x) + pdiff(psi,1)*x.diff(x) so differentiation wrt n comes in again through the back door. I have worked around this problem by changing function::diff(). In the above case it would see that n.diff(x).is_zero() and then refrain from trying to compute pdiff(psi,0). It seems to work so far. In ginsh, this allows me to write: psi(2,x) psi(n+1,x)
diff(psi(n,x),n); cannot diff psi(n,x) with respect to n
Any objections? (It's in CVS, for those of you who have access to it.) So, once more we can live without inert differentiation, let's see how long... On another note: who has implemented atan2::diff() and why didn't it return something slightly simpler (i.e. x/(x^2+y^2) instead of 1/x/(1+y^2/x^2))? Is there some reason for this?? Did I break anything??? Cheers -rbk. -- Richard Kreckel <Richard.Kreckel@Uni-Mainz.DE> <http://wwwthep.physik.uni-mainz.de/~kreckel/>