Hi Jason,

On Fri, 18 Sep 2009 13:15:46 -0500
Jason Grout <jason-s...@creativetrax.com> wrote:

> 
> On alpha.sagenb.org, I get the following:
> 
> sage: t=var('t')
> sage: diff(cot(t),t)
> D[0](cot)(t)
> sage: diff(cos(t)/sin(t),t)
> -cos(t)^2/sin(t)^2 - 1
> 
> 
> Does Sage not know that cot(t) is cos(t)/sin(t)?  Or am I just being
> silly?

Unfortunately it doesn't. 

GiNaC doesn't define the function cot. Sage defines it in the file
sage/functions/trig.py starting at line 184. I suppose it was written
quickly by Mike during the symbolics switch.

Defining a custom derivative function (named _derivative_()) in that
class should fix this.

I opened a ticket:

http://trac.sagemath.org/sage_trac/ticket/6956


Thanks.


Burcin

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