Hi,

A short remark. It seems that taking the derivative of an element of a
fraction field is not supported at this point. This feels somewhat
inconsistent (tested with sage 2.10.4)

sage: R=QQ['x']
sage: x=R.gen()
sage: derivative(x^2,x)
2*x
sage: derivative(1/x,x)
---------------------------------------------------------------------------
<type 'exceptions.TypeError'>             Traceback (most recent call
last)
<snip>

More fundamentally, I wonder if it makes sense to define the general
concept of a derivation.
Derivations are given by their values on generators so they fit well
in the sage framework.
The advantage of having abstract derivations would be that one could
add them, take their
commutatior etc....

Regards,
Michel


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