Hi,

On Wed, Jul 22, 2009 at 9:25 PM, Maurizio<maurizio.gran...@gmail.com> wrote:
>> (5) Looses information irrecoverably:
>>
>> From "D[0](f)(x-a)" its not possible to decide whether original
>> variable of differentiation was "x" as in f(x-a).diff(x)  or "a"
>> as in -f(x-a).diff(a). This again affects integration algorithm.
>>
>
> Is this caused by the representation or by how the information is
> stored?
> In case its just representation, it should be trivial to fix.
> In case the information is not stored... Well, I don't think this is
> possible, it does not make sense that the definition of a derivative
> doesn't include the variable of derivation.


Unfortunately, it is the later. Pynac fderivative doesn't store
variable of differentiation by design.

This is the reason why it must continue applying chain rule
until the end.


> At the very end, my personal opinion is that the community should plan
> the work on derivatives AND integrals at the same time, otherwise it
> does not make sense to stick with some derivatives we are not going to
> support in the long term (integrals are going to take a lot of time
> probably).

I agree. Both Sage derivative and anti-derivative should be made compatible
to each other by design from the very beginning. Having them in two
separate sub-system can make thing only worse.

Regarding Maxima, I strongly believe that Sage needs Maxima for
symbolic integration for quite some time.

Cheers,
Golam

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