On Jul 18, 2009, at 5:00 PM, Tim Lahey wrote:

> On Jul 18, 2009, at 7:49 PM, Jason Grout wrote:
>
>>
>> Burcin Erocal wrote:
>>
>>> I attached a patch to the trac ticket that contains an initial
>>> attempt
>>> at the MMA notation:
>>>
>>> http://trac.sagemath.org/sage_trac/ticket/6344
>>
>> FYI, a few days ago Burcin uploaded a new patch on 6344 and asked for
>> review.  Here are the examples:
>>
>> OLD:
>>
>> sage: var('x,y')
>> sage: f = function('f')
>> sage: f(x).derivative(x)
>> D[0](f)(x)
>> sage: f(x,x).derivative(x,2)
>> D[0, 0](f)(x, x) + 2*D[0, 1](f)(x, x) + D[1, 1](f)(x, x)
>>
>>
>> NEW:
>>
>> sage: f(x).derivative(x)
>> D[1](f)(x)
>> sage: f(x,x).derivative(x,2)
>> D[2, 0](f)(x, x) + 2*D[1, 1](f)(x, x) + D[0, 2](f)(x, x)
>>
>> NEW LATEX:
>>
>> sage: latex(f(x).derivative(x))
>> f'\left(x\right)
>> sage: latex(f(x,x).derivative(x,2))
>> f^{(2,0)}\left(x, x\right) + 2 \, f^{(1,1)}\left(x, x\right) +
>> f^{(0,2)}\left(x, x\right)
>
> Is standard partial derivative notation going to be used ever?
> Say in latex(f(x,y).derivative(x,2))?
>
> Also, is it possible to have some intelligence on when to use
> \left and \right? Certainly for (x) they aren't really needed.
>
>> If you have an issue with the above printing, please speak now!

Just a sec, I thought we were going to move away from the D[i,j,...]  
notation for text as well as latex, and it my mind

sage: f(x,y).derivative(x,2)

is much more evocative of (df/dx^2)(x,y) than as used above. Golam  
brings up a good point about paste-ability as well, and though this  
could be fixed by introducing a D object with __getitem__ I would  
much prefer the default to be the admittedly less powerful but much  
more intuitive diff(f(x), x) and df/dx notations.

- Robert


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