2009/6/14 Burcin Erocal <bur...@erocal.org>:
>
> Hi again,
>
> There were long discussion about the typesetting of partial derivatives
> in the new system, but I don't think we got to a conclusion yet. The
> previous thread is here:
>
> http://groups.google.com/group/sage-devel/browse_thread/thread/7479c3eeb96348a2
>
>
> I agree that this is annoying and trivial to typeset better:
>
> sage: version()
> 'Sage Version 4.0.1, Release Date: 2009-06-06'
> sage: f = function('f')
> sage: f(x).derivative(x,5)
> D[0, 0, 0, 0, 0](f)(x)
>
>
> However, how to typeset these is not so clear:
>
> sage: f(x+2*y).derivative(x,2)
> D[0, 0](f)(x + 2*y)
> sage: f(x+2*y).derivative(y,2)
> 4*D[0, 0](f)(x + 2*y)
>
> In these examples, keep in mind that we did not define what the first
> argument of the function is called, so we can't just replace D[0, 0]
> with d/dx.
>
> The power of this notation is seen mainly with more than one argument:
>
> sage: f(x+y, x-y).derivative(y)
> D[0](f)(x + y, x - y) - D[1](f)(x + y, x - y)
>
>
> Here is what MMA does:
>
> In[1]:= D[F[x], x]
>
> Out[1]= F'[x]
>
> In[2]:= TeXForm[%]
>
> Out[2]//TeXForm= F'(x)
>
> In[3]:= D[F[x], x, x, x, x, x]
>
> (5)
> Out[3]= F [x]
>
> In[4]:= TeXForm[%]
>
> Out[4]//TeXForm= F^{(5)}(x)
>
> In[5]:= D[F[x+2*y], x, x]
>
> Out[5]= F''[x + 2 y]
>
> In[6]:= TeXForm[%]
>
> Out[6]//TeXForm= F''(x+2 y)
>
> In[7]:= D[F[x+2*y], y, y]
>
> Out[7]= 4 F''[x + 2 y]
>
> In[8]:= TeXForm[%]
>
> Out[8]//TeXForm= 4 F''(x+2 y)
>
> In[9]:= D[F[x+y, x-y], y]
>
> (0,1) (1,0)
> Out[9]= -F [x + y, x - y] + F [x + y, x - y]
>
> In[10]:= TeXForm[%]
>
> Out[10]//TeXForm= F^{(1,0)}(x+y,x-y)-F^{(0,1)}(x+y,x-y)
>
>
> And Maple:
>
>> diff(f(x),x);
> d
> -- f(x)
> dx
>
>> diff(f(x),x$5);
> 5
> d
> --- f(x)
> 5
> dx
>
>> diff(f(x+2*y), y$2);
> (2)
> 4 (D )(f)(x + 2 y)
>
>> convert(%, diff);
> / 2 \|
> | d ||
> 4 |---- f(t1)||
> | 2 ||
> \dt1 /|t1 = x + 2 y
>
>> diff(f(x+y, x-y), y);
> D[1](f)(x + y, x - y) - D[2](f)(x + y, x - y)
>
>> convert(%, diff);
> D[1](f)(x + y, x - y) - D[2](f)(x + y, x - y)
>
>
>
> I like the way MMA handles this. It's compact and consistent. So I
> suggest we change things to use the MMA convention.
The MMA convention seems to include as a special case a prime (') for
derivatives of functions of one variable Is that right? Seems good
to me.
John
>
>
> Comments?
>
>
> Cheers,
> Burcin
>
> >
>
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