On Jun 14, 12:38 pm, Burcin Erocal <bur...@erocal.org> wrote: > 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/7479c3... > > 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. > > Comments? > > Cheers, > Burcin
I don't like the D[1] notation at all. By the way, when we have a function f of two variables, should we automatically assume that the mixed partials are equal? Does this affect our choice of notation? (Another notation I've seen: f_n is the derivative with respect to the nth variable, so f_12 is (f_1)_2: if the variables are x and y, take partial with respect to x, then y; in contrast, the other mixed partial is f_21.) John --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
