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Re: Re: Re: Re: Forcing a Derivative

I agree that Mathematica's notion of function MAY be broader than in 
Mathematics in some respects (but in others is MUCH narrower -- that's 
quite another topic).  But I don't quite see how that necessarily 
precludes a reasonable implementation of such an algebra of 
numerically-valued functions of numerical arguments.

After all, I would not try to evaluate


either!  But that doesn't prohibit me from evaluating, say, Sin'[x].

Likewise, just because I would not dream of asking for the syntactically 
correct expression

   Plot + NumberForm

to have meaning does not preclude a meaning for, say, Sin + Exp.

Andrzej Kozlowski wrote:

> But one does not need to introduce x in f:
> f[x_]:=x^3
> Derivative[2][f]
> 6 #1&
> No x was needed.
> As has been pointed out already a number of times, what is not 
> implemented by default is the algebra of complex  functions, that is, 
> if f and g are functions then 2f + 3 g or 5 f*g are not considered by 
> Mathematica to be functions. One reason for that maybe that in 
> Mathematica the notion of a "function" is broader than in Mathematics. 
> In any case the algebras of functions and operators are easy to 
> implement oneself and this has already been done more than once on this 
> list....

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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