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Re: Re: Re: Re: Forcing a Derivative

• To: mathgroup at smc.vnet.net
• Subject: [mg50835] Re: [mg50800] Re: [mg50793] Re: [mg50778] Re: Forcing a Derivative
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Thu, 23 Sep 2004 05:27:16 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <cijej8$hlp$1@smc.vnet.net> <200409200139.VAA27554@smc.vnet.net> <200409210749.DAA27779@smc.vnet.net> <200409220410.AAA18643@smc.vnet.net>
• Reply-to: murray at math.umass.edu
• Sender: owner-wri-mathgroup at wolfram.com

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

   Plot'[x]

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 math.umass.edu
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

• Follow-Ups:
  • Re: Re: Re: Re: Re: Forcing a Derivative
    • From: Andrzej Kozlowski <andrzej@akikoz.net>

• References:
  • Re: Forcing a Derivative
    • From: Karl_boehme_9@msn.com (Klaus G)
  • Re: Re: Forcing a Derivative
    • From: Murray Eisenberg <murray@math.umass.edu>
  • Re: Re: Re: Forcing a Derivative
    • From: Andrzej Kozlowski <andrzej@akikoz.net>