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>