Re: f + g

*To*: mathgroup at smc.vnet.net*Subject*: [mg7155] Re: [mg7120] f + g*From*: jpk at max.mpae.gwdg.de*Date*: Tue, 13 May 1997 01:57:53 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, it is not a good idea produce a general simplification like this. I suggest that You produce two rule sets opExpand={ (f_+g_)[x_] :> f[x]+g[x], (c_*f_)[x] /; FreeQ[c,x] :> c*f[x]} opCollect={a_*f_[x_]:> (a*f)[x],f_[x_]+g_[x_] :> (f+g)[x]} and two functions OperatorExpand[any_]:=any //. opExpand OperatorCollect[any_]:= any //. opCollect That will do what You want with out touching the build in rules and more over it will do it when You want. Hope that helps Jens > In mathematics, we define the sum f + g of two arbitrary real-valued > functions f and g (with the same domain) by the rule (f + g)(x) = f(x) > + g(x), so that, for example, (cos + exp)(0) = 2. Similarly, for a > constant c and an arbitrary function f we define the product cf by the > rule (cf)(x) = c (f(x)). [Generalizations to other kinds of values > and to other operations, such as the product of two functions, are > possible but not of interest to me in this question.) > > My question is: is there some way directly to express this in > Mathematica (3.0)? That is, I would like to input > > (Cos + Exp)[0] > > and get result 2 -- WITHOUT having to give first a specific rule for > the sum of that particular pair of functions. The sort of thing I > have in mind is a general rule such as > > (f_ + g_)[x_] := f[x] + g[x] > > but that certainly won't be acceptable to Mathematica (Tag Plus is > Protected!) > > The only thing I could come up with was: > > Unprotect[Plus] > (f_ + g_)[x_] := f[x] + g[x] > Protect[Plus] > > But I find that most unsatisfactory: it seems to me that such a basic, > common operation in mathematics ought to be directly accessible in "a > software system for doing mathematics"! > > Any other ways except the above, which I regard as something of a > kludge? > > -- > Murray Eisenberg Internet: murray at math.umass.edu > Mathematics & Statistics Dept. Voice: 413-545-2859 (W) > University of Massachusetts 413-549-1020 (H) > Amherst, MA 01003 Fax: 413-545-1801 >