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Re: f + g
*To*: mathgroup at smc.vnet.net
*Subject*: [mg7574] Re: [mg7120] f + g
*From*: "C. Woll" <carlw at u.washington.edu>
*Date*: Sun, 15 Jun 1997 16:33:05 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
On Sun, 11 May 1997, Murray Eisenberg wrote:
> 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"!
>
> ...
Hi Murray,
Since this message is now old, I don't know if you're interested in it
anymore, but how about this approach, sort of combining your approach with
Through as suggested by Steve Luttrell. Thus,
CirclePlus[f__]:=Through[(Plus[f])[##]]&
Now, you can define a new function h in terms of other functions f and g
as
h := f :c+: g
where :c+: is the alias for the infix form of CirclePlus. This method
works for both pure functions and regular functions.
Carl
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