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MathGroup Archive 1993

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Re: Distribute

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Distribute
  • From: Frank Zizza <zizza at pioneer.willamette.edu>
  • Date: Sat, 6 Mar 93 09:35:09 -0800

[I have combined all the responses to the original message into
one since most of the answers are similar. - steve c, moderator]

1) >I have a function that I want to be additively distributive.  The
>standard way for doing this
>
>f[a_+b_]:=f[a]+f[b];
>
>But this is a problem when distributing over long sums, because it
>leads to Recursion errors.  Mathematica has a command Distribute, but
>if I just say
>
>f[a_+b_]:=Distribute[f[a+b]]
>
>I am immediately in a loop.  Thus, the simplest way I can see to use
>it in this situation is
>
>f[a_+b_]=Distribute[temp[a+b]]/.{temp->f}
>
>Is there way to do this without the introduction of a temporary
>variable?  Thanks in advance.
>
>                - Ian Robertson
>                  Oberlin College
>                 iroberts at cs.oberlin.edu

Add the rule
f[S_Plus] := f /@ S
to the end of the definitions you have made for f.
Here's an example:

Mathematica 2.1 for NeXT
Copyright 1988-92 Wolfram Research, Inc.
 -- NeXT graphics initialized --

In[1]:= f[S_Plus] := f /@ S

In[2]:= f[a+b+c]

Out[2]= f[a] + f[b] + f[c]

Frank Zizza
Willamette University
Salem, OR 97301
zizza at willamette.edu

2) From: tgayley at wri.com (Todd Gayley)

How about this:

f[x_Plus] := f /@ x


Todd Gayley
WRI


3) From: John Lee <lee at math.washington.edu>

Here is a simple solution, which avoids recursion:

  In[1]:= f[x_Plus] := f /@ x;

  In[2]:= f[a + b + c + d + e]

  Out[2]= f[a] + f[b] + f[c] + f[d] + f[e]

Jack Lee
Dept. of Mathematics
University of Washington
Seattle, WA

4) From: reiszig at e-technik.tu-dresden.dbp.de



Hi,
sb. asked how to define a function to be additive (orig. mail see
below).
The simplest way I know is:
f[x_Plus] := Map[f,x]
(use level specific. for special effects)
If needed, use in addition:
f[x_Plus y_] := f[ Expand[x y]]

G.Reiszig, Dresden, 8 Mar 93

5) From: wmm at chem.wayne.edu (Martin McClain)

At the top of your script, write
        SetAttributes[Distribute, HoldAll]
Now Distribute will work the way you want.  Of course, this may introduce
undesirable behaviour in other aspects of your problem.  If it does, define
another  operator identical to Distribute and give it the HoldAll
attribute.






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