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Re: Sum pattern

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128289] Re: Sum pattern
  • From: Fred Simons <f.h.simons at tue.nl>
  • Date: Fri, 5 Oct 2012 02:48:27 -0400 (EDT)
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On Oct 3, 12:12 am, "Dave Snead"<dsne... at charter.net>  wrote:

> Hi,
>
> I'm trying to put together a rule whose left hand side is a sum of arbitrary
> length whose elements all have the same head f.
>
> For example:
>
> In[4]:= x = f[a1, s] + f[a2, s] + f[a3, s]
>
> Out[4]= f[a1, s] + f[a2, s] + f[a3, s]
>
> In[6]:= y = f[First /@ x, s]
>
> Out[6]= f[a1 + a2 + a3, s]
>
> which is what I want.
>
> However when I turn this into a rule
>
> In[7]:= z = x /. (p : Plus[__f]) -> f[First /@ p, s]
>
> Out[7]= f[f[a1, s], s] + f[f[a2, s], s] + f[f[a3, s], s]
>
> Why isn't z equal to y?
> How can I make this rule work?
>
> Thanks in advance,
> Dave Snead

Your solution is almost correct, but fails since you did not take into account that both sides of your rule are evaluated before it is applied.

In[1]:= (p:Plus[__f])->f[First/@p,s]
Out[1]= p__f->f[p,s]

Your rule wraps every expression with head f in another f, as you see in your output.

To prevent the evaluation, use RuleDelayed for keeping the right-hand side and HoldPattern for the left-hand side:


In[2]:= x=f[a1,s]+f[a2,s]+f[a3,s]
x /. (p:HoldPattern[Plus[__f]]):>f[First/@p,s]

Out[2]= f[a1,s]+f[a2,s]+f[a3,s]
Out[3]= f[a1+a2+a3,s]

Fred Simons
Eindhoven University of Technology




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