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Re: Through[(a+b+b)[x]]

• To: mathgroup at smc.vnet.net
• Subject: [mg109186] Re: Through[(a+b+b)[x]]
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Fri, 16 Apr 2010 05:51:07 -0400 (EDT)
• References: <hq61oh$3h6$1@smc.vnet.net>

Derek Yates wrote:
> Through[(a+b)[x]] yields a[x]+b[x] as expected, but Through[(a+b+b)
> [x]] yields a[x]+(2b)[x]. Through[(2b)[x]] yields 2[x]b[x]. Now, I can
> obviously get around this in this specific case, but generically is
> there a way to solve this so that Through[(a+b+b)[x]] yields a[x]
> +2b[x]? The case where I envisage this happening is when a sum of
> functions is supplied (say, for a given value of y, Through[(f[y]+g[y]
> +h[y]+j[y])[x]] and for some values of y, g = h. Then one will end up
> with the problem above. Other than some post processing using pattern
> matching, which feels a bit clunky, I can't think of a way around this.
> 
Why not describe the problem you are trying to solve - probably there is 
a better way than using Through. As You presumably realise, a+b+b gets 
simplified before the Through operation is performed.

David Bailey
http://www.dbaileyconsultancy.co.uk