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Re: How is it possible to factor Sum[a]+Sum[b] to Sum[a+b] ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg42044] Re: How is it possible to factor Sum[a]+Sum[b] to Sum[a+b] ?
  • From: "Steve Luttrell" <luttrell at _removemefirst_westmal.demon.co.uk>
  • Date: Tue, 17 Jun 2003 05:43:29 -0400 (EDT)
  • References: <bcjtid$hn3$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

This will will define the property you need:

Unprotect[Sum];
Sum /: Sum[a_[n_], {n_, 1, Infinity}] + Sum[b_[n_], {n_, 1, Infinity}] :=
    Sum[a[n] + b[n], {n, 1, Infinity}];
Protect[Sum];

You could make more a general definition if you want to widen the scope of
the transformation rule.

--
Steve Luttrell
West Malvern, UK

"Eric Duault" <eduault at yahoo.com> wrote in message
news:bcjtid$hn3$1 at smc.vnet.net...
> Hello
>
> I looking for a way to transform an expression in the form
> Sum[a[n], {n, 1, Infinity}] + Sum[b[n], {n, 1, Infinity}]
> to :
> Sum[a[n]+b[n], {n, 1, Infinity}]
> where a[n] and b[n] are numerical.
>
> I tried quite a faw Mathematica fuctions, but none of the gives the
required
> result.
> There is still the possibility to define custom transformation rules, but
> Mathematica should provide a function for doing that.
>
> Thank you for your answer.
>
>
>
>



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