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Re: Re: simplifying inside sum, Mathematica 5.1

  • To: mathgroup at
  • Subject: [mg53790] Re: [mg53749] Re: simplifying inside sum, Mathematica 5.1
  • From: DrBob <drbob at>
  • Date: Thu, 27 Jan 2005 05:41:31 -0500 (EST)
  • References: <ct4h70$av2$> <ct56p1$eca$> <> <> <> <>
  • Reply-to: drbob at
  • Sender: owner-wri-mathgroup at

Exactly. We get farther by working WITH Mathematica, not against it.

Paying attention to examples like these is a part of that, of course; it never hurts to know where the gaps and pitfalls may lurk.


On Wed, 26 Jan 2005 22:36:18 +0000, Andrzej Kozlowski <akoz at> wrote:

> On 26 Jan 2005, at 18:14, Richard Fateman wrote:
>> As for Andrzej's comment, that this does the job...
>> Block[{Power,Infinity},
>>     0^(i_) := KroneckerDelta[i, 0]; Sum[a[i]*x^i, {i, 0, Infinity}]/. x
>> -> 0]
>> Here are some comments:
>> 1. There is no need for Infinity to be bound inside the Block.
> Indeed, I did not check that. I had reasons to think it was needed.
>> 4. Your solution gives the wrong answer for
>> Sum[a[i]*x^i, {i, -1, Infinity}]
> Since any sum can be split into a finite sum over the negative indices
> and an infinite sum over indices >=0 and since finite sums are handled
> correctly this is essentially a cosmetic issue. In fact it is easy to
> modify Sum to automatically split all sums in this way, and to use the
> Block trick for the infinite part. But I don't think this is important
> enough to bother.
>> It also doesn't work for
>> Sum[a[i]*x^(i^2), {i, -1, Infinity}]
>> This latter problem suggests an inadequacy in the treatment of the
>> simplification of   Sum[KroneckerDelta[...]....]
> Well, yes. One can always find ways to trip up Mathematica (and all
> other CAS) in this sort of thing. It's a bit like playing chess with a
> computer program; however strong it is if you get to know it well
> enough you will find ways to beat it (assuming of course you are a good
> chess player and understand computers). But the difference is that CAS
> is not meant to be your opponent and trying to trip it up (which is
> also what most of Maxim's examples involve) is a pointless exercise,
> which may amuse people who like such things but has nothing to do with
> any serious work.
> Andrzej Kozlowski

DrBob at

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