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Re: Re: simplifying inside sum, Mathematica 5.1
*To*: mathgroup at smc.vnet.net
*Subject*: [mg53790] Re: [mg53749] Re: simplifying inside sum, Mathematica 5.1
*From*: DrBob <drbob at bigfoot.com>
*Date*: Thu, 27 Jan 2005 05:41:31 -0500 (EST)
*References*: <ct4h70$av2$1@smc.vnet.net> <ct56p1$eca$1@smc.vnet.net> <200501260936.EAA00194@smc.vnet.net> <opsk7uawdtiz9bcq@monster.ma.dl.cox.net> <41F7DE08.7090001@cs.berkeley.edu> <B2077717-6FEA-11D9-A87F-000A95B4967A@mimuw.edu.pl>
*Reply-to*: drbob at bigfoot.com
*Sender*: owner-wri-mathgroup at wolfram.com
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.
Bobby
On Wed, 26 Jan 2005 22:36:18 +0000, Andrzej Kozlowski <akoz at mimuw.edu.pl> 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 bigfoot.com
www.eclecticdreams.net
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