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>
• 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]
>>
>>
>>
>> 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.
>
>> 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

```

• Prev by Date: Re: Re: simplifying inside sum, Mathematica 5.1
• Next by Date: Re: Periodic functions & attributes
• Previous by thread: Re: Re: simplifying inside sum, Mathematica 5.1
• Next by thread: Re: simplifying inside sum, Mathematica 5.1