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

**References**:**Re: simplifying inside sum, Mathematica 5.1***From:*Richard Fateman <fateman@cs.berkeley.edu>