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Re: Interaction of Sum/Plus and KroneckerDelta
*To*: mathgroup at smc.vnet.net
*Subject*: [mg55237] Re: [mg55178] Interaction of Sum/Plus and KroneckerDelta
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Thu, 17 Mar 2005 03:29:39 -0500 (EST)
*References*: <200503161035.FAA23756@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
On 16 Mar 2005, at 11:35, Ofek Shilon wrote:
> I'm fighting Mathematica 5.1.0 to perform a (seemingly) elementary
> simplification, and Mathematica - so far - wins, so i thought i'd
> consult some veterans.
> Here's a simplified example of the problem.
>
> type:
> Sum[KroneckerDelta[i, j], {i, 1, 5}]
>
> and you get:
> KroneckerDelta[1, j] + KroneckerDelta[2, j] +
> KroneckerDelta[3, j] + KroneckerDelta[4, j] + KroneckerDelta[5, j]
>
> which i want to simplify to 1. The direct approach:
> Simplify[%, Assumptions -> {j â?? Integers, 0 < j < 3}]
>
> still gives:
> KroneckerDelta[1, j] + KroneckerDelta[2, j]
>
> Can Mathematica somehow automatically transform this to 1?
> modification of the original sum are welcome too, of course.
>
> thanks for any ideas,
>
> Ofek Shilon
>
>
>
I think the closest you can get to the answer you want is by using
Matheamtica 5.1's new function Piecewise. You have to define your own
KroneckerDelta:
KD[i_, j_] := Piecewise[{{1, i == j}}]
and then use Simplify:
In[2]:=
Simplify[KD[1, j] + KD[2, j] +
KD[3, j] + KD[4, j] + KD[5, j]]
Out[2]=
Piecewise[{{1, j == 1 ||
j == 2 || j == 3 ||
j == 4 || j == 5}}]
Unfortunately the answer is a Piecewise object rather than one and
including assumption sin Simplify such as 1<=j<=5 does not help.
Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/andrzej/index.html
http://www.mimuw.edu.pl/~akoz/
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