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/

**References**:**Interaction of Sum/Plus and KroneckerDelta***From:*"Ofek Shilon" <ofek@simbionix.com>