Re: Dealing with sums
- To: mathgroup at smc.vnet.net
- Subject: [mg41167] Re: Dealing with sums
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Tue, 6 May 2003 06:01:05 -0400 (EDT)
- Organization: The University of Western Australia
- References: <b8g114$pg5$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <b8g114$pg5$1 at smc.vnet.net>, Stepan Yakovenko <yakovenko at ngs.ru> wrote: > I want to get a derivative in terms of KroneckerDelta function: > > \!\(\[PartialD]\_\(a\_3\)\(\[Sum]\+\(i = 0\)\%N a\_i\)\) > > But I get 0. > > Is there a way to do it in Mathematica ? In many situations, the summation symbol is not intended to imply explicit summation but is just a notational device: the Einstein summation convention, where summation over repeated indices is implied rather than explicitly stated, e.g., \!\(TraditionalForm\`\(\(\[Sum]\+\(i = 1\)\%n\( a\_i\) b\^i \[Rule] \(a\_i\) b\^i\)\(,\)\)\) can often be used to simplify the algebra. Interestingly, this convention translates into a general principle for analyzing and evaluating integrals and products of sums in Mathematica -- just focus on the summand (i.e., the general term of the sum) and drop the summation symbol. Cheers, Paul -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul