Re: Sums and Products: Compact Notation and Differentiation
- To: mathgroup at smc.vnet.net
- Subject: [mg23941] Re: Sums and Products: Compact Notation and Differentiation
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 16 Jun 2000 00:57:27 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <8i9qoc$2oh@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, it is possible but you have to do it by your self because simply Clear[sum] sum /: D[sum[a_, range_], x_] /; FreeQ[range, x] := sum[D[a, x], {i, n}] will do it but a) what is with the index shifts ? the {i,n} iterator mean {i,1,n} and this works only for the first derivative of the sum, with a sum over {i,0,n} your equations is not true and for a power series one have D[sum[a_*x^i_,{i_,n1_,n2_}],x] /; FreeQ[{i,n1,n2},x]:= sum[D[a*x^i],x],{i,n1+1,n2}] because the i=0 term depends not on x b) how to "normalize" expressions like sums of sum[] ? collect them ? shift the index in the terms until one can make a sum[a,i]+sum[b,i] :> sum[a+b,i] Regards Jens Justus Piater wrote: > > Hi, > > I am relatively new to Mathematica (Version 3.0), and have been able > to get sensible results using expressions involving Sum and Product > symbols only if the summation/multiplication ranges are given by > constants. I have the following specific problems: > > 1. When I have Mathematica operate on a formula involving Sum and > Product symbols with constant ranges, it always displays the result > in expanded form, without these symbols, even though it often seems > easily possible and much more compact to use Sums and Products. Is > is possible to have Mathematica retain the convenient notation, and > prevent it from expanding the terms? > > 2. I can't get Mathematica to give me simple derivatives of > expressions involving Sums and Products, unless the ranges are > known to Mathematica so it can expand them. For example, I would > like to type: > > D[Sum[Subscript[a,i]x^i,{i,n}],x] > > and get as output some rendering of: > > Sum[i Subscript[a,i]x^(i-1),{i,n}] > > Is this really not possible? > > Thanks, > Justus > > -- > Justus Piater Laboratory for Perceptual Robotics U of Mass > www.cs.umass.edu/~piater Computer Vision Laboratory Amherst