Sums and Products: Compact Notation and Differentiation

*To*: mathgroup at smc.vnet.net*Subject*: [mg23901] Sums and Products: Compact Notation and Differentiation*From*: Justus Piater <piater at cs.umass.edu>*Date*: Thu, 15 Jun 2000 00:51:44 -0400 (EDT)*Organization*: Department of Computer Science, UMass/Amherst*Sender*: owner-wri-mathgroup at wolfram.com

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