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MathGroup Archive 2000

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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


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