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MathGroup Archive 2001

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Re: A Question about Expression Simplication

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31572] Re: A Question about Expression Simplication
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 14 Nov 2001 03:41:48 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <9sl2mo$dhu$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

it does not work at all, because Sum[] has the attribute HoldAll
and this will prevent almost all simplifications. The reason
is, that Sum[a+b,{i,1,Infinity}] may be convergent but
Sum[a,{i,1,Infinity}+Sum[b,{i,1,Infinity}]
may be undetermined.

You notation  Sum[x_i, {i,1,2,T}] would mean run i from 1 to 2 in steps
of T.

You  must use rules explicit to handle
 Sum[x_i, {i,1,T}] - x_2

and 
Sum[x[i], {i, 1, T}] - x[2] /. 
  Sum[a_, {i_, 1, n_}] :> Sum[a, {i, 2}] + Sum[a, {i, 3, T}]

works as it should but will be an error for T<3

Regards
  Jens

Lewis wrote:
> 
> Hi MathGroup,
> 
> I am a beginner to Mathematica.  Please help me solve the following problem.
> 
> I am trying to manipulate expressions like:
> 
>     Sum[x_i, {i,1,T}] - x_2    or    Sum[x_i, {i,1,T}] - Sum[x_i, {i,1,2,T}]
> 
> I want to keep the upper limit as T, not any specific numeric value.  I
> tried to use Simplify as in
> 
>     Simplify[Sum[x_i, {i,1,T}] - x_2]
> 
> But the x_2 term doesn't get cancelled out.  I also tried:
> 
>     Simplify[Sum[x_i, {i,1,T}] - x_2, T>2],
> 
> but it didn't seem to work either.  So I am wondering if the simplication
> only works when I specify the value for T.  Any advice, please?
> 
> Thank you very much!
> 
> Best,
> Lewis.


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