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Please Help with Sums with the same StandardForm but different InputForm

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89002] Please Help with Sums with the same StandardForm but different InputForm
  • From: "Jose Luis Gomez" <jose.luis.gomez at itesm.mx>
  • Date: Fri, 23 May 2008 03:08:54 -0400 (EDT)

(* Dear group

 

In Mathematica 6.0 it is possible to generate Sums with the same
StandardForm but different InputForm

 

In other words, they look exactly the same for the final user, but they are
considered different by Mathematica

 

Please evaluate: 

(PLEASE NOTICE THAT HERE INDEX j GOES FIRST)

*)

 

Clear[f,j,k,ja,jb,ka,kb];

 

Sum[f[j,k],{j,ja,jb},{k,ka,kb}]

 

(* You obtain the sum in "sigma notation" (StandardForm).

Next evaluate the following

(PLEASE NOTICE THAT HERE INDEX k GOES FIRST)

 *)

 

Sum[  Sum[f[j,k],{k,ka,kb}],  {j,ja,jb}]

 

(*As you can see, both expressions display exactly the same, they look the
same in StandardForm,

 However they are considered different by Mathematica.

To see this, evaluate:

*)

 

Sum[f[j,k],{j,ja,jb},{k,ka,kb}] == Sum[  Sum[f[j,k],{k,ka,kb}],  {j,ja,jb}]

 

(* I was expecting to obtain True, as both Sums look exactly the same in the
Mathematica notebook.

However Mathematica does Not answer True or False, it just returns
unevaluated,  

 

So I have the following questions for those who would like to help me:

FIRST: Am I right? Both expressions are the same? Or is there a situation
where these two expressions, which look almost identical in StandardFrom,
are actually different? 

SECOND: I have try FullSimplify, Reduce and Refine, trying to obtain True,
but it does Not work. Is there any command or simplification to make
Mathematica answer True, maybe under certain assumptions?

THIRD: Could this behavior be considered a bug?

I am using Mathematica 6.0

Thank you for your time and help

 

Jose

Mexico

*)

 


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