Re: Please Help with Sums with the same StandardForm but

*To*: mathgroup at smc.vnet.net*Subject*: [mg89026] Re: [mg89002] Please Help with Sums with the same StandardForm but*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Sat, 24 May 2008 03:52:18 -0400 (EDT)*References*: <200805230708.DAA25851@smc.vnet.net>

Jose Luis Gomez wrote: > (* 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 > > *) > They are not identical, and there is a bug. i1 = Sum[f[j, k], {j, ja, jb}, {k, ka, kb}] i2 = Sum[Sum[f[j, k], {k, ka, kb}], {j, ja, jb}] If I convert the StandardForm to InputForm for each result, then I get identical results: Sum[f[j, k], {j, ja, jb}, {k, ka, kb}] The FullForm shows they are different, and in particular, that i2 remains a nested Sum. In[14]:= FullForm[i2] Out[14]//FullForm= Sum[Sum[f[j,k],List[k,ka,kb]],List[j,ja,jb]] Thus this as a bug in InputForm. Daniel Lichtblau Wolfram Research

**References**:**Please Help with Sums with the same StandardForm but different InputForm***From:*"Jose Luis Gomez" <jose.luis.gomez@itesm.mx>