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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
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