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RE: Re: Workaround for an unexpected behavior of Sum

Dear Andrzej

Thank you for answering my post. First let me answer your comment, second I
will ask if you can do something for me

The "advantage" (not really an advantage, better: the behavior that I like)
is that, after evaluating one time the (yes, very complex) code of my
approach, after that the behavior of Sum is changed for "ever" (in that
Mathematica session, of course), then you can use Sum (even better, you can
use the palette BasicMathInput) as many times as you want, using the
standard notation for sums, and not worrying about names of dummy indices
conflicting with names of global variables.

Oversimplifying: if I want to do only few sums, it is better your Module
approach. I want to use many many times the command Sum, and I do Not want
to check for possible conflicts with global variables, neither use Module
every time I use sum, then evaluating one time the complex code I posted
could be a good idea.

Now Andrzej, would you be so kind to use some of your time to comment on the
documentation for my Mathematica package Quantum in the following two links?
Both are related with this issue, and I am very very interested in your
comments and criticisms to the behavior of our package. These are the two
links:
(please notice that long urls are usually broken in this forum, so you might
have to "glue together" each hyperlink)

http://homepage.cem.itesm.mx/lgomez/quantum/sums/sums.html 

http://homepage.cem.itesm.mx/lgomez/quantum/tprodtpow/tprodtpow.html 

I really hope you find them interesting enough to comment

Regards!

Jose 
Mexico


-----Mensaje original-----
De: Andrzej Kozlowski [mailto:akoz at mimuw.edu.pl] 
Enviado el: Martes, 05 de Agosto de 2008 03:02
Para: mathgroup at smc.vnet.net
Asunto: [mg91067] Re: [mg91036] Workaround for an unexpected behavior of Sum

I don't understand what you consider to be the advantage of your  
approach over the (to my mind) much simpler:

j = 7;
Module[{j}, Sum[g[j], {j, 1, n}]]
Sum[g[j$679], {j$679, 1, n}]

Andrzej Kozlowski

On 4 Aug 2008, at 09:23, Jose Luis Gomez wrote:

> Workaround for an unexpected behavior of Sum
>
>
>
> Let me describe the problem, before describing the solution  
> (workaround)
> that I found.
>
>
>
> First: Next calculation works fine for me:
>
>
>
> j = 7;
>
>
>
> Sum[j^2, {j, 1, n}]
>
>
>
> Mathematica gave the answer I was expecting (n*(1 + n)*(1 + 2*n))/6,  
> It
> means the global j and the dummy index j are actually different That  
> is
> o.k., that is what I was expecting
>
>
>
> HOWEVER Next calculation gives an unexpected answer:
>
>
>
> Clear[f];
>
>
>
> j = 7;
>
>
>
> Sum[f[j], {j, 1, n}]
>
>
>
> Now Mathematica answers n*f[7]. That is NOT what I was expecting
>
>
>
> I was expecting that Mathematica will return the Sum unevaluated,  
> Sum[f[j],
> {j, 1, n}], and also with j unevaluated, so that the global j and  
> the dummy
> index j remain different.
>
>
>
> NOW MY WORKAROUND FOR THIS "PROBLEM": AUTOMATICALLY CREATE A NEW  
> DUMMY INDEX
> IF THERE EXISTS A VARIABLE WITH THE SAME NAME AS THE DUMMY INDEX.  
> Evaluate
> this in your Mathematica session:
>
>
>
> Unprotect[Sum];
>
>
>  ReleaseHold[
>
>    Hold[Sum[sumando, before, {dummyindex, rest}, after]] /.
>
>     HoldPattern[dummyindex] :>
>
>      Evaluate[
>
>       Unique[ToString[Unevaluated[dummyindex]]]]] /;
>
>         (dummyindex =!= Unevaluated[dummyindex]); Protect[Sum];
>
>
>
> Now, after the evaluation of the previous code, Mathematica behaves  
> the way
> I was expecting:
>
>
>
> Clear[f];
>
>
>
> j = 7;
>
>
>
> Sum[f[j], {j, 1, n}]
>
>
>
> This time Mathematica answers Sum[f[j1],{j1,1,n}].
>
> The price we have to pay is that the dummy index was renamed.
>
> But it is a DUMMY INDEX, it can have any name.
>
> And the code makes the new name totally new, thanks to the Unique[]  
> command.
>
> AFAIK this code does Not affect the answers of Sum in other cases.
>
>
>
> I hope this simple solution is somehow useful.
>
> Notice that the command Integrate has a similar (in my opinion odd)
> behavior, mixing dummy integration variables with global variables  
> when the
> definite integral cannot be immediately performed.
>
>
>
> Best regards!
>
>
>
> Jose Luis Gomez-Munoz
>
>
>
> Mexico
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