Re: Workaround for an unexpected behavior of Sum

• To: mathgroup at smc.vnet.net
• Subject: [mg91078] Re: Workaround for an unexpected behavior of Sum
• From: magma <maderri2 at gmail.com>
• Date: Tue, 5 Aug 2008 04:04:19 -0400 (EDT)
• References: <g76aq6\$dfs\$1@smc.vnet.net>

```On Aug 4, 9:23 am, "Jose Luis Gomez" <jose.luis.go... at itesm.mx> 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];
>
> Sum[sumando_, before___, {dummyindex_, rest___}, after___] :=
>
>   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

It is very kind of Jose to call this "odd behaviour", I would call it
a serious bug.
It means the that the iteration variables are not really localized, at
least in some cases.
WRI should correct it asap.

```