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Re: Workaround for an unexpected behavior of Sum
*To*: mathgroup at smc.vnet.net
*Subject*: [mg91067] Re: [mg91036] Workaround for an unexpected behavior of Sum
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Tue, 5 Aug 2008 04:02:15 -0400 (EDT)
*References*: <200808040723.DAA13823@smc.vnet.net>
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];
>
> 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
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