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Workaround for an unexpected behavior of Sum
*To*: mathgroup at smc.vnet.net
*Subject*: [mg91036] Workaround for an unexpected behavior of Sum
*From*: "Jose Luis Gomez" <jose.luis.gomez at itesm.mx>
*Date*: Mon, 4 Aug 2008 03:23:54 -0400 (EDT)
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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