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MathGroup Archive 2012

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unexpected behaviour of Sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126483] unexpected behaviour of Sum
  • From: perplexed <yudumbo at gmail.com>
  • Date: Mon, 14 May 2012 01:34:06 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

I do not want to say that this is a bug, however I did
not find, in the Sum documentation, an explanation of this
behaviour (v8.0.4)

I defined an innocent function like
sod[n_]:=Plus@@IntegerDigits[n]
that compute the sum of the digits of a number.
(I tried with other functions, so the culprit is not IntegerDigits)

Then I compute two sums:
Sum[sod[k],{k,10^6}] which gives 27000001 (ok)
then 
Sum[sod[k],{k,1+10^6}] which gives 500001500001 (nonsense).
then 
Sum[sod[k],{k,2,1+10^6}] which gives 27000002 (ok)

so, it seems to me that Sum has a problem when the iterator
works in a range greater than 10^6.

Indeed, I made an experiment:
I set L={}; and defined
sod[n_]:=(AppendTo[L,n];Plus@@IntegerDigits[n])
Then Sum[sod[k],{k,1+10^6}] still gives 500001500001 
and at the end L is equal to {k}, so it seems that
Sum tried to do something symbolic (??).

Is this a bug or a feature whose documentation I was not
able to find? Say, is there an option to fix things ?

Btw, using ParallelSum instead of Sum works fine (and faster).
thanks



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