       Re: unexpected behaviour of Sum

• To: mathgroup at smc.vnet.net
• Subject: [mg126501] Re: unexpected behaviour of Sum
• From: Andrzej Kozlowski <akozlowski at gmail.com>
• Date: Tue, 15 May 2012 04:54:18 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201205140534.BAA27699@smc.vnet.net>

```Your guess about "something symbolic" was correct:

SetSystemOptions["SymbolicSumThreshold" -> 10^7];

sod[n_] := Plus @@ IntegerDigits[n]

Sum[sod[k], {k, 1 + 10^6}]

27000003

Andrzej Kozlowski

On 14 May 2012, at 07:34, perplexed wrote:

> 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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