Re: unexpected behaviour of Sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg126499] Re: unexpected behaviour of Sum*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Tue, 15 May 2012 04:53:36 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201205140534.BAA27699@smc.vnet.net>

The problem is not with Sum it is with your definition of sod. Note what happens with a symbolic input to sod: sod[k] k This happens because IntegerDigits is not evaluated then Apply replaces its head with Plus and returns k. Restrict the definition of sod to numeric input sod[n_Integer] := ... Bob Hanlon On May 14, 2012, at 1:34 AM, perplexed <yudumbo at gmail.com> 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 >

**References**:**unexpected behaviour of Sum***From:*perplexed <yudumbo@gmail.com>