Re: unexpected behaviour of Sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg126540] Re: unexpected behaviour of Sum*From*: Dana DeLouis <dana01 at me.com>*Date*: Fri, 18 May 2012 05:24:04 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

> Sum[sod[k],{k,10^6}] which gives 27000001 (ok) Hi. Just for a mental exercise, this is the best I could do for a non Brute-Force method. There are probably better ways: (* Sum the individual digits between 1 and n Dana DeLouis *) AllDigitSum[n_]:=Module[ { k,j,fn,fx,lst,w, dig = IntegerDigits[n] }, fn[z_]:=Power[10,z-1]*(z*45); fx[start_,step_,z_]:=1/2 z((z-1) step+2 start); lst=FoldList[Plus,0,dig]; w=Length[dig]; Sum[ k=Power[10,w-j]; fx[lst[[j]]*k+fn[w-j],k,dig[[j]]], {j,1,w}]+lst[[-1]] ] Here, the function f[ ] is the Brute Force looping method as given by your Sum function. f[1000000] // Timing {3.78069, 27000001} AllDigitSum[1000000] //Timing {0.00026, 27000001} f[9876543] //Timing {37.8118, 309922302} AllDigitSum[9876543] //Timing {0.000285, 309922302} = = = = = = = = = = HTH :>) Dana DeLouis Mac & Math 8 = = = = = = = = = = On May 14, 1:34 am, perplexed <yudu... 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