Re: Re: Re: Just another bug in MMA 3.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg7587] Re: [mg7532] Re: [mg7491] Re: [mg7431] Just another bug in MMA 3.0*From*: Allan Hayes <hay at haystack.demon.co.uk>*Date*: Thu, 19 Jun 1997 03:13:50 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On 13 Jun 1997 Kai Koehler<koehler at math.uni-bonn.de> in [mg7532] Re: [mg7491] Re: [mg7431] Just another bug in MMA 3.0 wrote as copied after ************** The original problem [mg7491] was that Sum[Sum[Log[Log[k+j]],{k,1,n}],{j,1,5}] gives 5*Sum[Log[Log[k + j]], {k, 1, n}]. The behaviour seems to be explained by the fact that with j set to 1 (j =1) then Sum[Log[Log[k+j]],{k,1,n}] does not sum and so is returned unevaluated; similarly with j = 2,3,4,5. Thus we end up adding together 5 copies of it. The following two examples show up the processm (I change the 5 to 3 to reduce the print out) (1) If we put n = 2 then the summations are done Sum[Sum[Log[Log[k+j]],{k,1,2}],{j,1,3}] Log[Log[2]]+2 Log[Log[3]]+2 Log[Log[4]]+Log[Log[5]] (2) If we drop the outer Log then again the summations are done Sum[Sum[Log[k+j],{k,1,n}],{j,1,3}] -Log[2]-Log[6]+Log[Gamma[2+n]]+Log[Gamma[3+n]]+Log[Gamma[4+n]] Allan Hayes hay at haystack.demon.co.uk http://www.haystack.demon.co.uk/training.html voice:+44 (0)116 2714198 fax: +44 (0)116 2718642 12 Copse Close, Leicester, LE2 4FB, UK ******* In article <5nfpv3$5qp at smc.vnet.net>, Paulo Mouat <mouat at mail.telepac.pt> wrote: > Kai Koehler wrote: > > Sum[Sum[Log[Log[k+j]],{k,1,n}],{j,1,5}] > > > > gives > > > > 5*Sum[Log[Log[k + j]], {k, 1, n}]. > If you want to do a multiple sum, the input should read > > Sum[Log[Log[k+j]],{k,1,n},{j,1,5}] > > What you have typed is a simple sum over k with a function that has an > unknown j. The j on the outer Sum is a dummy variable, with no > relation to the one in Log[k+j]. > > This is not a bug. Mathematica simply interpreted what you did type, > which is not quite what you intended to do. If this where true, Sum[Sum[j,{k,1,n}],{j,1,5}] should give 5 n j as output. Instead you get 15 n (correctly, IMHO). Also, in StandardForm, the difference between Sum[Sum[Log[Log[k+j]],{k,1,n}],{j,1,5}] and Sum[Log[Log[k+j]],{k,1,n},{j,1,5}] is just the insertion of a factor (e.g. 1) between the two sums: \!\(\+\(j = 1\)\%5 1 \(\+\(k = 1\)\%n Log[Log[k + j]]\)\) gives a different output then \!\(\+\(j = 1\)\%5\(\+\(k = 1\)\%n Log[Log[k + j]]\)\) Similarly, \!\(\+\(j = 1\)\%5\((\ \+\(k = 1\)\%n Log[Log[k + j]])\)\) gives a different output then \!\(\+\(j = 1\)\%5\((\ \+\(k = 1\)\%n Log[Log[k + j]] + 1)\)\) What you wrote is actually what Michael Trott from Wolfram support mailed me 2 days ago: It's not a bug, it's a feature. This really worries me: If they do not even recognize a bug when you show it to them, then what can you expect them to do? Kai Koehler