Re: Integrate 'learns'?
- To: mathgroup at smc.vnet.net
- Subject: [mg106337] Re: Integrate 'learns'?
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Fri, 8 Jan 2010 04:19:21 -0500 (EST)
- References: <hi42e4$n46$1@smc.vnet.net>
On 2010.01.07. 8:28, Tony Harker wrote:
> If I open a clean notebook in Version 7.0 for Microsoft Windows (32-bit)
> and enter
> Integrate[x/(3 Sin[x]),{x,\[Pi]/4,\[Pi]/2}]
> the result (after a warning message) is
> (8*Catalan - I*Pi^2 + Pi*(-Log[1 - (-1)^(1/4)] + Log[1 + (-1)^(1/4)]) -
> (4*I)*(PolyLog[2, -(-1)^(1/4)] - PolyLog[2, (-1)^(1/4)]))/12
> and if I then repeat the command I get no error and
> (5*Catalan)/6 - ((23*I)/288)*Pi^2 + (Pi*ArcTanh[(-1)^(1/4)])/6 +
> ((2*I)/3)*PolyLog[2, (-1)^(1/4)]
> which seems to be Mathematica's final answer.
>
> I am happy that the results are equivalent, but puzzled about what has
> been saved, and where, to generate this difference. Did Mathematica ask the
> audience or phone a friend? Can anyone enlighten me?
>
I believe that this is because intermediate results are cached (see
ClearSystemCache[]) and because some computations are time constrained
(i.e. some transformations are tried only for a limited time). Caching
results speeds up computations, and thus may influence the result.
Notice that the second evaluation is also faster.
I get the first result you cite only when the system is under load (and
also got it when running the computation right after reboot). I think
people with fast computers won't get it at all.