Re: Wolfram, meet Stefan and Boltzmann
- To: mathgroup at smc.vnet.net
- Subject: [mg117349] Re: Wolfram, meet Stefan and Boltzmann
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Wed, 16 Mar 2011 06:24:52 -0500 (EST)
Your initial set of timings for the integrals still seems
extraordinarily high. For your first three inputs, the timings I get are:
0.000012
0.915221
1.94602
This is for:
$Version
8.0 for Mac OS X x86 (64-bit) (February 23, 2011)
[i.e., 8.0.1]
MacBook 13", couple of months old
CPU: 2.26 GHz Intel Core 2 Duo
RAM: 2 GB 1067 MHz DDR3
OS: Mac OS X 10.6.6
On 3/15/2011 7:05 AM, AES wrote:
> In article<ilksd8$6aq$1 at smc.vnet.net>, Peltio<peltio at twilight.zone>
> wrote:
>
>> It is not clear if you had already started up a kernel before
>> evaluating the integral.
>> Try it this way: first thing first evaluate
>> 1+1
>> Then evaluate your integral.
>
> Good idea. Prepared a notebook with Input cells shown just below, Saved
> this notebook to desktop, Quit Mathematica. Double-clicked the notebook, waited
> until Mathematica had re-started and notebook had Opened. Selected All, hit
> Enter, got results below:
>
> In[1]:= Timing[1+1//N]
>
> Out[1]= {0.000017,2.}
>
> In[2]:= Timing[Integrate[x/(Exp[x]-1),{x,0,Infinity}]]
>
> Out[2]= {5.52206,\[Pi]^2/6}
>
> In[3]:= Timing[Integrate[x^3/(Exp[x]-1),{x,0,Infinity}]]
>
> Out[3]= {19.1595,\[Pi]^4/15}
>
> Did a Delete Output Cells, repeated the Select All and hit Enter, got
> following results:
>
> In[4]:= Timing[1+1//N]
>
> Out[4]= {0.000016,2.}
>
> In[5]:= Timing[Integrate[x/(Exp[x]-1),{x,0,Infinity}]]
>
> Out[5]= {0.059286,\[Pi]^2/6}
>
> In[6]:= Timing[Integrate[x^3/(Exp[x]-1),{x,0,Infinity}]]
>
> Out[6]= {0.085411,\[Pi]^4/15}
>
> Seems to be repeatable behavior. No other messy stuff running on my
> MacBook.
>
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305