RE: SquareFreeQ vs. MoebiusMu
- To: mathgroup at smc.vnet.net
- Subject: [mg30162] RE: [mg30144] SquareFreeQ vs. MoebiusMu
- From: "Harvey P. Dale" <hpd1 at nyu.edu>
- Date: Wed, 1 Aug 2001 02:19:17 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Andrzej:
Try to use the functions across a list. Here's what I got (Pentium
3 at 733 mHz under Windows 2000):
Select[Range[1000], SquareFreeQ]; // Timing
{8.442 Second, Null}
Select[Range[1000], MoebiusMu[#] != 0 &]; // Timing
{0.01 Second, Null}
Best,
Harvey
-----Original Message-----
From: Andrzej Kozlowski [mailto:andrzej at tuins.ac.jp]
To: mathgroup at smc.vnet.net
Sent: Tuesday, July 31, 2001 5:35 AM
To: Harvey P. Dale
Cc: mathgroup at smc.vnet.net
Subject: Re: [mg30144] SquareFreeQ vs. MoebiusMu
Several thousand times as fast???
Not on my computer:
In[1]:=
<<NumberTheory`NumberTheoryFunctions`
In[4]:=
SquareFreeQ[2^101-1]//Timing
Out[4]=
{19.98 Second,True}
In[5]:=
MoebiusMu[2^101-1]//Timing
Out[5]=
{19.65 Second,1}
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/
On Tuesday, July 31, 2001, at 05:27 PM, Harvey P. Dale wrote:
> The function SquareFreeQ[n], in NumberTheory`NumberTheoryFunctions`,
> appears
> to do the same thing as testing for MoebiusMu[n] being unequal to
> zero. The
> latter, however, is several thousand times as fast. Is there ever any
> reason for using SquareFreeQ? If not, why is it included in the
> standard
> Add-On package?
> I should add that at page 317 of the Mathematica 4 Standard Add-On
> Packages volume, SquareFreeQ is erroneously described. It says the
> function will give True if n contains a squared factor, False otherwise.
> That is exactly backwards.
> Best,
> Harvey
>
>
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