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MathGroup Archive 2001

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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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