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MathGroup Archive 2002

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Re: finite fields

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32790] Re: [mg32764] finite fields
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Sat, 9 Feb 2002 23:39:36 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Are you really sure this is all you did? I can't reproduce your output 
and in my case everything works fine (Mathematica 4.1 for MacOS X).

In[1]:=
<<Algebra`FiniteFields`

In[2]:=
PowerList[GF[5,3]]

Out[2]=
{{1,0,0},{0,1,0},{0,0,1},{3,2,0},{0,3,2},{1,4,3},{4,2,4},{2,2,2},{1,1,2},
{1,0,
     
1},{3,3,0},{0,3,3},{4,1,3},{4,0,1},{3,1,0},{0,3,1},{3,2,3},{4,4,2},{1,3,
     
4},{2,4,3},{4,3,4},{2,2,3},{4,3,2},{1,3,3},{4,2,3},{4,0,2},{1,3,0},{0,1,
     
3},{4,1,1},{3,1,1},{3,0,1},{3,0,0},{0,3,0},{0,0,3},{4,1,0},{0,4,1},{3,2,
     
4},{2,1,2},{1,1,1},{3,3,1},{3,0,3},{4,4,0},{0,4,4},{2,3,4},{2,0,3},{4,3,
     
0},{0,4,3},{4,1,4},{2,2,1},{3,4,2},{1,2,4},{2,4,2},{1,1,4},{2,4,1},{3,4,
     
4},{2,1,4},{2,0,1},{3,4,0},{0,3,4},{2,3,3},{4,3,3},{4,0,3},{4,0,0},{0,4,
     
0},{0,0,4},{2,3,0},{0,2,3},{4,1,2},{1,3,1},{3,3,3},{4,4,3},{4,0,4},{2,2,
     
0},{0,2,2},{1,4,2},{1,0,4},{2,4,0},{0,2,4},{2,3,2},{1,1,3},{4,2,1},{3,1,
     
2},{1,2,1},{3,3,2},{1,2,3},{4,2,2},{1,3,2},{1,0,3},{4,2,0},{0,4,2},{1,4,
     
4},{2,4,4},{2,0,4},{2,0,0},{0,2,0},{0,0,2},{1,4,0},{0,1,4},{2,3,1},{3,4,
     
3},{4,4,4},{2,2,4},{2,0,2},{1,1,0},{0,1,1},{3,2,1},{3,0,2},{1,2,0},{0,1,
     
2},{1,4,1},{3,3,4},{2,1,3},{4,3,1},{3,1,3},{4,4,1},{3,1,4},{2,1,1},{3,4,
     1},{3,0,4},{2,1,0},{0,2,1},{3,2,2},{1,2,2},{1,0,2}}

There are indeed all 124 distinct non-zero elements here. Setting 
PowerListQ[GF[5,3]]=True makes no difference. Try it again with  fresh 
kernel.

with regards

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/

On Saturday, February 9, 2002, at 07:11  PM, Luis wrote:

> With the finite fields package PowerList is suppossed to produce the
> powers of a primitive root, and hence it is suppossed that it will
> appear exactly once all the not null elements of the field. It seems
> that sometimes it doesn't; may be there is something wrong in the
> program? For instance, for the field with 125 elements, with the input
> <<Algebra`FiniteFields`
> PowerListQ[GF[5,3]]=True
> PowerList[GF[5,3]]
>
>  I obtain the following output (observe that all elements in the list
> appear twice, and half the non null elements of the field doesn't appear
> at all):
> {{1,0,0},{0,1,0},{0,0,1},{4,0,4},{1,4,1},{4,1,3},{2,4,3},{2,2,1},{4,2,1},
> {4,4,
>
>
> 1},{4,4,3},{2,4,1},{4,2,3},{2,4,4},{1,2,0},{0,1,2},{3,0,4},{1,3,1},{4,1,
>
>
> 2},{3,4,4},{1,3,0},{0,1,3},{2,0,3},{2,2,2},{3,2,0},{0,3,2},{3,0,1},{4,3,
>
>
> 4},{1,4,4},{1,1,0},{0,1,1},{4,0,0},{0,4,0},{0,0,4},{1,0,1},{4,1,4},{1,4,
>
>
> 2},{3,1,2},{3,3,4},{1,3,4},{1,1,4},{1,1,2},{3,1,4},{1,3,2},{3,1,1},{4,3,
>
>
> 0},{0,4,3},{2,0,1},{4,2,4},{1,4,3},{2,1,1},{4,2,0},{0,4,2},{3,0,2},{3,3,
>
>
> 3},{2,3,0},{0,2,3},{2,0,4},{1,2,1},{4,1,1},{4,4,0},{0,4,4},{1,0,0},{0,1,
>
>
> 0},{0,0,1},{4,0,4},{1,4,1},{4,1,3},{2,4,3},{2,2,1},{4,2,1},{4,4,1},{4,4,
>
>
> 3},{2,4,1},{4,2,3},{2,4,4},{1,2,0},{0,1,2},{3,0,4},{1,3,1},{4,1,2},{3,4,
>
>
> 4},{1,3,0},{0,1,3},{2,0,3},{2,2,2},{3,2,0},{0,3,2},{3,0,1},{4,3,4},{1,4,
>
>
> 4},{1,1,0},{0,1,1},{4,0,0},{0,4,0},{0,0,4},{1,0,1},{4,1,4},{1,4,2},{3,1,
>
>
> 2},{3,3,4},{1,3,4},{1,1,4},{1,1,2},{3,1,4},{1,3,2},{3,1,1},{4,3,0},{0,4,
>
>
> 3},{2,0,1},{4,2,4},{1,4,3},{2,1,1},{4,2,0},{0,4,2},{3,0,2},{3,3,3},{2,3,
>
>     0},{0,2,3},{2,0,4},{1,2,1},{4,1,1},{4,4,0},{0,4,4}}
>  With kindest regards,
>  Luis.
>
>
>
>



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