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MathGroup Archive 2002

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finite fields

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32764] finite fields
  • From: Luis <mtpmafel at lg.ehu.es>
  • Date: Sat, 9 Feb 2002 05:11:33 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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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