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MathGroup Archive 2000

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Re: Galois Field operations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24935] Re: [mg24891] Galois Field operations
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Tue, 22 Aug 2000 16:22:44 -0400 (EDT)
  • References: <200008190846.EAA09625@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Matthew Peacock wrote:
> 
> Hi,
> 
> I am trying to do some work with polynomials that have coefficients from
> GF(16) using Mathematica 2.2.  I have downloaded the package from MathSource
> that allows the manipulation of finite field elements, but Mathematica just
> carks it if I try to expand the following expression:
> 
> Expand[(x-GF[2])(x-GF[2]^2)(x-GF[2])(x-GF[2]^3)(x-GF[2]^4)(x-GF[2]^5)(x-GF[2
> ]^6)]
> Has anybody any idea whether:
>     - this is a reasonable thing to ask Mathematica to do
>     - there is a better package or (dare I say) software package to do this
> with?
> 
> Thanks,
> 
> Mat Peacock


Not clear to me exactly what you are trying to do in the example above.
As for general technology for working in finite fields, here are some
URLs.

These go to mathgroup posts that indicate how one might implement
specific finite field functionality

http://library.wolfram.com/mathgroup/archive/1997/Feb/msg00149.html

http://library.wolfram.com/mathgroup/archive/1998/Nov/msg00195.html


This is for a conference notebook that shows how one might do linear
algebra over a finite field.

http://library.wolfram.com/conferences/conference98/
--> "Under Logic and Symbolic Computation" (approximately mid-page)
click on "Symbolic FAQ"

I hope something from the above is of use to you.


Daniel Lichtblau
Wolfram Research


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