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Re: Solving finite field equations in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg80244] Re: [mg80186] Solving finite field equations in Mathematica
• From: danl at wolfram.com
• Date: Wed, 15 Aug 2007 04:26:08 -0400 (EDT)
• References: <200708141109.HAA09765@smc.vnet.net>

> Hi,
>
>   I would need to solve a system of finite field (GF(2)) equations
> with mathematica. I have looked around, and the only thing I can find
> is a 1993 ``finite field package''. What is the simplest way with
> current versions of mathematica?
>
>    Thanks,
>    Emanuele

If linear and over Z/<2> then easiest is to use

LinearSolve[mat,b,Modulus->2]

For nonlinear or proper extension fields it might be best to use
GroebnerBasis, also with Modulus->2, and a polynomial to represent the
defining extension. There is an example along the lines of handling an
extension in the SymbolicFAQ notebook at

http://library.wolfram.com/infocenter/Conferences/325/

See the section "Linear Algebra in a Galois field".

Daniel Lichtblau
Wolfram Research

• References:
  • Solving finite field equations in Mathematica
    • From: emanuele.viola@gmail.com