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