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We can solve a system of equations over reals using Mathematica as follows.

Solve [x^2+y^2+z^2==1 && x+y==1, {x,y,z}] 

How one can solve a system of equations over a finite field like GF(2) using Mathematica?

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Solve[x^2+y^2+z^2==1 && x+y==1, {x,y,z}, Modulus->2]

  • 2
    Alternatively, `Solve[{x^2 + y^2 + z^2 == 1, x + y == 1}, {x, y, z}, Modulus -> 2]`.2011-12-01
  • 0
    This is fine, if you work over the prime field. But has Wolfram implemented support for other finite fields? I asked around about that may be 15 years ago (an am still running Mathematica ver 3.0 :-)2011-12-04
  • 1
    I think so: `Modulus->8` works.2011-12-04
  • 0
    I don't think it works. Modulus -> 8 means solve the equation in $\mathbb{Z}_8$. $\mathbb{Z}_8$ is not a field since is characteristic is $8$.2018-04-24