The realization space is
  [1   0   1   0   1   0   x1*x2 + x1 - x2                        x1*x2 + x1 - x2                                      x1^2*x2 + x1^2 - x1*x2          x1*x2 + x1 - x2                             x1^2*x2 + x1^2 - x1*x2]
  [1   1   0   1   0   0          -x1 + x2   x1^2*x2 + 2*x1^2 - 2*x1*x2 - x1 + x2            x1^2*x2^2 + 2*x1^2*x2 - 2*x1*x2^2 - x1*x2 + x2^2                 -x1 + x2   x1^2*x2^2 + 2*x1^2*x2 - 2*x1*x2^2 - x1*x2 + x2^2]
  [1   1   0   0   1   1                 0                 x1^2*x2 + x1^2 - x1*x2   x1^2*x2^2 + 2*x1^2*x2 + x1^2 - 2*x1*x2^2 - 2*x1*x2 + x2^2   x1*x2^2 + x1*x2 - x2^2                      x1^2*x2^2 + x1^2*x2 - x1*x2^2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1*x2 + x1 - x2, x2 - 1, x2, x1 - x2, x1^2*x2^2 + x1^2*x2 - x1^2 - 2*x1*x2^2 + x2^2, x1^2*x2 + 2*x1^2 - 2*x1*x2 - x1 + x2, x1 - 1, x1, x1^2*x2^2 + x1^2*x2 + x1^2 - x1*x2^2 - 2*x1*x2 + x2^2, 2*x1^2*x2 + x1^2 - x1*x2^2 - 2*x1*x2 + x2^2, x1^2*x2^3 + x1^2*x2^2 + x1^2 - 2*x1*x2^3 - x1*x2^2 - 2*x1*x2 + x2^3 + x2^2, x1^2*x2^3 + 2*x1^2*x2^2 + x1^2*x2 + x1^2 - 2*x1*x2^3 - 2*x1*x2^2 - 2*x1*x2 + x2^3 + x2^2, x1*x2 + 2*x1 - 2*x2, x1^2 + x1*x2^2 - x2^2, x1*x2^2 + x1*x2 + x1 - x2^2 - x2]