The realization space is
  [1   1   0   x1^2*x2 - x1^2 - x1*x2^2 + 2*x1*x2 - x2^2   1                         x1*x2 - x2^2   0           x1*x2 - x2^2                                    0          x1^2*x2 - x1^2 - x1*x2^2 + 2*x1*x2 - x2^2          x1^2*x2 - x1^2 - x1*x2^2 + 2*x1*x2 - x2^2]
  [1   0   1                        -x1^3*x2^2 + x1^3*x2   0                 -x1^2*x2^2 + x1^2*x2   0   -x1^2*x2^2 + x1^2*x2                 -x1^2*x2^2 + x1^2*x2                               -x1^3*x2^2 + x1^3*x2                             -x1^2*x2^3 + x1^2*x2^2]
  [0   0   0                                           0   1   x1^2*x2^2 - x1^2*x2 + x1*x2 - x2^2   1           x1*x2 - x2^2   x1^2*x2^2 - x1^2*x2 + x1*x2 - x2^2   x1^3*x2 - x1^3 - x1^2*x2^2 + 2*x1^2*x2 - x1*x2^2   x1^2*x2^2 - x1^2*x2 - x1*x2^3 + 2*x1*x2^2 - x2^3]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 - x2, x1, x2, x2 - 1, x1*x2 - x1 + x2, x1^3*x2^3 - 2*x1^3*x2^2 + 2*x1^3*x2 - x1^3 - x1^2*x2^2 + x1^2*x2 + x1^2 - 2*x1*x2 + x2^2, x1 - 1, x1*x2^2 - x1*x2 + x1 - x2, x1^3*x2^2 - x1^3*x2 + x1^2*x2 - x1^2 - x1*x2^2 + 2*x1*x2 - x2^2, x1^2*x2^3 - x1^2*x2^2 + x1^2*x2 - x1^2 - x1*x2^2 + 2*x1*x2 - x2^2, x1^2*x2^2 - x1^2*x2 + x1^2 + x1*x2^2 - 2*x1*x2 + x2^2, x1^2 - x1 + x2, x1^4*x2^2 - 2*x1^4*x2 + x1^4 + x1^3*x2 - x1^3 - x1^2*x2^2 + x1^2*x2 + x1^2 - 2*x1*x2 + x2^2, x1^3*x2^2 - 2*x1^3*x2 + x1^3 + x1^2*x2^2 - x1^2*x2 - x1^2 + 2*x1*x2 - x2^2, x1^2*x2 - 2*x1^2 + x1*x2 + x1 - x2, x1^2*x2 - x1*x2 + x1 - x2]