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