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