The realization space is
  [1   0   1       x2   0   1    0              x2 - 1                      x2              x2 - 1    1]
  [0   1   1   x2 - 1   0   0    1              x2 - 1                  x2 - 1          x1*x2 - x1   x1]
  [0   0   0        0   1   1   -1   x1*x2 + x2^2 - x2   x1*x2 + x2^2 - x2 + 1   x1*x2 + x2^2 - x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^2*x2 + x1*x2^2 - 2*x1*x2 + x1 - x2^2 + x2)
avoiding the zero loci of the polynomials
RingElem[x2, x1, x1 - 1, x1^2*x2 + 2*x1*x2^2 - 3*x1*x2 + x1 - 2*x2^2 + 3*x2 - 1, x1 + x2, x1 + x2 - 1, x1*x2 + x2^2 - 2*x2 + 1, x1^2 + x1*x2 - x1 - x2 + 1, x1*x2 - x2 + 1, x2 - 1, x1*x2 - 2*x2 + 1, x1^2*x2 + x1*x2^2 - 2*x1*x2 + x1 - 2*x2^2 + 3*x2 - 1, 2*x1^2*x2^2 - x1^2*x2 + 2*x1*x2^3 - 6*x1*x2^2 + 5*x1*x2 - x1 - 2*x2^3 + 5*x2^2 - 4*x2 + 1, 2*x1^3*x2^2 - x1^3*x2 + 4*x1^2*x2^3 - 9*x1^2*x2^2 + 6*x1^2*x2 - x1^2 + 2*x1*x2^4 - 11*x1*x2^3 + 17*x1*x2^2 - 10*x1*x2 + 2*x1 - 2*x2^4 + 7*x2^3 - 9*x2^2 + 5*x2 - 1, 2*x1*x2 - x1 + x2^2 - x2, 2*x1*x2 - x1 + x2^2 - 2*x2 + 1, x1^2*x2 + 3*x1*x2^2 - 3*x1*x2 + x1 + x2^3 - 3*x2^2 + 3*x2 - 1, x1^3*x2^2 + 2*x1^2*x2^3 - 4*x1^2*x2^2 + 2*x1^2*x2 + x1*x2^4 - 7*x1*x2^3 + 11*x1*x2^2 - 6*x1*x2 + x1 - 2*x2^4 + 7*x2^3 - 9*x2^2 + 5*x2 - 1, x1^2*x2^2 + x1*x2^3 - x1*x2^2 - x2^3 + 2*x2 - 1, x1^2*x2 + 2*x1*x2^2 - 3*x1*x2 + x1 + x2^3 - 4*x2^2 + 4*x2 - 1, x1*x2 + x2^2 - 1, x1*x2 + x2^2 - x2 + 1, x1^2*x2^2 + x1*x2^3 - 3*x1*x2^2 + 2*x1*x2 - 2*x2^3 + 4*x2^2 - 3*x2 + 1]