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