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