The realization space is
  [1    1   1    1   -x1 + 1   0   0    1                    1                    1              1]
  [1   x1   0    0       -x1   1   0    1                   x1         -x1^2 + 2*x1   -x1^2 + 2*x1]
  [1   x1   0   x1         0   0   1   x2   -x1^2*x2 + 2*x1*x2   -x1^2*x2 + 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 - 1, x2, x1, x1 - 2, x1^2 - 3*x1 + 3, x1^3*x2 - 3*x1^2*x2 + 2*x1*x2 + x1 - x2, x1*x2 - 2*x2 + 1, x1^2 - 3*x1 + 1, x1^2*x2 - 3*x1*x2 + x1 + x2, x2 - 1, x1 - x2, x1^3 - 3*x1^2 + 3*x1 - x2, x1^3 - 3*x1^2 + x1*x2 + 3*x1 - 2*x2, x1^2 - 2*x1 + x2, x1^2*x2 - 2*x1*x2 + 1, x1^2 + x1*x2 - 3*x1 - 2*x2 + 3, x1^2*x2 - x1^2 - 4*x1*x2 + 3*x1 + 4*x2 - 3]