The realization space is
  [1              1    1    1   1   0   0   x1^2 - 2*x1 + 1                  x1^2 - 2*x1 + 1      x1^2 - 2*x1 + 1    0]
  [1   -x1^2 + 2*x1   x1   x1   0   1   0   x1^2 - 2*x1 + 1   -x1^4 + 4*x1^3 - 5*x1^2 + 2*x1                    0    1]
  [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[x1^2 - 2*x1 - x2 + 1, x1^3*x2 - 4*x1^2*x2 + x1^2 + 6*x1*x2 - 2*x1 - 4*x2 + 1, x2, x1, x1^2 - 3*x1 + 3, x1^2*x2 - x1^2 - 3*x1*x2 + 2*x1 + 3*x2 - 1, x1 - 2, x1^4*x2 - 4*x1^3*x2 + 5*x1^2*x2 - x1^2 - 2*x1*x2 + 2*x1 + x2 - 1, x1^2 + x1*x2 - 2*x1 - 2*x2 + 1, x1^3 - 3*x1^2 + 2*x1 + 1, x1^3*x2 - 3*x1^2*x2 - x1^2 + 2*x1*x2 + 2*x1 + x2 - 1, x2 - 1, x1*x2 - 2*x2 + 1, x1 - 1, x1*x2 - x2 + 1, x1^2*x2 + x1^2 - 2*x1*x2 - 2*x1 + 1, x1*x2 + x1 - 2*x2 - 1, x1^3 - 2*x1^2 + x1 - x2]