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