The realization space is
  [1   1   0            2*x2   0   1   1        0              2*x2    1        2]
  [1   0   1   4*x1 - x2 - 1   0   1   0   x2 - 1     4*x1 - x2 - 1   x1   x2 + 1]
  [0   0   0               0   1   1   1     2*x2   6*x1 - 2*x2 - 2   x1     2*x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1*x2 - 3*x1 + x2 + 1)
avoiding the zero loci of the polynomials
RingElem[x2, 2*x1^2*x2 - 6*x1^2 + x1*x2 + x1 + 2*x2, x1, 2*x1*x2 - 6*x1 + x2 + 3, x1 - x2, 2*x1^2*x2^2 - 8*x1^2*x2 + 2*x1^2 + 3*x1*x2^2 - x1 + x2^2 + x2, 2*x1*x2 - 8*x1 + 3*x2 + 3, x1 - 1, 2*x1*x2^2 - 7*x1*x2 - x1 + 2*x2^2 + 4*x2, 2*x1 - x2 - 1, 2*x1^2*x2 - 6*x1^2 + x1*x2 + 3*x1 + x2 - 1, 2*x1*x2^2 - 8*x1*x2 + 2*x1 + 3*x2^2 + 2*x2 - 1, 2*x1^2*x2^2 - 6*x1^2*x2 - x1*x2^2 + 11*x1*x2 - 2*x1 - 2*x2^2 - 3*x2 + 1, 2*x1^2*x2^2 - 6*x1^2*x2 - x1*x2^2 + 13*x1*x2 - 2*x1 - 4*x2^2 - 3*x2 + 1, 2*x1*x2^2 - 7*x1*x2 + x1 + 2*x2^2 + 3*x2 - 1, 2, x1*x2 - 3*x1 + x2 + 2, 2*x1*x2^2 - 8*x1*x2 + 2*x1 + 2*x2^2 + 3*x2 - 1, 2*x1*x2^2 - 6*x1*x2 + 2*x2^2 + 3*x2 - 1, 2*x1*x2^2 - 6*x1*x2 + 2*x2^2 + 5*x2 - 1, 2*x1*x2 - 6*x1 + 5*x2 + 1, 2*x1*x2 - 6*x1 + 3*x2 + 3, x2 - 1, 4*x1*x2^2 - 10*x1*x2 + 2*x1 + 4*x2^2 + 3*x2 - 1, 2*x1*x2 - 6*x1 + 3*x2 + 1, 4*x1*x2^2 - 10*x1*x2 + 2*x1 + 2*x2^2 + 3*x2 - 1, 2*x1 - 1, 2*x1*x2 - 2*x1 + x2 + 1, x1*x2 + x1 - 2*x2, x2 + 1, x1*x2 + x1 + x2 - 1, x1*x2 - x1 + x2 + 1, x1*x2 - x1 + 2*x2, 4*x1*x2 - 2*x1 - x2 + 1, 3*x2 - 1, x1*x2 - x1 + x2]