The realization space is
  [1   1   0    2   0   1   1          0      2           2         2]
  [1   0   1   x1   0   1   0          1     x1     -x1 + 2   -x1 + 2]
  [0   0   0    0   1   1   1   2*x1 - 2   2*x1   -2*x1 + 4      2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^2 - 2*x1 + 2, 128*x1^7 - 896*x1^6 + 2432*x1^5 - 3200*x1^4 + 1920*x1^3 - 128*x1^2 - 384*x1 + 128)
avoiding the zero loci of the polynomials
RingElem[x1^2 + 2, 2, x1, x1^2 - 2, x1 - 1, x1^3 + 2*x1 + 4, x1^3 + 2, x1^4 + 2*x1^2 + 4*x1 - 4, x1^4 - 2*x1^2 + 4*x1 - 4, x1^2 - 4*x1 + 2, x1^2 + 4*x1 - 2, x1^2 - 2*x1 - 2, x1 - 2, x1^2 - 2*x1 + 4, x1^2 + 2*x1 - 2, x1^3 - 2*x1 + 2, x1^4 - 6*x1^2 + 4*x1 - 4, 5*x1^2 - 4*x1 + 2, x1^2 - x1 + 1, x1^3 - x1^2 + 4*x1 - 2, 3*x1^2 - 4*x1 + 2, x1^2 + 2*x1 + 2, x1^3 + 2*x1 - 4, x1^4 - 2*x1^2 - 4*x1 + 4, x1^4 + 2*x1^2 - 4*x1 + 4, x1^2 + 1, x1^4 + 2*x1^2 + 4, x1 + 1, x1^4 - 2*x1^2 + 4]