The realization space is
  [1   1   0   0        1        1   0            x1 - 1        x1 - 1            x1 - 1      x1^2 - 2*x1 + 1]
  [0   1   1   1   x1 - 1       x1   0                 0        x1 - 1   x1^2 - 2*x1 + 1   x1^3 - 2*x1^2 + x1]
  [0   0   0   1   x1 - 1   x1 - 1   1   x1^2 - 3*x1 + 1   x1^2 - 2*x1       x1^2 - 2*x1        x1^3 - 2*x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 + 9*x1^7 - 31*x1^6 + 51*x1^5 - 41*x1^4 + 15*x1^3 - 2*x1^2)
avoiding the zero loci of the polynomials
RingElem[x1 - 2, x1, x1^2 - 3*x1 + 1, x1 - 1, x1^3 - 4*x1^2 + 5*x1 - 1, x1^3 - 5*x1^2 + 6*x1 - 1, x1^4 - 4*x1^3 + 6*x1^2 - 5*x1 + 1, 2*x1^2 - 4*x1 + 1, x1^2 - 4*x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1]