The realization space is
  [1   0   1   0   1   0   x1^2 - x1                x1     x1^2 - x1                  x1^3 - x1^2                x1^2]
  [1   1   0   1   0   0    2*x1 - 1   x1^2 - 2*x1 + 1      2*x1 - 1   2*x1^3 - 5*x1^2 + 4*x1 - 1   2*x1^2 - 3*x1 + 1]
  [1   1   0   0   1   1           0              x1^2   2*x1^2 - x1                2*x1^3 - x1^2                x1^3]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (16*x1^13 - 128*x1^12 + 408*x1^11 - 680*x1^10 + 657*x1^9 - 382*x1^8 + 132*x1^7 - 25*x1^6 + 2*x1^5)
avoiding the zero loci of the polynomials
RingElem[x1^2 - 3*x1 + 1, 2*x1 - 1, x1 - 1, x1, x1^4 - 3*x1^3 + 7*x1^2 - 5*x1 + 1, x1^3 - 2*x1^2 + 3*x1 - 1, 3*x1 - 1, x1^3 - 5*x1^2 + 4*x1 - 1, x1^2 + x1 - 1]