The realization space is
  [1   x1 - 1   1   x1 - 1    1   0   0   x1^3 - 3*x1^2 + 3*x1 - 1   x1^4 - 4*x1^3 + 6*x1^2 - 4*x1 + 1      x1^3 - 3*x1^2 + 3*x1 - 1                          0]
  [1       x1   0        0   x1   1   0   x1^3 - 3*x1^2 + 3*x1 - 1         x1^4 - 3*x1^3 + 3*x1^2 - x1   x1^4 - 3*x1^3 + 3*x1^2 - x1   x1^3 - 3*x1^2 + 3*x1 - 1]
  [1       x1   0       x1    0   0   1                         x1                 -x1^3 + 3*x1^2 - x1                            x1                         x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^15 - 8*x1^14 + 28*x1^13 - 57*x1^12 + 75*x1^11 - 66*x1^10 + 38*x1^9 - 13*x1^8 + 2*x1^7)
avoiding the zero loci of the polynomials
RingElem[x1^3 - 2*x1^2 + x1 - 1, x1, x1 - 2, x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^2 - x1 + 1, x1^4 - 3*x1^3 + 3*x1^2 - 3*x1 + 1, x1^2 - 3*x1 + 1, x1^4 - 4*x1^3 + 5*x1^2 - 2*x1 + 1]