The realization space is
  [1   x1 - 1   1   x1 - 1    1   0   0   x1^2 - 2*x1 + 1   x1^3 - 3*x1^2 + 3*x1 - 1      x1^2 - 2*x1 + 1                 0]
  [1       x1   0        0   x1   1   0   x1^2 - 2*x1 + 1         x1^3 - 2*x1^2 + x1   x1^3 - 2*x1^2 + x1   x1^2 - 2*x1 + 1]
  [1       x1   0       x1    0   0   1                x1                         x1                   x1                x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^11 - 8*x1^10 + 26*x1^9 - 43*x1^8 + 34*x1^7 - x1^6 - 22*x1^5 + 19*x1^4 - 7*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[2*x1^2 - 4*x1 + 1, x1 - 1, x1, x1 - 2, 2*x1 - 1, 2, x1^2 - 3*x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^3 - 4*x1^2 + 5*x1 - 1]