The realization space is
  [1   1   x1^2 - 2*x1 + 1   0   0   1              x1             x1^2 - 2*x1 + 1        0               1              x1]
  [1   0     x1^2 - x1 + 1   1   0   1               0               x1^2 - x1 + 1       x1   x1^2 - x1 + 1            x1^2]
  [0   0                 0   0   1   1   x1^2 - x1 + 1   -x1^3 + 4*x1^2 - 4*x1 + 2   x1 - 1   x1^2 - x1 + 1   x1^2 - x1 + 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^4 - 2*x1^3 + x1 - 1, x1^10 - 7*x1^9 + 21*x1^8 - 36*x1^7 + 40*x1^6 - 29*x1^5 + 13*x1^4 - 3*x1^3)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 + 1, x1, x1 - 1, x1 - 2, x1^3 - 2*x1^2 + x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^3 - 2*x1^2 + 2*x1 - 2, x1^2 - x1 - 1, x1^2 - 2*x1 + 2]