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