The realization space is
  [1   0   1                      1   0   1    0   x1^2 - 2*x1 + 2                      1                 1                 1]
  [0   1   1   x1^3 - 2*x1^2 + 2*x1   0   0    1   x1^2 - 2*x1 + 2   x1^3 - 2*x1^2 + 2*x1   x1^2 - 2*x1 + 2   x1^2 - 2*x1 + 2]
  [0   0   0                      0   1   1   -1     x1^2 - x1 + 1                     x1                 1                x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^10 + 7*x1^9 - 25*x1^8 + 58*x1^7 - 95*x1^6 + 113*x1^5 - 97*x1^4 + 58*x1^3 - 22*x1^2 + 4*x1)
avoiding the zero loci of the polynomials
RingElem[x1^2 - 2*x1 + 2, x1 - 1, x1, x1^2 - x1 + 1, x1^2 - x1 + 2, x1 - 2, x1^2 - 2*x1 + 3, x1^3 - 3*x1^2 + 4*x1 - 3, x1^4 - 3*x1^3 + 6*x1^2 - 6*x1 + 3, x1^3 - 2*x1^2 + 3*x1 - 1, 2*x1^2 - 3*x1 + 3]