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