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